Most long-lived contrails form within cirrus clouds with uncertain climate impact

Domain: earth_science
Published: 2025-11-03
Editorial outcome: minor_revision

Abstract
Contrail-cirrus is considered the most important component of aviation-induced climate impact. However, a reliable assessment requires better understanding of their radiative effects. Analysis of seven years of humidity observations by instrumented passenger aircraft shows that conditions promoting long-lived contrails are fulfilled most often in regions already covered by subvisible or visible cirrus: ~90% over the Northern midlatitudes and almost 100% in the Southeast Asian subtropics, approximately equally distributed among visible and subvisible cirrus clouds. A conceptual analysis shows that subvisible cirrus and clear-sky cover ~10% of the cruise altitude over Northern midlatitudes (<2% in the subtropics) and contrails within these regions are expected to cause additional warming. However, most contrails in the thicker, visible cirrus, only slightly enhance the cirrus warming effect or possibly reverse it to cooling. Our results suggest that potential flight rerouting concepts for contrail avoidance need to consider cirrus cloud coverage in addition to ice-supersaturation.

Introduction
According to most recent analyses, global aviation operations contribute about 3.5% to the total net anthropogenic warming, quantified by the metric ‘effective radiative forcing (ERF) of climate’ which measures the way these effects perturb the earth-atmosphere energy balance relative to pre-industrialization1. The climate impact of aviation results from both the direct emissions of carbon dioxide (CO2), water vapour (H2O), nitrogen oxides (NOx) and aerosol particles (soot, organics, and sulphate)2, and from indirect effects like aviation-NOx induced ozone formation, aerosol–cloud interactions, and the formation of persistent contrails and contrail-cirrus,. With an ERF of 60 mW m−2, contrail-cirrus is estimated to be the largest non-CO2 ERF contributing 60% (present-day) to the aviation net total ERF of 100 mW m−23,4. Other than the well-understood CO2 effect and its small uncertainty, the quantified non-CO2 effects of aviation are associated with large uncertainties, mostly for contrail-cirrus with a substantial associated uncertainty of ∼70%5. In particular, the feedbacks of contrail-cirrus radiative effects and surface temperature are largely unknown, but a most-recent model study including these effects reports that the climate sensitivity is lower for contrail-cirrus than for aviation-related CO2 emissions6.

Uncertainties of the climate effects of contrail-cirrus are largely related to unanswered questions about the extent to which contrails form inside cirrus clouds, their influence on cirrus cloud coverage and optical depth, and the radiative implications7,8. However, it is obvious that contrail-cirrus formed in clear sky or in or above pre-existing subvisible cirrus clouds have a stronger radiative effect than contrail-cirrus embedded in pre-existing visible cirrus, because the difference in the optical contrast with and without contrail is much larger. The related microphysical and optical properties of the contrail ice particles develop more complexly inside pre-existing cirrus clouds than in an otherwise clear sky9–11, although contrail formation itself is not affected by pre-existing cirrus clouds12.

The analysis of linear contrail occurrence over the Northern hemisphere in MODIS data for the year 2006 revealed that contrails were detected within an environment with ice clouds in 33% of the cases, compared to 46% with low liquid water clouds, and 17% in clear skies13. The same dataset14 yields that the net contrail radiative forcing (RF), i.e., the sum of short-wave and long-wave RF, during daytime (~13:30 LT) is 3.9 Wm−2 for clear sky and 1.3 Wm−2 for contrails in a column already filled with visible cirrus clouds. During night, when no shortwave RF occurs, the long wave RF for clear and cloudy scenes is 16.9 and 11.0 Wm−2, respectively. Thus, daytime net contrail RF is increased by a factor of 3 while nighttime long wave RF still is increased by a factor of 1.5 for contrails formed in clear sky or subvisible cirrus, compared to those having formed inside, above or below pre-existing cirrus.

Two studies using CALIPSO observations and flight track recordings reported an increase in cloud optical depth by 22% after an aircraft had crossed the cirrus15, and a statistically significant increase by as large as a factor of 2 in the concentration of ice crystals in clouds affected by aviation16. A recent modelling study on the impact of existing uncertainty in contrail cirrus optical depth on the resulting contrail-cirrus ERF reports an eightfold uncertainty5.

Observation-based knowledge on long-lived contrails within cirrus clouds and their radiative effects is severely limited. To narrow that knowledge gap, we study the occurrence of conditions favouring the formation and existence of long-lived contrails inside pre-existing cirrus clouds from observations of relative humidity with respect to ice (RHice) taken on board of passenger aircraft equipped with suitable instrumentation. The formation of contrails occurs when the Schmidt-Appleman criterion (SAC)17 is fulfilled, i.e. when the hot, humid exhaust emitted from an aircraft engine mixes rapidly with cold and humid ambient air, causing the relative humidity in the cooling plume to exceed saturation with respect to liquid water (RHw > 100%). Only when liquid water saturation is reached at a certain point in time of the plume evolution, water droplets form on the available aerosol particles, which subsequently freeze to contrail ice particles during the strong cooling caused by further mixing with the surrounding air. The validity of SAC for determining the contrail formation threshold temperature was confirmed by extensive observational data18.

After reaching the ambient temperature, the contrail ice particles grow or shrink in size depending on the ambient humidity. If the environment remains ice-supersaturated (RHice ≥ 100%), the contrails can persist with lifetimes from 4 to >10 h17,19. If the ambient air is ice-subsaturated (RHice < 100%), the ice particles sublimate and the contrail dissolves. For a contrail to survive more than approx. 10 minutes and to spread out to radiatively impactful contrail-cirrus, ambient RHice must be close to or above ice-saturation7,17,20–22.

From an observation-based climatology of ice crystal number concentrations as well as from a model analysis of contrail formation conditions we know that long-lived contrails and contrail-cirrus exist at temperatures from 205 K to 230 K for ice-supersaturated (RHice ≥ 100%)23,24 and slightly ice-subsaturated (90% ≤ RHice < 100%) conditions25,26. Aircraft flying through an ice-supersaturated or even slightly subsaturated air mass will thus form a persistent contrail and finally a contrail-cirrus as soon as ambient air temperature is below 230–225 K, which is almost always the case for Northern midlatitude cruise altitudes. Only for warmer temperatures above 230 K, as met, e.g., in the subtropics or at lower altitudes in the midlatitudes, these regions may be crossed by commercial aircraft without generating a contrail.

Today, the occurrence of contrail-cirrus is discussed in relation to cold (T < 230 K) ice-supersaturated regions (ISSR: RHice ≥ 100%). To include the observationally confirmed existence of contrail-cirrus also at slight ice-subsaturation in the consideration of aviation climate impacts, we introduce the term “potential contrail-cirrus region” (PCCR) which we define as an air mass with RHice ≥ 90% and SAC fulfilled. In such an air mass, a contrail would form and develop through the stage of ice-supersaturation during continuing mixing of hot exhaust with ambient air, where the ice crystals grow. The resulting contrail, formed of larger ice crystals, would then transition to sublimation with a limited but long-enough lifetime for becoming radiatively impactful. Model calculations of ice crystal sublimation in a dissolving contrail demonstrated that it can take approximately 4 h for ice particles to sublimate until RHice declines to below 80%26. Therefore, the “embedded contrails” is used synonymously with PCCR. Thus, PCCRs include ISSRs and represent areas with the potential for contrail and contrail-cirrus of lifetimes ranging from 4 to over 10 h when crossed by an aircraft. A first observation-based estimate of the areal fraction of air masses prone to contrail-cirrus formation for the North Atlantic flight corridor yielded an increase from 30% for ISSRs to 43% when considering RHice ≥ 90% as a sufficient pre-requisite for contrail-cirrus existence, i.e., for PCCRs26. This significant increase in the fractional area justifies the definition of a specific term to allow the differentiation from ISSRs.

The formation conditions and occurrence characteristics of ice-supersaturated regions (ISSRs) as well as their links to the formation of contrail-cirrus have been intensely studied for both clear-sky and in-cloud conditions27–31. Vertically, ISSRs occur most frequently in the upper troposphere just below the tropopause layer, whereas the upper free troposphere farther below the tropopause layer becomes less humid with respect to ice. However, the prediction of ISSRs is difficult because they are highly variable in space and time and depend crucially on the driving weather systems32–34. As a further complication, forecast models suffer from an underrepresentation of ice-supersaturation in the upper troposphere31,35 which is compensated by assuming model fields of RHice > 93% as ice-supersaturated36 or adjust humidity model fields to observations37,38. In addition, a not yet achieved precision of representation of ISSRs in numerical weather models9,31,36,39 is needed for a better forecast of ISSRs. The known difficulties in predicting ISSRs are most certainly valid also for PCCRs. It also needs to be mentioned that forecasting cirrus cloud formation and its properties is challenging for the same reasons as those for ISSRs and potentially PCCRs, since ISSRs are an indispensable pre-requisite for cirrus cloud formation.

There are several measures discussed for reducing aviation’s climate impact, including technological advancements for reducing the emissions of short-lived climate forcers such as NOx and aerosols, and the availability of sustainable aviation fuels for reducing long-lived greenhouse gases40. On the short term, operational concepts for avoiding contrails have been proposed as a strategy for reducing aviation’s climate impact41,42. However, they are intensively discussed with respect to potential trade-offs between longer flight trajectories for avoiding potential contrail-cirrus regions and resulting additional CO2 emission from extra fuel burn43,44. It is also not clear how atmospheric conditions in future climate may have an impact on the occurrence of PCCRs45. Additionally, the latest IPCC report highlights the role of clouds in a warming climate46 which makes the reduction of anthropogenically generated high ice clouds even more urgent.

Here, we provide an extensive analysis of contrail-cirrus occurrence in clear sky, as well as in subvisible and visible cirrus for the two densest airspaces globally and discuss the consequences of moving from ISSRs to PCCRs for the fractional air masses prone to a strong aviation climate impact. Additionally, we discuss the potential radiative effects of contrails in clear sky as well as in the presence of subvisible, visible and optically thick cirrus clouds. The database of this study builds on about 7 years of continuous in-situ observations of temperature and RHice by the European research infrastructure IAGOS47 which measures these properties along with atmospheric composition by passenger aircraft carrying scientific instrumentation during their regular operations.

Results
The data analysis strategy behind our results relies on four pillars: (1) the distribution of RHice from in-situ observations, and the subsequent determination of areal fractions, or occurrence probabilities, respectively, fulfilling PCCR or ISSR conditions; (2) fulfilment of SAC using in-situ measured temperature data for the identification of regions where contrails will form; (3) cirrus cloud coverage from ERA5 reanalysis cloud ice water content (CIWC), which can reliably capture cloud presence by the assimilation of comprehensive satellite radiance measurements; and (4) the distinction between areas covered by clear sky or subvisible clouds and areas covered by visible clouds, by means of a CIWC-based threshold value separating subvisible from visible cirrus.

The expected radiative effects in terms of warming or cooling by contrail-cirrus in clear sky or embedded in existing cirrus clouds are illustrated in Fig. 1 which has been adapted from Krämer et al.23. The lower and upper bounds of the cooling or warming effects of cirrus clouds as a function of cloud optical depth result from radiative transfer calculations. Since only a single set of conditions, (solar zenith angle at 50° North) was used and the results for other angular conditions, latitudes, and backgrounds will be highly variable, the figure only serves as a descriptive sketch. The radiative effects of contrail-cirrus developing in the various environments are categorised in the context of radiative effects of the embedded contrail-cirrus in addition to the radiative effects of the unperturbed clouds.

The qualitative categorisation of the climate impact of contrail-cirrus for the various environments considers five contrail development scenarios: if only short-lived contrails with low cloud optical depth (OD) form, there is no resulting climate impact (Case 0); contrails formed in clear sky developing into visible contrail-cirrus lead to net warming (Case 1); contrails formed in subvisible cirrus developing into visible contrail-cirrus lead to stronger net warming (Case 2); contrails formed within visible cirrus clouds (embedded contrail-cirrus) only lead to an additional minor but still net warming effect (Case 3); contrails forming in already optically thick cloud can enhance optical depth to overall cooling effect (Case 4). The net warming of Cases 1 and 2 and the minor net warming of Case 3 are confirmed by MODIS observations14, whereas a model study11 speculates that ignoring the impact of cirrus on contrail formation may possibly underestimate the cooling of the contrail perturbations within optically thicker clouds (Case 4).

In summary, we conclude that areas covered by clear sky (Case 1) or subvisible cirrus (Case 2), with SAC fulfilled, and at least qualified as PCCR with RHice > 90% are associated with enhanced positive contrail RF causing stronger warming (category “warming). Areas already covered by visible cirrus clouds (Case 3, Case 4) are associated with an ambiguous RF effect, ranging from minor warming to cooling (category “ambiguous”). These differences need to be kept in mind in the following when we distinguish three different categories: clear sky, subvisible cirrus, and visible cirrus which are distinguished using thresholds in CIWC (see ‘Methods’).

PCCRs and ISSRs in major air traffic regions
This IAGOS data set provides unprecedented in-situ measurements taken exactly in the regions of major air traffic. The fractions of all PCCRs and ISSRs were quantified for the densest airspace globally between North America and Europe (approx. 10 million IAGOS flight kilometres; see Fig. 2a and ‘Methods’) in the Northern midlatitudes and, for comparison, for the second densest airspace globally over Southeast Asia (approx. 6 million IAGOS flight kilometres) in the subtropics. For the Northern midlatitudes, we further specified the analysis for Eastern North America, North Atlantic and Western Europe to illustrate the variability of our findings for areas over land and over the ocean; see Figure S1 in the supplementary information.

The vertical distribution of data used in our study is illustrated in Fig. 2b relative to the pressure of the thermal tropopause according to WMO48 (pTTP) which separates the dry lowermost stratosphere with an almost negligible potential of contrail formation from the humid and cold tropopause layer and uppermost troposphere. The definition of the pressure levels follows established IAGOS concepts30,49 and is described in ‘Methods’. The resulting vertical distributions of occurrence of PCCRs and ISSRs are illustrated in Fig. 2c, d as fractional occurrences per pressure level. Obviously, the occurrence frequency of PCCRs—and associated long-lived contrails—is by about 10% higher than that of ISSRs.

While the cruising levels of civil aviation fall within a certain pressure range globally, the thermal tropopause in the subtropics is located at higher altitudes than in the midlatitudes. Consequently, in the extratropics, e.g., at Northern midlatitudes, civil aviation cruising altitude overlaps with the cold and humid layers just below the thermal tropopause, where cirrus clouds are frequent28,30, while in the subtropics, the main cruising levels are located deeper inside the troposphere where the temperatures are warmer and SAC is not fulfilled. Thus, the occurrence probability of PCCRs and ISSRs is reduced by a factor of three or larger.

Distribution of potential contrail-cirrus in clear sky and inside natural cirrus clouds
The differences in the vertical distributions of cruising levels and atmospheric layers of frequent PCCRs and ISSRs occurrence between midlatitudes and subtropics have immediate consequences on all aviation non-CO2 effects and particularly for contrail-cirrus. This includes both clear-sky and cloudy conditions which are distinguished by a CIWC threshold of CIWCclear = 0.001 ppmv, marking the onset of subvisible cirrus (see ‘Methods’). Conditions favouring contrail-cirrus existence at cruise altitude are met frequently in the midlatitudes, while they are sparsely met in the subtropics, which becomes clearly visible in Fig. 3. For the midlatitudes (Fig. 3a), the fraction of air masses in which no contrails can form (SAC not fulfilled), is of the order of 1% of the observations made, i.e., indistinguishable from the data noise level, while for the warmer subtropical region they can reach up to 15% for both clear-sky and in-cloud conditions.

Conditions favouring the formation of short-lived contrails (defined as SAC fulfilled, RHice < 90%) dominate in all regions with fractions of 70% and more of the probed air masses (sum of dark and light blue bars in Fig. 3), indicated as short-lived). Long-lived contrails, i.e., those fulfilling the SAC criterium and exceeding the RHice threshold naturally occur more frequently for PCCR than for ISSR. For the midlatitudes and for both threshold RHice values, however, the number of persistent contrails or contrail-cirrus forming inside pre-existing clouds (light blue bars in Fig. 3, indicated as long-lived) exceeds the number of cases in clear sky (respective dark blue bars in Fig. 3) by at least a factor of five, whereas in the subtropics, contrail persistence is only met inside clouds.

The total fraction of long-lived contrails in PCCRs (ISSRs) for both clear-sky and in-cloud conditions with respect to all probed air masses, is on average 28% (20%) for the Northern midlatitudes (Fig. 3a) and varies between 23% (15%) over Western Europe and 33% (24%) over the North Atlantic (Fig. 3c–e). Our observations over Europe are in good agreement with results from radiosonde-based studies50,51, while for the North Atlantic no referenced data are available. Overall, the increase in the fractional area prone to contrail-cirrus formation is almost 10% for the midlatitudes when considering PCCR instead of ISSR only, which is in accordance with earlier analyses of IAGOS data26. For Southeast Asia (Fig. 3b), the respective PCCR (ISSR) fraction is less than 14% (7%), reflecting the larger distance and warmer temperatures of cruising altitudes to the thermal tropopause and thus reduced RHice levels compared to the midlatitudes.

As discussed in the context of Fig. 1, the climate impact of contrail-cirrus depends crucially on the cloudiness of its environment. For the transition from subvisible to visible cirrus lidar observations52 define an optical thickness of 0.03 while theoretical calculations yield a value between 0.01 and 0.015 for a 500 m thick cloud53. Here, cloud optical depth is derived from the cloud ice water content through the relationship between cloud optical depth, CIWC and ice crystal effective diameter (Deff) for different CIWC and Deff values; details are described in ‘Methods’. We applied the CIWC threshold values CIWCvis to quantify the dependence of our results on the doubling of the CIWC visibility threshold value. A statistical analysis of the conditions and the connected climate impact of these three formation categories (clear sky, subvisible, visible) is given in Table 1. Details on the definition of the regions, CIWC categorization, and the results of the full statistical analysis are given in ‘Methods’ and in Table S1 of the supplementary information.

From this categorization it can be deduced that in the Northern midlatitudes, PCCR (ISSR), i.e., conditions prone to contrail-cirrus formation are found for max. ~4% (~2% or less) of the studied area in clear sky, ~9% (~6%) inside subvisible cirrus clouds, and ~15% (~12%) inside visible cirrus clouds (Fig. 3a). For the subtropics, the distribution is even more pronounced with almost all PCCR and ISSR conditions observed inside visible clouds, while observations in clear sky or subvisible clouds contribute max. 1% which, however, is considered below the noise level (Fig. 3b).

Recalling that the largest part of the studied regions is covered by air masses well below ice-saturation, conditions promoting long-lived contrails (PCCR, ISSR) are fulfilled most often in regions already covered by cirrus. If all air masses at or above the clear-sky threshold (CIWC ≥ CIWCclear) are considered (Fig. 3a, category long-lived), then between 87% (PCCR conditions) and 90% (ISSR conditions) of contrails form either in sub-visible or visible clouds. If only the visible clouds with CIWC ≥ 2.0 ppmv are taken into account, then these fractions reduce to 46% and 52%; see the right column in Table 1. In the Southeast Asian subtropics, contrail-cirrus conditions are met only inside clouds (Fig. 3b, category long-lived). See Table 1 for details and Fig. 3c–e for the variability across the Northern midlatitudes. Numerical values are provided in Table S2 of the supplementary information.

The above-mentioned study on properties of linear contrails using MODIS data13 reports 33% of contrails formed in areas already covered by clouds. The applied method distinguishes contrails from other cirrus by their linear shape and relatively large 11–12 µm brightness temperature difference. We apply a combination of in-situ based criteria such as the fulfilment of SAC, exceedance of RHice threshold for PCCR, and exceedance of ERA5 CIWCvis to a non-flight-level dataset and obtain a fraction of 46% (PCCR, CIWCvis = 2.0 ppmv). Taking into account that about ~20% of clouds classified in the MODIS analysis as water were likely to consist of non-opaque cirrus over lower liquid water clouds and a few more water clouds were misclassified as ice than ice clouds misclassified as water54, the agreement between the two studies is reasonable.

RH distributions in clear sky and inside cirrus clouds
The distribution of RHice inside clouds is important for the understanding of the respective cloud types. Figure 4a illustrates the frequencies of measured RHice for the midlatitude regions with their peak RHice values slightly above 100% inside visible cirrus clouds (blue shaded area), mostly below 100% in subvisible cirrus (light-blue shaded area), and predominantly at low RHice values in clear sky (red line). Figures 4c–e show the variability of RHice distributions for the different study regions of the Northern midlatitudes. While the overall features maintain, details of the split between subvisible and visible clouds vary between over-land and over-ocean regions. We interpret our observations of the larger fraction of subvisible cirrus in subsaturation such that these cirrus clouds are mostly slowly dissolving clouds, while visible cirrus clouds are more often in the developing stage at or above ice-saturation.

For the Southeast Asian Subtropics (Fig. 4b), the peak value of RHice inside clouds is found at slightly sub-saturated conditions, while sub-visible clouds are almost not present. That can be understood because (i) in the subtropics the cruising level of civil aviation is farther below the ice-supersaturated layer near the tropopause where cirrus form regularly, and (ii) the relative occurrence of ice-subsaturated air masses inside clouds increases with the distance from the cloud top55. Thus, in the subtropics, contrail-cirrus occur almost exclusively in physically and optically thick clouds closer to the cloud base. For clear-sky conditions, the most frequently observed RHice values represent dry conditions with RHice < 25% at temperatures above 225 K, while the coldest air masses probed at temperatures below 215 K are frequently close to ice-saturation; see Fig. S2 and discussion in the supplementary information.

RHice distribution patterns like the IAGOS-based observations have been reported for cirrus clouds in the midlatitude uppermost troposphere20,49,56, but without the separation of subvisible from visible cirrus. The cloud categorisation successfully applied here, in combination with the visibility criterion now allow the separation of clear-sky and in-cloud conditions with consideration of cloud thickness and thus optical depth.

Methods
IAGOS in-situ RHice and cloud datasets, ERA5 cloud ice water content
The analysed dataset covers the period from June 2014 to December 2021 and contains in total more than 17×106 data points with each data point corresponding to 4 s sampling time, or 1 km flown distance at an average cruising speed of 250 ms−1, respectively. Figure 2a shows the normalized data density per 5°x5° grid. Four regions of interest were identified for in-depth statistical analyses, with three of them located in the Northern midlatitudes (30–60°N), namely Eastern North America (Region 1: 105–65°W, 1.57×106 data points), the North Atlantic flight corridor (Region 2: 65–5°W, 4.43×106 data points), and Western Europe (Region 3: 5°W–30°E, 4.72×106 data points), and one in the Southeast Asian subtropics (Region 4: 0–30°N, 45–120°E, 6.14×106 data points). Here, we mainly refer to the total of regions 1–3 as Northern midlatitudes but also show the results for the individual regions to illustrate the variability depending on geographical differences. The Southeast Asian tropical and subtropical region is of potential interest because of the high traffic density, though the cruise levels are farther below the tropopause level and thus at warmer temperatures than in the midlatitudes where cruise altitudes are close to the tropopause; see Fig. 2b.

The combined IAGOS RHice, air temperature, and ERA5 CIWC dataset spans from June 2014 to December 2021. To restrict the analysis on the air masses of the upper troposphere and the tropopause layer with respect to the thermal tropopause (TTP) and to focus on ice clouds only, data were selected based on the following criteria30:

1. Pressure below 350 hPa (~8.1 km) to focus on cruise altitude,
2. Pressure above pTTP – 15 hPa to exclude dry stratospheric air masses that are too dry for cirrus clouds, and
3. Air temperature below 235 K (the threshold for spontaneous freezing of water droplets) to exclude air masses containing supercooled liquid water droplets.

According to WMO48, the thermal tropopause (TTP) is defined as the lowest level at which the lapse rate decreases to 2 K km−1 or less. In our study, vertical atmospheric layers relative to the thermal tropopause are defined as:

Thermal tropopause layer TTP: p = pTTP ± 15 hpa

Upper troposphere layer UT1: pTTP + 15 hpa < p < pTTP + 45 hpa

Upper troposphere layer UT2: pTTP + 45 hpa < p < pTTP + 75 hpa

Upper troposphere layer UT3: pTTP + 75 hpa < p < pTTP + 105 hpa

These separation of UT layers was only used for the analysis of the PCCR/ISSR occurrence with altitude (Fig. 2b). For all other analyses, the pressure band reaching from 350 hPa down to pTTP - 15 hPa was considered.

We quantified the contrail formation conditions for all sampled air masses by applying the Schmidt-Appleman criterion (SAC)17, and added the information on cloudiness by applying the herein developed cloud categorisation based on ERA5 Cloud Ice Water Content (CIWC). This means that if a cloud is detected, there is also a contrail in the air mass, since the data points are based on real flight paths. The observations were then sub-divided into clear-sky and in-cloud sequences (clear sky: CIWC < 0.001 ppmv, subvisible cirrus: 0.001 ppmv ≤ CIWC < 1.0 ppmv (2 ppmv), visible cirrus: CIWC ≥ 1.0 ppmv (2 ppmv), see Table 1). For each subset, conditions were rated as “no contrail formation” if SAC was not fulfilled, as favouring the formation of “short-lived contrails” if SAC was fulfilled and RHice < threshold RHice (threshold for contrail-cirrus occurrence, either 90% or 100%, see Table 1), and as favouring the formation of “contrail-cirrus” if SAC was fulfilled and RHice ≥ threshold RHice. The complete overview over the statistical analysis is compiled in Table S1 of the supplementary information.

The in-situ RHice data are calculated from direct measurements of relative humidity with respect to liquid water (RHliq) and ambient temperature by the IAGOS Capacitive Hygrometer (ICH). The ICH combining a thin-film HUMICAP® capacitive sensor (Vaisala) with a platinum resistance temperature sensor Pt100, is calibrated in the laboratory against an MBW dew-point chilled mirror analyser for RHliq30,59. A comparison of the ICH with the research-grade FISH fluorescence hygrometer indicates an uncertainty of ± (5-6) % RHliq and ± 0.5 K59.

The along-track cloud ice water content (CIWC) is derived by collocating the 5th version of ECMWF’s atmospheric reanalysis meteorological fields, ERA560, to IAGOS flight trajectories. The interpolation of ERA5 data at flight positions was conducted at a downgraded spatial and temporal resolution of 1°×1° longitude/latitude resolution and 6 h time resolution. The 137 levels in the vertical from the surface to 0.01 hPa remained unchanged. The CIWC at Tair < 235 K is treated as ice water content and serves as the cloud indicator, given that supercooled liquid water droplets freeze instantaneously into ice crystals at temperatures below 235 K. Along-track CIWC, air temperature TERA5 and specific humidity SH are extracted using a weighted-mean method, i.e., selecting the ERA5 grid points that are temporally and spatially closest to the IAGOS observations and calculate the mean values based on their proximity. Additionally, the WMO thermal tropopause height48 is calculated along flight tracks to distinguish between upper tropospheric and lower stratospheric air masses.

ERA5 CIWC—based cloud categorisation
To our best knowledge, the ERA5 CIWC has not yet been applied as a cloud indicator to field observations, apart from climatological comparisons with satellite observations61, or a machine-learning approach towards adjusting ERA5 humidity data to IAGOS observations62. In this study, we establish an appropriate CIWC threshold to indicate in-cloud conditions. This is achieved by evaluating ERA5 CIWC against a comprehensive climatology of CIWC data from in-situ observations of total water and gas phase water (CIWC detection limit 0.001 ppmv)23, and from cloud particle measurements with the NIXE-CAPS21 (CIWC detection limit 0.05 ppmv)63 in 24 field campaigns across the globe23. We validate the selected threshold by the in-situ measured RHice distributions from IAGOS as described in the following.

Panel (a) of Fig. 7 display the probability distribution of ERA5 RHice in relation to various ERA5 CIWC thresholds or for the separation of clear-sky and in-cloud conditions at cruise altitude (<350 hPa and T < 235 K) with RHice and CIWC collocated to research aircraft flight trajectories during the field campaign ML-CIRRUS, one of the 24 field campaigns20,22, conducted over Central and Western Europe and the Northeast Atlantic. The blue curve, representing ERA5 CIWC = 0.000 ppmv illustrates ideal clear-sky conditions, where ice-supersaturation is rarely observed. As the CIWC threshold for in-cloud categorisation increases to 0.001, 0.005, and finally 0.05 ppmv, the frequency of ice-supersaturation gradually rises due to the in mixing of moist cloud air, and the “shoulder” of the RHice distribution function around RHice = 100% develops, which is a clear sign of the presence of ice clouds. This ‘shoulder’ is also found in the measurements: in theory, regions in which NIXE-CAPS detects no cloud particles should be classified as cloud-free. However, the noticeable local maximum in the 80–120% RHice range (black curve in Fig. 7a) for these air masses indicates that the NIXE-CAPS, like every cloud instrument, missed detecting the presence of few small cloud particles in the sampled air which caused a low CIWC < 0.05 ppmv in these nominally cloud-free air masses. When the ERA5 CIWC threshold is raised to 0.05 ppmv (purple curve in Fig. 7a), again the occurrence of ice supersaturation significantly increases compared to lower CIWC thresholds.

When applying the CIWC threshold value of 0.001 ppmv from the in-situ observation of cloud ice water from the total and gas phase water measurements of the climatology23 to the RHice distributions shown in Fig. 7a (orange curve), the ‘shoulder’ vanishes and the RHice PDF is similar to that of clear sky (blue curve), indicating that no clouds were mixed into the air volume. Thus, we adopt an ERA5 threshold CIWC = 0.001 ppmv as an indicator of cloud presence in the reanalysis data.

The relation between a local maximum in the RHice distribution function around 100% and the presence of ice crystals is validated by simulating the occurrence frequencies of RHice at different thresholds of ice crystal number concentrations, using the Ice module within the Chemical Lagrangian Model of the Stratosphere (CLaMS-Ice)64. These simulations are based on ML-Cirrus flight trajectories. CLaMS-Ice employs a two-moment ice microphysics scheme, incorporating both heterogeneous and homogeneous freezing mechanisms, ice crystal growth, evaporation and sedimentation. The model runs 24 h trajectories ending at grid points distributed over the 3D region probed during ML-CIRRUS64, with boundary conditions provided by reanalysis data. Clear-sky air masses are defined as those that did not encounter cloud formation along the trajectories. As shown in Fig. 7b, increasing the threshold of the ice crystal number concentration from 0.002 cm⁻³ to 0.05 cm⁻³ enhances the fraction of ice supersaturation, with the typical ‘shoulder’ emerging at RHice ≅ 100%. The ‘shoulder’ is most pronounced when all clouds are included in the RHice distribution (Fig. 7b, purple curve).

Cloud optical depth thresholds
To estimate the cloud optical depth from the cloud ice water content, we used the relationships between cloud optical depth, CIWC and ice crystal effective diameter (Deff) as provided by Equation (3.9a) of Fu65 and by Equation (3) of Gayet66, and assumed a vertical extension of the cloud of 500 m, which is a typical extension for a fully developed contrail67. The conversion of CIWC from ppmv into gm−3 was conducted for fixed temperature values (in Kelvin) and a related mean pressure inside cirrus clouds following the empirical relationship pmean = 2.89319×10−4×T2.66906-247.724 hPa68.

Effective diameter values Deff were taken from sources based on observations, from which we selected Deff = 10 µm for a contrail at T = 217 K and older than 30 min69, Deff = 20 µm for a young cirrus at 10.6 km altitude and T = 213 K69, and Deff = 40 µm as the most probable effective diameter for cirrus clouds with CIWC values between 0.1 ppmv and 1.0 ppmv at Northern Midlatitudes26,70.

The discrimination threshold between subvisible and visible cirrus was taken from two sources. From lidar observations52 an overall optical depth in the visible spectral range of 0.03 is generally accepted as visibility threshold. From theoretical calculations53, a limiting extinction coefficient of 2–3×10−5 m−1 is reported, which turns into an optical depth of 0.01 to 0.015 for a cloud of 500 m vertical extension.

The results shown in Fig. 8 indicate that a CIWC between 1.0 ppmv and 2.0 ppmv, a vertical extension of 500 m, and a temperature range from 205 K to 230 K produce a cloud optical depth between the visibility thresholds from lidar observations52 and theoretical considerations53, independent of the selected relationship between optical depth, CIWC and Deff. Therefore, we used CIWC values of 1.0 ppmv and 2.0 ppmv to distinguish subvisible from visible clouds (CIWCvis).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors present data from seven years of airborne in-situ observations of temperature, relative humidity, and ice-crystal number concentration to assess the occurrence of conditions that, in principle, support the formation of short or long-lived contrails. They find that those conditions are often met within existing cirrus clouds and argue that the effective radiative forcing of those contrails in clouds, though highly uncertain, might be qualitatively assessed based on current knowledge. The authors also propose the use of potential contrail-cirrus region (PCCR) as a more inclusive metric compared to ice super-saturated regions (ISSR) which are commonly consulted to estimated contrail formation but hardly seem to be predict accurately.\nOverall, the paper focusses on an important topic that is of high relevance: The best conditions for contrail formation are found within clouds. However, we have no estimate of their radiative forcing as this is currently assessed only for line-shape contrails and contrail cirrus. This reviewer believes that the work makes for a good fit in Nature Communications.\nNevertheless, the authors could sharpen their message by addressing the comment below.\nMajor comments:\nThe authors build their argument on the observation of a high occurrence rate of PCCR. However, it might be worthwhile to add a paragraph as to whether or not an aircraft that flies through a PCRRs in a cirrus cloud automatically forms a contrail. Are there scenarios in which this might not happen? In the context of the later part of the paper, it would be good to know if PCCR in cirrus and (embedded) contrails are synonymous.\nThe message of the paper isn’t ideally represented in the current title. I suggest to simplify to something like “Most contrails form within cirrus clouds with uncertain climate impact.” Here is my take-home message.\n1. Conditions for forming long-living contrails are fulfilled most often in regions already covered by cirrus.\n2. There are almost no studies of the resulting embedded contrails and nothing is known about their radiative effect.\n3. This study provides a qualitative assessment of the radiative forcing of embedded contrails, e.g., for considering the potential impact of re-routing.\nIn that context, I am missing a clearer statement that our observation-based knowledge on contrails within cirrus clouds is severely limited. This would emphasise the relevance of the authors’ findings and allow for defining knowledge gaps to be filled in future research.\nWhile reading the manuscript, I had the feeling that the authors are looking at their dataset from a variety of angles and with slight modification. It might be worthwhile to provide a conceptual description or a flowchart of their line of reasoning. I also have the impression that the authors could optimise their (use of) figures and tables. Some information is provided in both figures and the table, which seems redundant. Some information is also nicely conveyed in the text and doesn’t seem to necessitate the addition of a corresponding figure. Finally, the layout of the figures could also be homogenised.\nWhile I appreciate the separation between 3 regions in the northern hemisphere, it seems to me that the overall message of the paper might just as well be conveyed by contrasting just two areas – a combination of what’s currently shown for mid-latitudes and the one in the tropics. This would simplify most of the figures and focus the presentation on the conclusions.\nI do understand the purpose of Figure 4. Given the broader readership of Nature Communications and the fact that large parts of the figure are not explained in the caption or the text, I recommend, though, to revise Figure 4 to something more of the nature of a conceptual sketch.\nIt is really hard to extract information from Figure 6. As the assessment of the climate impact is qualitative, why not just mark if a pixel is dominated by strong or weak climate impact? It would be completely fine to me as reader if this was to be done for the annual average with a discussion of seasonal variation restricted to the text, i.e., without an addition figure.\nMinor comments:\nI suggest to either add a more quantitative summary of the findings in the Abstract or to clearly state that the findings with respect to the radiative effect are the outcome of a qualitative analysis.\nLines 154 to 158: it is not quite clear how the authors got to these numbers.\nPlease make sure that your numbering of Tables and Figures is consistent.", "reviewer_2": "This is an important piece of work that should be published, subject to some revisions/addressing of points.\nThe m/s addresses the occurrence of persistent contrails within existing cirrus clouds on an observational basis with an impressively large database, which is a largely missing but important contribution to the debate over the role of aviation contrails in climate warming, since evidence for climate warming largely originates from either a very limited number of climate models (2) or diagnostic schemes (1) that have many missing processes. Thus, observational evidence is an important line of additional evidence. Moreover, most calculations that result in net warming are made under simple clear-sky conditions.\nI think the abstract could be written a little better, to contain the ‘hard-hitting’ results (notes below).\nThere is a tendency throughout the m/s to conflate estimating the ‘climate impact’ with a premise that there is a necessity for re-routing. The primary contribution of the paper is observational evidence and quantification for the circumstances when persistent contrails occur, i.e. clear sky or within natural cirrus, and then investigating their relative importance. The authors additionally and correctly caution that re-routing proposals consider ISS but do not consider the pre-existence of cirrus clouds. While re-routing as a mitigation approach is of relevance the authors should be clear to the reader that there is really not a demonstrated case for the necessity of this (see recent paper of Bickel et al., 2025, which provides an updated model study of contrail cirrus ERF and temperature response [efficacy]). A clearer separation of the two aspects (size of effect; necessity for mitigation) would make the m/s much clearer and the contribution of the observations more prominent.\nDetailed notes:\nAbstract\nL19-20 This is a premature recommendation that ignores that we cannot predict ISS well on the necessary time/space basis for avoidance, although the “…thorough assessment..” is well stated. It also ignores the fact that the authors’ own important findings are not fully understood in terms of ‘climate impact’ – what is the outcome of persistent contrails formed within pre-existing cirrus.\nL15 “…which will change…” do you mean “reduce”?\nWith the authors’ consideration of the above, they can ‘spend’ more of the limited number of abstract words on their own findings? Candidates for this are points such as “…most contrail-cirrus potentially form in regions already covered by natural cirrus” (L149/150). This is stated quantitatively in the abstract but maybe the statements could be combined.\nInstead of the rather vague last sentence, could something more hard-hitting be stated along the lines of “The results of the analysis suggest that contrail cirrus of potentially warming significance rarely forms (or “forms under only limited circumstances”) and need to be further analysed and verified in terms of their radiative impact” (just a suggestion).\nMain text\nL27 nitrogen oxide -> nitrogen oxides\nL29 My understanding is that ozone depletion from aircraft NOx would only occur in the mid stratosphere, where current subsonic aircraft do not fly.\nL30 please insert “present day” after 60%, since the proportion depends entirely on recent growth rates of aviation (there is a misconception that this is somehow a fixed proportion).\nL32 “mostly for contrail cirrus” this is not necessarily true, considering the poorly quantified aerosol cloud interactions. The authors could correctly nuance this with “of the quantified non-CO2 effects…”.\nL41-42 It may be helpful to cross reference lifetimes and radiative response from the overview paper of Karcher (2018, same journal), from his Table 1. There is a general misconception that ‘persistent contrails’ are radiatively important, which Karcher makes clear that they are not (unless they spread). It is only really persistent contrails that have a lifetime >10 min that spread into contrail-cirrus clouds that matter, radiatively. Indeed, the authors’ own results (fig 2 show that most contrails formed, are short-lived and consequently are of trivial radiative importance).\nL47-48 may need a little rewording? It could be read as implying that contrail cirrus can sometimes exist without the SAC being fulfilled.\nL48-50 may need some nuancing as without qualification, it implies that persistent contrails evolving into contrail cirrus form at ISSR <100%. The observed conditions of pre-formed persistent contrails surviving <100% would only seem plausible under the condition that their formation occurs at >100% in order to be persistent (otherwise they would sublimate) but the contrail cirrus thus formed of larger ice crystals is transitioning to sublimation with a limited lifetime, possibly as a result of them dehydrating the surrounding atmosphere and/or the atmosphere warming.\nL52-53 This may need some rewording, as the impression is given that ref 7 is supportive of the definitions made here of PCCRs. Ref 7 does not deal with RHice statistics.\nL55-58 Similarly (to L48-50), I find this a little problematic: the existence of contrail cirrus from persistent contrails at >90% does not mean that they were formed at <100% (as above). Their existence at <100% is an observation that needs some additional interpretation to make sense of it.\nL60-L69 On a re-read, I think there is an argument missing, which is important for the authors’ conclusions. They focus on ISS in L69-79, a prerequisite for persistent contrail formation. While ISS is also prerequisite for cirrus formation, NWPs do not predict cirrus clouds well (in space and time, properties) and many challenges remain. If one of the arguments is that re-routing proposals do not consider persistent contrail formation within clouds, it is worth pointing out that predicting cirrus cloud formation and its properties itself is challenging. This further increases the uncertainty of a re-routing outcome based on a NWP forecast and the risk of re-routing failing to produce a positive climate outcome (let alone verification of it…).\nL67-68, I think reference 19 would be highly appropriate here, as would be the work that developed from it: https://acp.copernicus.org/articles/24/7911/2024/\nI would be hesitant to cite ref 31, since while the reference is supportive of the present authors’ statement, it is only partially so, with ref 31 unconvincingly applauding their own model (their Figure 3) as predicting ISS successfully (a dubious conclusion in my view), which their Figure 3 conceals much detail, which is more honestly exposed in the format of Figure 2 of reference 19.\nL71-72. It may be helpful to the reader to be more nuanced here, along the lines of mitigating LLGHG (i.e. CO2), the primary focus of SAF/tech advancements, and SLCFs such as NOx products/contrails.\nL73-74. The citation of “so called big-hits” is made rather uncritically as if this is a well quantified and therefore real phenomenon. While it is an attractive shorthand which has gained traction in the non-scientific community, the quantification of the statistical distribution of contrail cirrus phenomena in relation to RF is very poor and generally points back to one regional study of Ref 34. I think “individually” could be replaced by “allegedly”. Also, I think it would be more accurate to say “have been proposed as a strategy”.\nL77-79 While not taking away from the cited study, this was actually highlighted by the IPCC WGI AR6 in 2021, Chapter 7, see IPCC WGI AR6 Chapter 7 FAQ 7.2.\nL71-79 in general; good points but I am missing the fundamental discussion on the size of the contrail cirrus forcing remains under debate and is only poorly quantified (2 climate models) This is present in L81 but I think the presentation of points could be clearer.\nL84 missing “when” between “than they”?\nL85 The passing mention in a reference list (ref 40) of Tesche et al does the study rather an injustice, since it is the only observational study (that this reviewer knows of) that attempts to quantify the impact in terms of optical thickness, of an aircraft forming a persistent contrail within a cirrus cloud. I would have thought the authors would maybe consider the results (later in the paper) in comparison to their own, and indeed, acknowledging this single prior observational study bolsters the importance of this present study in filling a much-needed gap.\nGeneral. The authors may find a few additional references an interesting/useful part of the story. Gierens 2012 appears to be one of the first authors to investigate aspects numerically (https://doi.org/10.5194/acp-12-11943-2012, 2012). Singh et al. (2024) make a few useful points in their review that this is a neglected topic (end of section 2.4) (https://doi.org/10.5194/acp-24-9219-2024). Marjani et al. (2022) make some remote sensing measurements (https://doi.org/10.1029/2021GL096173).\nSection ‘PCCRs and ISSRs in major air traffic regions’\nThe authors base their analysis and reinforcement of the importance of PCCRs over ISSRs on heavily trafficked regions. This may not be for this study, but I would encourage them to look for what happens in very sparsely trafficked regions where they have observations. Is the ratio/occurrence of persistent contrails <100% the same?\nL118 “aviation non-CO2 effects”? Do you mean contrail cirrus, rather than generalizing all aviation’s non-CO2 effects?\nL125 Referring to Figure 2. An awkward question, I realise but there is no sense of the uncertainties associated with the percentage splits. Can this be addressed at all (maybe in the SI). Further, on Figure 2 – my understanding is that the outcomes (no contrail, short-lived, persistent) are contingent on the constraints of the observations. To say that “no contrails” are formed in <1% of the air masses in that region is surely ‘for the observations made’, not an absolute truth? Am I missing the point here, or does the text need some small/simple adjustment to account for this?\nL140 “mere” ? I’m not sure that this is adding clarity – omit? Or is this supposed to be “more”?\nL141” Subvisible clouds are distinguished from optically thick clouds by means\nCIWC < 1.0 ppmv”. This is a critical/foundational assumption for the analysis of the data and its interpretation, so needs a reference; maybe https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2006JD008214 ?\nIt would be helpful to point forwards in the text that the authors have explored the sensitivity of this assumption.\nL140-L145 The concept of “potential climate impact” is introduced here and results given in Table 2 but not the concept is not explained until the discussion (L191). The whole definition is a little problematic. Figure 4 shows this kind of discrimination in a ‘direction of travel’ basis. The only means of getting to a ‘potential climate impact’ in a quantitative sense that allows a sensible comparison in the different sets of circumstances, is a radiative transfer (RT) calculation, which the authors clearly do not do. Thus, we are left with indicators of ‘directions of travel’, except for the most important phenomenon that the authors identify – that most persistent contrails are formed within pre-existing cirrus. This is a complex topic, hardly researched at all, and with an ambiguous outcome. So, my understanding is that for this category, we do not have a clear ‘direction of travel’. That is OK, it should be more clearly acknowledged and a recommendation made as how to address this with future research.\nI think the definition/explanation of “potential climate impact” is better placed here, not in the discussion, if such categorization is to be placed in the results. In Table 2, the entry “no” is confusing. I don’t know what this means. The authors omit to tell the reader that “potential climate impact” is a loose approximation. There will be times that, for example, solar zenith angle will reverse findings via radiative transfer calculations. In (related) L195-L196 for the optically thick cirrus cloud, a “minor effect” is cited. This is vague. If the potential outcome is ambiguous, please say so. It could be cooling or minor warming.\nL149-150 States: “That means, most contrail-cirrus potentially form in regions already covered by natural cirrus”. Again, it is unclear what the outcome of this will be. If the pre-existing cirrus is ‘optically thick’, additional contrail cirrus MAY further thicken an already optically-thick (naturally cooling) cloud further. But this is not clear unless more is known, and a full RT calculation is undertaken. All this is incredibly important as this could turn ‘conventional wisdom’ on its head about the net warming effect of contrail cirrus, or at the least, provide observational indirect evidence for a much smaller net warming (since most radiative transfer calculations are made under clear sky conditions). But we simply do not know from these observations. There is some (neglected here) further suggestive, if not definitive, evidence from the modelling study of Verma and Burkhardt (ref 39) who state: “Since corrections in ice nucleation are large in clouds with large ice water content, which are likely connected to large optical depth, *we speculate that disregarding the impact of cirrus on contrail formation may possibly underestimate the cooling of the contrail perturbations within optically thicker clouds*. It should be noted that the cirrus optical depth at which a further increase in optical depth, caused by contrail formation, leads to a cooling is dependent on the cirrus ice crystal habit.” (in ref 39’s conclusions). [* to * is this reviewer’s emphasis]\nL193 “change” should this be “increase”?\nL200 “relevance is rated as limited”…my understanding is that Verma and Burkhardt (ref 39) found that the additional water mass of ice crystals had a negligible effect (in agreement with earlier work of Gierens (2012, see reference above). If I am correct, would it be useful to be clearer as the sentence addresses ‘climate impact’ through to ‘vortex phase’ with little explanation.\nL204 “significant effect” please be more explicit.\nL219-225 Figure 4. Please be clearer over what you mean by “stronger” and “weaker” impact. By “stronger”, I am interpreting a greater potential climate impact (as you define it), which I interpret as a positive RF. I am less clear over “weaker” – weaker than what? Is it a cooling impact? Or a less warming impact than clear sky conditions/subvisible conditions? As per above, it seems as if adding optical thickness to an already optically thick cloud (which is ‘cooling’) as the negative forcing of the natural cloud, is made ‘more negative’ which then becomes a negative RF effect (as per the definition of RF, i.e. something interfering with the pre-industrial radiation balance).\nL227-232. Same comment over “stronger” and “weaker”. I’m not sure how much value this figure is adding, and if short of space, might be relegated to the SI.\nL234. Interesting statement. I don’t disagree from the analysis presented, but this offers quite a different perspective of the ‘big hits’ terminology (of which I remain unconvinced).\nL235 I disagree. I think that suggesting this is premature. What is more to the point is that all this needs to be better understood before formulating strategies (which may turn out to be pointless). L236 says this better.\nL238 “should help minimizing trade-off effects…” I think this is subtly wrong. I think accounting for all this reduces risks of doing the wrong thing. At the moment, given the authors’ results, the outcome of re-routing has just become far more uncertain.\nL234-248. This all makes sense, but it would be nice to have a stronger recommendation as to what research would firm this up (ERF vs occurrence conditions). Can this be accounted for/studied in global models, or can some hybrid observational/radiative transfer study be undertaken?\nL242-248. This seems like people-pleasing. We do not know - and this paper adds to the evidence – that re-routing is either a sensible or viable option for mitigating aviation’s impacts on climate. As they say, “get off the fence”! More seriously, simply reiterate the importance of these findings for re-routing proposals.\nIN CONCLUSION\nI think that the findings are of great importance and significance, but I am uncomfortable with their simplistic treatment of “potential climate impact”. This seems relatively clear, based on prior work with RT models/GCM calculations with RT, that clear sky conditions will net warm. Similarly, this may be the case for sub-visible cirrus with low OD. For persistent contrails forming contrail cirrus clouds within pre-existing cirrus, which seems to be the majority of incidence of persistent contrails from this study, then without much more information, we don’t know what the outcome of this will be. This should be stated much more clearly, and provide a recommendation for further work, given that the authors’ findings suggest that we should have an increased concern over what was already known to be a huge uncertainty – formation of persistent contrails within pre-existing cirrus. The title of the article says it all!", "reviewer_3": "Summary of the manuscript:\n“Contrails inside cirrus clouds predominate with uncertain climate impact” by Petzold et al. examines the potential occurrence of contrails, short-lived or persistent, as a function of humidity and ambient cirrus occurrence. Contrails form when the Schmidt-Appleton criterion is met and nominally can persist in ice-supersaturated regions (ISSR) where RHice > 100%. Recent research shows that contrails can also persist when RHice > 90%, giving rise to a larger range of humidities and, hence, a greater number of regions (43% more) of potential contrail coverage. Those regions are designated as potential contrail-cirrus regions (PCCRs). Results are presented for both ISSRs and PCCRs.\nThe motivation for the study is that a certain class of tropospheric conditions could be eliminated from any aircraft rerouting system that might be established to minimize contrail effects. That particular class of conditions is defined as the presence of thick cirrus clouds at planned flight levels. For this class, the radiative forcing induced by the development of contrail cirrus clouds is assumed to be small, or negligible enough to be ignored. Ergo, there is no need to reroute the flight because of contrail effects.\nThe analysis uses 7 years of IAGOS aircraft RHice measurements matched with interpolated ERA 5 to determine the ambient cloud conditions at flight level. A threshold of ERA5 CIWC > 0.001 ppmv is used to differentiate between clear and cloudy conditions. To further classify the cloud conditions, a cloud optical depth (OD) of 0.03, equivalent to CIWC = 1.0 ppmv, was used as the threshold differentiating sub-visible from thick cirrus for a given cloudy datapoint. Thus, any preexisting cirrus with cloud OD > 0.03 is assumed to be thick cirrus. Radiative forcing (RF) as a function of cloud OD is characterized using a plot of RF as a function of cirrus OD provided by Ref 11. The plot reproduced from Ref 11 indicates that RF increases with cloud OD up to a value of ~0.85 then drops precipitously for greater cirrus ODs to negative values for OD > 1.0.\nThe results of the analysis show that for the 4 regions examined, only 20% (ISSRs) - 30% (PCCRS) of the air masses can support contrail cirrus formation. Of these, roughly 64% of the contrails have a weaker impact on RF (climate) and the remaining 36% have a stronger impact. The overall effects vary regionally and seasonally, with minima over SE Asia and maximum effects during spring and winter. The results lead to the recommendation that any plan to adjust flight levels should include model predictions of cirrus locations, so that planes could fly in areas with thick cirrus and height adjustments would only be needed for clear areas and those with sub visible cirrus. The results also suggest that ~90% of contrails form within thick cirrus over SE Asia, it would probably be of little benefit to undertake any flight rerouting.\nReview:\nThe uncertainty in radiative forcing by contrails is high, leading to low confidence in our understanding of this somewhat small component of the climate change equation. Rerouting aircraft to avoid forming contrail cirrus is probably the most straightforward solution to minimizing contrail effects. However, it involves expenditure of more fuel and would further complicate air traffic control procedures. Thus, minimizing the number of possible aircraft reroutes by eliminating suspect air masses is a worthy effort. Thus, the goal of this study is of interest to the aviation and climate communities.\nThe premise is logical: contrails forming in a clear sky or in sub visible cirrus should have greater radiative impacts than those forming in thick cirrus. Persistent contrail development in already thick cirrus adds little to either the LW or SW impact of the existing cirrus because of the small change in OD for optically thick cirrus clouds. Yet, there are some shortcomings in how this premise is addressed.\n1) The first issue is that the authors looked to no later than 2010 (ref 29) for information about contrail cloud overlap. There are observations of persistent contrail coverage available for 2006 and 2012 (Duda et al., 2013; 2019).\nDuda et al. (2013) combined contrail analyses of 1 year of Northern Hemisphere Aqua MODIS data with MODIS cloud retrievals (Minnis et al. (2011). Using these, Bedka et al. (2013) differentiated between contrails over/within ice clouds (cirrus) and contrails detected in clear skies or over low-level water clouds. Passive satellite retrievals have difficulty detecting cirrus with OD < 0.05. The hit rates for clouds having OD < 0.1 are around 50% (Trepte et al., 2019). Thus, the clear category would include both clear and subvisible clouds and the ice clouds would be thick according to the definition used here. With that in mind, Bedka et al. (2013) found that contrails were detected with ice clouds predominating in 33% of the cases, compared to 46% with low liquid water clouds, and 17% in clear skies. Seasonal variations are superimposed on those averages. There are likely a few more percent contrails having ice cloud concurrence as ~20% of clouds classified as water were likely to consist of non-opaque cirrus over lower liquid water clouds and a few more water clouds were misclassified as ice than ice clouds misclassified as water (Sun-Mack et al., 2024). Nevertheless, the observed fraction of weaker impact conditions (33% coincidence with ice clouds) is significantly smaller than the 64% computed here. Perhaps, the selection of CIWC = 0.001 ppmv as the cloud threshold produces too many clouds. It is not all that different from 0.000 ppmv in frequency. This would be consistent with Reference 57, which indicates that ERA5 generates too much ice cloud in the upper troposphere relative to CALIPSO.\nSpangenberg et al. (2013; S13) computed RF for all of the contrails.The resulting mean values support the premise of this paper. Indeed, one could look at those averages and come to the same conclusion as the results of this paper: Flying in an atmosphere with preexisting visible cirrus will cause less RF than flying in other conditions. In fact, the observations actually quantify the differences. S13 found that the net unit contrail RF during the daytime (~13:30 LT) was 3.9 Wm-2 for clear skies and 1.3 Wm-2 for contrails in the same column as ambient cirrus clouds. That is a factor of 3 decrease, a change that would support the use of the sub visible threshold. Yet, the LW RFs for clear and cloudy scenes are 18.5 and 11.7 Wm-2, respectively, a difference of only 36%. That LW difference is the same at night when no SW RF occurs to balance the LW RF.\n2) The premise of this paper seems too limited in scope. One would expect that a contrail developing above or below a thick cirrus would also have a similar impact as a contrail imbedded in the cirrus since the ice cloud OD added to the total column is nearly the same in both cases. Perhaps, that is implied here somehow.\n3) The somewhat vague notion of weaker and stronger impacts is not particularly satisfying. Given the observed RF results, what average difference in RF is considered to be enough to separate weak and strong impacts? Is the use of cloud OD > 0.03 as a thick cirrus optimal? Is the characterization “thick”warranted or should visible be used always. Normally one would consider a cirrus cloud to be thick when the emissivity approaches unity or the change in emissivity with unit optical depth is relatively small, typically when OD is between 3 and 6. While it is true that adding a contrail to sub visible cirrus will have nearly the same impact as adding a contrail to a clear-sky, there could still be significant contrail RF impacts when the extant cirrus has an OD < 1.5 (e.g., Meerkötter et al.1999). Hong and Liu (2015) show that a large portion of ice clouds observed by CALIPSO have ODs between 0.05 and 1.5, while the mode of the total distribution is OD = 1.2. Thus, there will be a range of significant RFs that could be produced by contrails. Determining the optimal cirrus OD threshold would require a sensitivity study and possibly consideration of low-level clouds.\nThis need for quantification is more apparent when considering that the weaker impacts constitute almost 100% of persistent contrail diagnoses in SE Asia. That suggests that overall RF should be smaller in that region compared to North America or Europe. The RF results from S13 suggest otherwise. They suggest that over the SE Asia flight corridors are much like their USA and European counterparts, and even greater at night.\nOther comments\nIt should be noted that the RF results in Fig. 4 are based on a single set of conditions, noon at SZA = 50 deg?. There is no consideration for the ERF at night, which is all warming. The results for other angular conditions, latitudes, and backgrounds will be highly variable.\nLine 331 red curve is for 0.01, not 0.05. Purple curve is for 0.05 in Fig. &a.\nDespite the issues and reservations described above, not to mention the uncertainties in current model representations of RHice and clouds, the authors have laid the groundwork for a reasonable method to define cirrus cloud conditions that could theoretically be used to reduce the magnitude of flight rerouting in a future contrail avoidance system.\nReferences\nBedka, S. T., P. Minnis, D. P. Duda, T. L. Chee, and R. Palikonda, 2013: Properties of linear contrails in the Northern Hemisphere derived from 2006 MODIS observations. Geophys. Res. Lett., 40, 772-777, doi:10.1029/2012GL054363.\nDuda, D. P., P. Minnis, K. Khlopenkov, T. L. Chee, and R. Boeke, 2013: Estimation of 2006 Northern Hemisphere contrail coverage using MODIS data. Geophys. Res. Lett., 40, doi:10.1002/grl.50097, 612-617.\nDuda, D. P., S. T. Bedka, P. Minnis, D. Spangenberg, K. Khlopenkov, T. Chee, and W. L. Smith, Jr., 2019: Analysis of interannual variability in Northern Hemisphere contrail properties from Terra and Aqua data. Atmos. Chem. Phys., 19, 5313-5330, doi:10.5194/acp-19-5313-2019.\nHong, Y. And G. Liu, 2015: The characteristics of ice cloud properties derived from CloudSat and CALIPSO measurements. J. Climate, 28, 3880- 3901. Doi:10.1175/JCLI-D-14-00666.1\nMeerkötter, R., U. Schumann, D. R. Doelling, P. Minnis, T. Nakajima, and Y. Tsushima, 1999: Radiative forcing by contrails, Annales Geophysicae, 17, 1070-1084.\nMinnis, P., S. Sun-Mack, D. F. Young, P. W. Heck, D. P. Garber, et al., 2011: CERES Edition-2 cloud property retrievals using TRMM VIRS and Terra and Aqua MODIS data, Part I: Algorithms. IEEE Trans. Geosci. Remote Sens., 49, 11, 4374-4400, doi:10.1109/TGRS.2011.2144601.\nSpangenberg, D. A., P. Minnis, S. T. Bedka, R. Palikonda, D. P. Duda, and F. G. Rose, 2013: Contrail radiative forcing over the Northern Hemisphere from 2006 Aqua MODIS data. Geophys. Res. Lett., 40, doi:10.1002/grl.50168, 595-600.\nTrepte, Q. Z., P. Minnis, S. Sun-Mack, C. R. Yost, Y. Chen, Z. Jin, F.-L. Chang, W. L. Smith, Jr., K. M. Bedka, and T. L. Chee, 2019: Global cloud detection for CERES Edition 4 using Terra and Aqua MODIS data. IEEE Trans. Geosci. Remote Sens., 57, 9410-9449, doi:10.1109/TGRS.2019.2926620.\nSun-Mack, S., P. Minnis, Y. Chen, G. Hong, and W. L. Smith, Jr., 2024: Identification of ice-over-water multilayer clouds using an artificial neural network with multispectral satellite data. Atmos. Meas. Tech., 17, 3323–3346, doi:10.5194/amt-17-3323-2024."}, "author_response": "POINT-BY-POINT RESPONSE TO REVIEWER COMMENTS\nThe authors gratefully acknowledge the thorough and constructive reviews by the three anonymous\nreferees. All points raised were carefully considered and taken up in the revision of the manuscript.\nAs recommended by the referees, we strengthened the focus on the presentation and discussion of\nour observational results, rewrote the entire abstract, and concentrate the discussion of results on the\ntopic of contrail-cirrus appearance in clear sky and subvisible as well as visible cirrus.\nWe describe with more detail the approach of our study which is now presented in Figure 1. The\n‘climate impact’ concept is replaced by the concept that contrail-cirrus in clear sky and subvisible cirrus\ncauses considerable warming while the warming effect of contrail-cirrus in visible clouds is not only\nminor but also ambiguous since, depending on the optical thickness of the pre-existing cirrus, the effect\ncan shift from warming to cooling. Thanks to the referees’ comments , we are now able to quantify the\nenhancement of warming of contrails in clear sky and subvisible cirrus compared to visible clouds\n(Spangenberg et al., 2013; Bedka et al., 2013), and support the potential cooling of contrail-cirrus\nembedded in thick cirrus clouds by a reference to a model study (Verma and Burkhardt, 2022). In\nconsequence categorises ‘stronger climate impact’ and ‘weaker climate impact’ are replaced by the\ncategories ‘warming’ and ‘ambiguous’.\nTo make the results of our study more visible, we followed the recommendation of Reviewer 1 and\nmerged the former regions 1- 3 into one region on Northern Midlatitudes which is then directly\ncompared to the Southeast Asian Subtropics. The details for former regions 1 – 3 are added to the\nfigures to quantify the observed variability.\nSince this is a very active research field, we updated the manuscript with several publications which\nappeared recently (Zhang et al., 2025; Bickel et al., 2025; Prather et al., 2025). Also, the extensive\nreview by Singh et al. (2024) on the role of contrails and contrail cirrus in climate change was added.\nFor each referee, we will respond to the questions and recommendations point by point. Our answers\nare shown in italic green. Please note that we did not include the references in the text excerpts we\nadded to the response to reviewers. We also provide an annotated manuscript showing the\nmodifications in track-changes-mode. Line numbers refer to the clean revised manuscript.\nThe authors present data from seven years of airborne in-situ observations of temperature, relative\nhumidity, and ice-crystal number concentration to assess the occurrence of conditions that, in\nprinciple, support the formation of short or long-lived contrails. They find that those conditions are\noften met within existing cirrus clouds and argue that the effective radiative forcing of those contrails\nin clouds, though highly uncertain, might be qualitatively assessed based on current knowledge. The\nauthors also propose the use of potential contrail-cirrus region (PCCR) as a more inclusive metric\ncompared to ice super-saturated regions (ISSR) which are commonly consulted to estimated contrail\nformation but hardly seem to be predict accurately.\nOverall, the paper focusses on an important topic that is of high relevance: The best conditions for\ncontrail formation are found within clouds. However, we have no estimate of their radiative forcing as\nthis is currently assessed only for line-shape contrails and contrail cirrus. This reviewer believes that\nthe work makes for a good fit in Nature Communications. Nevertheless, the authors could sharpen\ntheir message by addressing the comment below.\nMajor comments:\nThe authors build their argument on the observation of a high occurrence rate of PCCR. However, it\nmight be worthwhile to add a paragraph as to whether or not an aircraft that flies through a PCRRs in\na cirrus cloud automatically forms a contrail. Are there scenarios in which this might not happen?\nReply: Very good point, we added the following paragraph to the manuscript on line 80 to 84:\n“Aircraft flying through an ice-supersaturated or even slightly subsaturated air mass will thus form a\npersistent contrail and finally a contrail-cirrus as soon as ambient air temperature is below 230 - 225\nK, which is almost always the case for Northern midlatitude cruise altitude. Only for warmer\ntemperatures above 230 K, as met, e.g., in the subtropics or at lower altitudes in the midlatitudes, these\nregions may be crossed by commercial aircraft without generating a contrail. “\nIn the context of the later part of the paper, it would be good to know if PCCR in cirrus and (embedded)\ncontrails are synonymous.\nReply: Indeed, PCCR in cirrus and embedded contrails are synonymous. This is clarified on line 94.\nThe message of the paper isn’t ideally represented in the current title. I suggest to simplify to\nsomething like “Most contrails form within cirrus clouds with uncertain climate impact.”\nReply: Thank you very much for this excellent suggestion, we modified the title accordingly but added\n‘long-living’ to be precise.\nHere is my take-home message.\n1. Conditions for forming long-living contrails are fulfilled most often in regions already covered by\ncirrus.\n2. There are almost no studies of the resulting embedded contrails, and nothing is known about their\nradiative effect.\n3. This study provides a qualitative assessment of the radiative forcing of embedded contrails, e.g., for\nconsidering the potential impact of re-routing.\nReply: We are grateful to the reviewer for this stringent formulation of our take-home message. We\nadopted the wording in our abstract and conclusion sections which reads now:\n2\n“The results of our study suggest that conditions necessary for the formation of contrail-cirrus are most\noften fulfilled in regions that are already covered by visible cirrus, which reduces their warming impact\nor even turns it into a cooling effect. Those of a stronger warming significance, however, form under\nonly limited circumstances in clear sky and subvisible cirrus. Unfortunately, our knowledge on the\nradiative effects of contrail-cirrus embedded in subvisible, visible and optically thick clouds, and\nfeedback mechanisms between contrail and cirrus ice particles is highly limited. There will be a range\nof radiative forcings than could be produced by embedded contrail-cirrus, and the quantification of the\nclimate impacts would require a sensitivity study and possibly consideration of low-level clouds.\nThis topic needs to be further analysed and verified in terms of their radiative impact for consideration\nof the potential impact of contrail avoidance strategies including flight rerouting. Finally, ice-\nsupersaturation only is by far not a reliable, stand-alone criterion for assessing contrail-cirrus climate\neffects. Instead, we need to include pre-existing cirrus clouds and their interactions with contrail-cirrus\ninto all our considerations.”\nIn that context, I am missing a clearer statement that our observation-based knowledge on contrails\nwithin cirrus clouds is severely limited. This would emphasise the relevance of the authors’ findings\nand allow for defining knowledge gaps to be filled in future research.\nReply: Indeed, a clearer statement is required, we added a sentence to the introduction part, starting\nat line 60:\n“Observation-based knowledge on long-lived contrails within cirrus clouds and their radiative effects is\nseverely limited. To narrow that knowledge gap, we study the occurrence of conditions favouring the\nformation and existence of long-lived contrails inside pre-existing cirrus clouds from observations of\nrelative humidity with respect to ice taken on board of passenger aircraft equipped with suitable\ninstrumentation. “.\nWhile reading the manuscript, I had the feeling that the authors are looking at their dataset from a\nvariety of angles and with slight modification. It might be worthwhile to provide a conceptual\ndescription or a flowchart of their line of reasoning.\nReply: We fully agree and start now the results section with a description of our conceptual approach.\nWe refer the reviewer to the manuscript from line 134 to line 159.\nI also have the impression that the authors could optimise their (use of) figures and tables. Some\ninformation is provided in both figures and the table, which seems redundant. Some information is\nalso nicely conveyed in the text and doesn’t seem to necessitate the addition of a corresponding figure.\nReply: Figures and table have been carefully revisited and adapted where necessary. We have paid\nparticular attention to the potential redundancy between figures and table. Although Table 1 still\ncontains some redundancy, we decided to keep it because we believe it is of good value to give numbers\nof cloud fractions etc. in addition to graphical presentation.\nFinally, the layout of the figures could also be homogenised.\nReply: Figures have been homogenised, as recommended.\nWhile I appreciate the separation between 3 regions in the northern hemisphere, it seems to me that\nthe overall message of the paper might just as well be conveyed by contrasting just two areas – a\ncombination of what’s currently shown for mid-latitudes and the one in the tropics. This would simplify\nmost of the figures and focus the presentation on the conclusions.\nNorth Atlantic region marked, we added the analyses for the separate regions of the Northern\nMidlatitudes as smaller panels to the Figures 3 and 4. Figure 5 on the climate impact is now shown only\nfor the entire Northern midlatitudes and the Southeast Asian subtropics. Detailed numbers for all\nregions are shifted to Tables S1 and S2 in the supplement.\nI do understand the purpose of Figure 4. Given the broader readership of Nature Communications and\nthe fact that large parts of the figure are not explained in the caption or the text, I recommend, though,\nto revise Figure 4 to something more of the nature of a conceptual sketch.\nReply: Figure 4 has been revised to a conceptual figure, as suggested. A detailed description has been\nadded to the first paragraph of the discussion section. Former Figure 4 is now put at the front of the\nresults section as Figure 1 to guide the reader through the concept. We refer the reviewer to lines 142\nto 159.\nIt is really hard to extract information from Figure 6. As the assessment of the climate impact is\nqualitative, why not just mark if a pixel is dominated by strong or weak climate impact? It would be\ncompletely fine to me as reader if this was to be done for the annual average with a discussion of\nseasonal variation restricted to the text, i.e., without an addition figure.\nReply: Figure 6 have been simplified and shows now distribution patterns for summer and winter\nseasons only. The resolution was reduced so that the appearance is now “blurrier” which makes the\nlateral distribution easier to recognise. Nevertheless, we want to keep this information in the\nmanuscript since it shows the regional and seasonal variabilities for the net warming and ambiguous\nimpact cases.\nMinor comments:\nI suggest to either add a more quantitative summary of the findings in the Abstract or to clearly state\nthat the findings with respect to the radiative effect are the outcome of a qualitative analysis.\nReply: We added the following sentence to the abstract: “A conceptual analysis shows that subvisible\ncirrus and clear-sky cover ~10% of the cruise altitude over Northern midlatitudes (< 2% in the subtropics)\nand contrails within these regions are expected to cause additional warming. However, most contrails\nin the thicker, visible cirrus, only slightly enhance the cirrus warming effect or possibly reverse it to\ncooling. Our results suggest that potential flight rerouting concepts for contrail avoidance need to\nconsider cirrus cloud coverage in addition to ice-supersaturation.\nLines 154 to 158: it is not quite clear how the authors got to these numbers.\nReply: The entire section on the overlap of regions covered by cirrus clouds and prone to contrail\nformation has been revised. The new section on the overlap between contrail-cirrus and visible cirrus is\nnow from line 230 to line 245. For all numbers we clearly indicate where the numbers are taken from\nor how they have been calculated.\nPlease make sure that your numbering of Tables and Figures is consistent.\nReply: The numbering of Tables and Figures has been carefully checked and modified where necessary.\nThis is an important piece of work that should be published, subject to some revisions/addressing of\npoints.\nThe m/s addresses the occurrence of persistent contrails within existing cirrus clouds on an\nobservational basis with an impressively large database, which is a largely missing but important\ncontribution to the debate over the role of aviation contrails in climate warming, since evidence for\nclimate warming largely originates from either a very limited number of climate models (2) or\ndiagnostic schemes (1) that have many missing processes. Thus, observational evidence is an important\nline of additional evidence. Moreover, most calculations that result in net warming are made under\nsimple clear-sky conditions.\nI think the abstract could be written a little better, to contain the ‘hard-hitting’ results (notes below).\nThere is a tendency throughout the m/s to conflate estimating the ‘climate impact’ with a premise that\nthere is a necessity for re-routing. The primary contribution of the paper is observational evidence and\nquantification for the circumstances when persistent contrails occur, i.e. clear sky or within natural\ncirrus, and then investigating their relative importance. The authors additionally and correctly caution\nthat re-routing proposals consider ISS but do not consider the pre-existence of cirrus clouds. While re-\nrouting as a mitigation approach is of relevance the authors should be clear to the reader that there is\nreally not a demonstrated case for the necessity of this (see recent paper of Bickel et al., 2025, which\nprovides an updated model study of contrail cirrus ERF and temperature response [efficacy]). A clearer\nseparation of the two aspects (size of effect; necessity for mitigation) would make the m/s much\nclearer and the contribution of the observations more prominent.\nReply: Fully agreed, see comment above on the overall structure of the study. Furthermore, the abstract\nhas been completely rewritten. We refer the reviewer to the revised abstract.\nDetailed notes:\nAbstract\nL19-20 This is a premature recommendation that ignores that we cannot predict ISS well on the\nnecessary time/space basis for avoidance, although the “…thorough assessment.” is well stated. It also\nignores the fact that the authors’ own important findings are not fully understood in terms of ‘climate\nimpact’ – what is the outcome of persistent contrails formed within pre-existing cirrus.\nReply: This recommendation is removed from the abstract, and the entire abstract was rewritten with\na stronger focus on the quantitative results we report.\nL15 “…which will change…” do you mean “reduce”?\nReply: The original wording was indeed not precise, and we followed the reviewer’s suggestion and use\nthe term “reduce” instead.\nWith the authors’ consideration of the above, they can ‘spend’ more of the limited number of abstract\nwords on their own findings? Candidates for this are points such as “…most contrail-cirrus potentially\nform in regions already covered by natural cirrus” (L149/150). This is stated quantitatively in the\nabstract but maybe the statements could be combined.\nInstead of the rather vague last sentence, could something more hard-hitting be stated along the lines\nof “The results of the analysis suggest that contrail cirrus of potentially warming significance rarely\n5\nforms (or “forms under only limited circumstances”) and need to be further analysed and verified in\nterms of their radiative impact” (just a suggestion).\nReply: As said above, the entire abstract was rewritten with a stronger focus on the quantitative results\nwe report. However, we decided to keep a reference to the rerouting discussion in the abstract which\nreads ‘Our results suggest that potential flight rerouting concepts for contrail avoidance need to\nconsider cirrus cloud coverage in addition to ice-supersaturation.’ The idea behind keeping this\nsentence is to make readers from the “rerouting business’ aware of our results which otherwise might\nget lost.\nMain text\nL27 nitrogen oxide -> nitrogen oxides\nReply: Corrected\nL29 My understanding is that ozone depletion from aircraft NOx would only occur in the mid\nstratosphere, where current subsonic aircraft do not fly.\nReply: This understanding is correct. However, from the REACT4C project there are also cases reported\nfor reduced ozone in the lowermost stratosphere at high latitudes. Since the climate change function\nof aviation-induced ozone are always positive, we rephrased the statement as: “aviation-NO induced\nx\nozone formation”.\nL30 please insert “present day” after 60%, since the proportion depends entirely on recent growth\nrates of aviation (there is a misconception that this is somehow a fixed proportion).\nReply: We changed the sentence to “With an ERF of 60 mW m-2 contrail-cirrus is estimated to be the\nlargest non-CO ERF contributing 60% (present-day knowledge) to the aviation net total ERF of\n2\n100 mW m-2”.\nL32 “mostly for contrail cirrus” this is not necessarily true, considering the poorly quantified aerosol\ncloud interactions. The authors could correctly nuance this with “of the quantified non-CO2 effects…”.\nReply: Thank you, we changed this accordingly.\nL41-42 It may be helpful to cross reference lifetimes and radiative response from the overview paper\nof Karcher (2018, same journal), from his Table 1. There is a general misconception that ‘persistent\ncontrails’ are radiatively important, which Karcher makes clear that they are not (unless they spread).\nIt is only really persistent contrails that have a lifetime >10 min that spread into contrail-cirrus clouds\nthat matter, radiatively. Indeed, the authors’ own results (fig 2 show that most contrails formed, are\nshort-lived and consequently are of trivial radiative importance).\nReply: Very good suggestion, indeed. We rephrased the related paragraph as follows (lines 71 – 75):\n‘After reaching the ambient temperature, the contrail ice particles grow or shrink in size depending on\nthe ambient humidity. If the environment remains ice-supersaturated (RH > 100%), the contrails can\nice\npersist with lifetimes from 4 to > 10 hours. If the ambient air is ice-subsaturated (RH < 100%), the ice\nice\nparticles sublimate and the contrail dissolves. For a contrail to survive more than approx. 10 minutes\nand to spread out to radiatively impactful contrail cirrus, ambient RH must be close to or above ice-\nice\nsaturation.’\nexist without the SAC being fulfilled.\nReply: Agreed, we simply removed the part of the sentence referring to SAC. It reads now (lines 86 –\n87): “Today, the occurrence of contrail-cirrus is discussed in its relationship to cold (T < 230 K) ice-\nsupersaturated regions (ISSR: RH  100%).”\nice\nL48-50 may need some nuancing as without qualification, it implies that persistent contrails evolving\ninto contrail cirrus form at ISSR <100%. The observed conditions of pre-formed persistent contrails\nsurviving <100% would only seem plausible under the condition that their formation occurs at >100%\nin order to be persistent (otherwise they would sublimate) but the contrail cirrus thus formed of larger\nice crystals is transitioning to sublimation with a limited lifetime, possibly as a result of them\ndehydrating the surrounding atmosphere and/or the atmosphere warming.\nReply: Indeed, this section requires clarification to avoid misunderstanding. We added the following\nsentences (lines 87 – 92):\n“To include the observationally confirmed existence of contrail-cirrus also at slight ice-subsaturation in\nthe consideration of aviation climate impacts, we introduce the term “potential contrail-cirrus region”\n(PCCR) which we define as an air mass with RH  90% and SAC fulfilled. In such an air mass with SAC\nice\nfulfilled, a contrail would form and go through the stage of ice-supersaturation during plume expansion\nwhere the ice crystals grow. The resulting contrail formed of larger ice crystals would then transition to\nsublimation with a limited but long-enough lifetime for becoming radiatively impactful.”\nL52-53 This may need some rewording, as the impression is given that ref 7 is supportive of the\ndefinitions made here of PCCRs. Ref 7 does not deal with RHice statistics.\nReply: Ref 7 was used as a source of information for the lifetime. Since this reference was made earlier,\nwe removed the reference here.\nL55-58 Similarly (to L48-50), I find this a little problematic: the existence of contrail cirrus from\npersistent contrails at >90% does not mean that they were formed at <100% (as above). Their existence\nat <100% is an observation that needs some additional interpretation to make sense of it.\nReply: The fact that contrail formation and first growth will always go through a stage of ice\nsupersaturation was explained on lines 87 – 92 and should be clear now.\nL60-L69 On a re-read, I think there is an argument missing, which is important for the authors’\nconclusions. They focus on ISS in L69-79, a prerequisite for persistent contrail formation. While ISS is\nalso prerequisite for cirrus formation, NWPs do not predict cirrus clouds well (in space and time,\nproperties) and many challenges remain. If one of the arguments is that re-routing proposals do not\nconsider persistent contrail formation within clouds, it is worth pointing out that predicting cirrus cloud\nformation and its properties itself is challenging. This further increases the uncertainty of a re-routing\noutcome based on a NWP forecast and the risk of re-routing failing to produce a positive climate\noutcome (let alone verification of it…).\nReply: Thank you very much for that excellent suggestion, we added the sentence on lines 112 – 114):\n“It also needs to be mentioned that forecasting cirrus cloud formation and its properties is challenging\nfor the same reasons as those for ISSRs and potentially PCCRs, since ISSRs are an indispensable pre-\nrequisite for cirrus cloud formation.“\nL67-68, I think reference 19 would be highly appropriate here, as would be the work that developed\nfrom it: https://acp.copernicus.org/articles/24/7911/2024/\nI would be hesitant to cite ref 31, since while the reference is supportive of the present authors’\nstatement, it is only partially so, with ref 31 unconvincingly applauding their own model (their Figure\n3) as predicting ISS successfully (a dubious conclusion in my view), which their Figure 3 conceals much\ndetail, which is more honestly exposed in the format of Figure 2 of reference 19.\nReply: We fully agree, removed Ref 31, inserted Ref 19 and its update (now 31 and 36) instead.\nL71-72. It may be helpful to the reader to be more nuanced here, along the lines of mitigating LLGHG\n(i.e. CO2), the primary focus of SAF/tech advancements, and SLCFs such as NOx products/contrails.\nReply: We extended the argument which reads now (lines 116 – 118):\n“There are several measures discussed for reducing aviation’s climate impact, including technological\nadvancements for reducing the emissions of short-lived climate forcers such as NO and aerosols, and\nx\nthe availability of sustainable aviation fuels for reducing long-lived greenhouse gases “\nL73-74. The citation of “so called big-hits” is made rather uncritically as if this is a well quantified and\ntherefore real phenomenon. While it is an attractive shorthand which has gained traction in the non-\nscientific community, the quantification of the statistical distribution of contrail cirrus phenomena in\nrelation to RF is very poor and generally points back to one regional study of Ref 34. I think\n“individually” could be replaced by “allegedly”. Also, I think it would be more accurate to say “have\nbeen proposed as a strategy”.\nReply: We fully agree, removed the term “big hit” which is indeed a bit sensational, and modified the\nsentence as (line 118 – 119): “On the short term, operational concepts for avoiding contrails that\nallegedly have the largest warming effects, have been proposed as a strategy for reducing aviation’s\nclimate impact “.\nL77-79 While not taking away from the cited study, this was actually highlighted by the IPCC WGI AR6\nin 2021, Chapter 7, see IPCC WGI AR6 Chapter 7 FAQ 7.2.\nReply: Thank you for the hint, the sentence was rephrased to “Additionally, the latest IPCC report\nhighlighted the role of clouds in a warming climate (IPCC, 2021) which makes the reduction of\nanthropogenically generated high ice clouds even more urgent.”\nL71-79 in general; good points but I am missing the fundamental discussion on the size of the contrail\ncirrus forcing remains under debate and is only poorly quantified (2 climate models) This is present in\nL81 but I think the presentation of points could be clearer.\nReply: We added the following sentence and reference to the last sentence of the first paragraph (lines\n32 - 36): “Other than the well-understood CO effect and its small uncertainty, the quantified non-CO\n2 2\neffects of aviation are associated with large uncertainties, mostly for contrail-cirrus with a substantial\nassociated uncertainty of approx. 70 %. In particular, the feedbacks of contrail-cirrus radiative effects\nand surface temperature are largely unknown, but a most-recent model study including these effects\nreports that the climate sensitivity is lower for contrail-cirrus than for aviation-related CO emissions.”.\nReply: Indeed, the sentence is unclear and was rearranged accordingly.\nL85 The passing mention in a reference list (ref 40) of Tesche et al does the study rather an injustice,\nsince it is the only observational study (that this reviewer knows of) that attempts to quantify the\nimpact in terms of optical thickness, of an aircraft forming a persistent contrail within a cirrus cloud. I\nwould have thought the authors would maybe consider the results (later in the paper) in comparison\n8\nto their own, and indeed, acknowledging this single prior observational study bolsters the importance\nof this present study in filling a much-needed gap.\nReply: Fully agreed. We discuss now the references Tesche et al. and Marjani et al. (refs 16 and 17)\nseparately and back it up with the recent paper by Zhang et al. (2025) who also report a strong impact\non contrail cirrus optical depth on the effective radiative forcing. The section added on line 55 reads\n“Two studies using CALIPSO observations and flight track recordings reported an increase in cloud\noptical depth by 22% after an aircraft had crossed the cloud, and a statistically significant increase by\nas large as a factor of 2 in the concentration of ice crystals in clouds affected by aviation. A most-recent\nmodelling study on the impact of existing uncertainty in contrail cirrus optical depth on the resulting\ncontrail-cirrus ERF reports an eightfold uncertainty.”\nGeneral.\nThe authors may find a few additional references an interesting/useful part of the story. Gierens 2012\nappears to be one of the first authors to investigate aspects numerically (https://doi.org/10.5194/acp-\n12-11943-2012, 2012). Singh et al. (2024) make a few useful points in their review that this is a\nneglected topic (end of section 2.4) (https://doi.org/10.5194/acp-24-9219-2024). Marjani et al. (2022)\nmake some remote sensing measurements (https://doi.org/10.1029/2021GL096173).\nReply: Thank you very much for these valuable hints. The references have been integrated at the\nsuitable points of the story.\nSection ‘PCCRs and ISSRs in major air traffic regions’\nThe authors base their analysis and reinforcement of the importance of PCCRs over ISSRs on heavily\ntrafficked regions. This may not be for this study, but I would encourage them to look for what happens\nin very sparsely trafficked regions where they have observations. Is the ratio/occurrence of persistent\ncontrails <100% the same?\nReply: The importance of PCCRs over ISSRs was developed from analyses of dedicated research flights\nin the field campaigns CONCERT 2008 (Kübbeler et al., 2008) and ML-CIRRUS (Li et al., 2023). Our\nanalysis used the observed evidence for defining PCCRs. Unfortunately, we cannot repeat this type of\nanalysis for low-traffic regions since we don’t have the data.\nL118 “aviation non-CO2 effects”? Do you mean contrail cirrus, rather than generalizing all aviation’s\nnon-CO2 effects?\nReply: We clarified this point and rephrased the sentence to “have immediate consequences on all\naviation non-CO effects in these different regions of the world, and particularly for contrail-cirrus“.\nassociated with the percentage splits. Can this be addressed at all (maybe in the SI).\nReply: Indeed, we cannot add uncertainties to the percentages since these values arise from a simple\nsplit of the entire data set into these three fractions. As suggested by Reviewer 1, we merged the three\nregions of the Northern midlatitudes to one and repeated the analysis. Now, the reader finds the\nfractional split in Figure 3a and check for the variability arising from the different regions in Figures 3c\nto 3e. This analysis gives at least some information on the uncertainty in this split. Same was done for\nice\nin Tables S1 and S2.\nFurther, on Figure 2 – my understanding is that the outcomes (no contrail, short-lived, persistent) are\ncontingent on the constraints of the observations. To say that “no contrails” are formed in <1% of the\nair masses in that region is surely ‘for the observations made’, not an absolute truth? Am I missing\nthe point here, or does the text need some small/simple adjustment to account for this?\nReply: Thank you for that hint, we added the suggested phrase “for the observations made” to the\nsentence on line 198. We also rephrased the next sentence to “Conditions favouring the formation of\nshort-lived contrails (defined as SAC fulfilled, RH < 90%) dominate in all regions with fractions of 70%\nice\nand more of the probed air masses “.\nL140 “mere” ? I’m not sure that this is adding clarity – omit? Or is this supposed to be “more”?\nReply: Agreed, we removed the word “mere”.\nL141” Subvisible clouds are distinguished from optically thick clouds by means\nCIWC < 1.0 ppmv”. This is a critical/foundational assumption for the analysis of the data and its\ninterpretation, so needs a reference; maybe\nhttps://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2006JD008214 ? It would be helpful to\npoint forwards in the text that the authors have explored the sensitivity of this assumption.\nReply: The details of our approach for cloud optical depth are described in the Methods section where\nwe also explored the sensitivity of this assumption. To point to the Methods, we modified the sequence\nstarting on line 224 accordingly to: “We applied the CIWC threshold values CIWC for cloud visibility of\nvis\n1.0 ppmv and 2.0 ppmv to quantify the dependence of our results on the doubling of the CIWC visibility\nthreshold value. A statistical analysis of the conditions and the connected climate impact of these three\nformation categories (clear sky, subvisible, visible) is given in Table 1. Details on the definition of the\nregions, CIWC categorization, and the results of the full statistical analysis are given in ‘Methods’ and\nin Table S1 of the supplementary information.\nIn ’Methods’, we further explain: “The discrimination threshold between subvisible and visible cirrus\nwas taken from two sources. From lidar observations (Sassen et al., 1992) an overall optical depth in\nthe visible spectral range of 0.03 is generally accepted as visibility threshold. From theoretical\ncalculations (Kärcher, 2001), a limiting extinction coefficient of 2 – 3 x 10-5 m-1 is reported, which turns\ninto an optical depth of 0.01 to 0.015 for a cloud of 500 m vertical extension.\nL140-L145 The concept of “potential climate impact” is introduced here and results given in Table 2\nbut not the concept is not explained until the discussion (L191). The whole definition is a little\nproblematic. Figure 4 shows this kind of discrimination in a ‘direction of travel’ basis. The only means\nof getting to a ‘potential climate impact’ in a quantitative sense that allows a sensible comparison in\nthe different sets of circumstances, is a radiative transfer (RT) calculation, which the authors clearly do\nnot do. Thus, we are left with indicators of ‘directions of travel’, except for the most important\nphenomenon that the authors identify – that most persistent contrails are formed within pre-existing\ncirrus. This is a complex topic, hardly researched at all, and with an ambiguous outcome. So, my\nunderstanding is that for this category, we do not have a clear ‘direction of travel’. That is OK, it should\nbe more clearly acknowledged and a recommendation made as how to address this with future\nresearch.\nI think the definition/explanation of “potential climate impact” is better placed here, not in the\ndiscussion, if such categorization is to be placed in the results. In Table 2, the entry “no” is confusing. I\ndon’t know what this means. The authors omit to tell the reader that “potential climate impact” is a\n10\nloose approximation. There will be times that, for example, solar zenith angle will reverse findings via\nradiative transfer calculations. In (related) L195-L196 for the optically thick cirrus cloud, a “minor\neffect” is cited. This is vague. If the potential outcome is ambiguous, please say so. It could be cooling\nor minor warming.\nReply: As indicate in the introduction to this reply-to-reviewers, we placed the concept of climate impact\nat the beginning of the results section. Thanks to the input from Reviewer #3, we could add references\nto the expected increase of radiative forcing by contrails placed in clear sky compared to those added\nto existing cirrus (Spangenberg et al. 2013). As described above, categorises ‘stronger climate impact’\nand ‘weaker climate impact’ are replaced by the categories ‘warming’ and ‘ambiguous’.\nL149-150 States: “That means, most contrail-cirrus potentially form in regions already covered by\nnatural cirrus”. Again, it is unclear what the outcome of this will be. If the pre-existing cirrus is ‘optically\nthick’, additional contrail cirrus MAY further thicken an already optically thick (naturally cooling) cloud\nfurther. But this is not clear unless more is known, and a full RT calculation is undertaken. All this is\nincredibly important as this could turn ‘conventional wisdom’ on its head about the net warming effect\nof contrail cirrus, or at the least, provide observational indirect evidence for a much smaller net\nwarming (since most radiative transfer calculations are made under clear sky conditions). But we\nsimply do not know from these observations. There is some (neglected here) further suggestive, if not\ndefinitive, evidence from the modelling study of Verma and Burkhardt (ref 39) who state: “Since\ncorrections in ice nucleation are large in clouds with large ice water content, which are likely connected\nto large optical depth, *we speculate that disregarding the impact of cirrus on contrail formation may\npossibly underestimate the cooling of the contrail perturbations within optically thicker clouds*. It\nshould be noted that the cirrus optical depth at which a further increase in optical depth, caused by\ncontrail formation, leads to a cooling is dependent on the cirrus ice crystal habit.” (in ref 39’s\nconclusions). [* to * is this reviewer’s emphasis]\nL193 “change” should this be “increase”?\nReply: Yes, indeed; we changed accordingly.\nL200 “relevance is rated as limited”…my understanding is that Verma and Burkhardt (ref 39) found\nthat the additional water mass of ice crystals had a negligible effect (in agreement with earlier work of\nGierens (2012, see reference above). If I am correct, would it be useful to be clearer as the sentence\naddresses ‘climate impact’ through to ‘vortex phase’ with little explanation.\nL204 “significant effect” please be more explicit.\nReply to both remarks: We clarify the explanation and modified the entire starting paragraph of the\nDiscussions to (from line 280 to 288):\n“The effects of contrails interacting with pre-existing cirrus clouds are generally known but have not\nyet been considered in the quantification of the contrail-cirrus climate impact. To start with, model\nstudies reported that pre-existing cirrus have no impact on the formation of contrails, that contrail\nformation within cirrus mostly leads to increasing cirrus ice crystal numbers, that cirrus ice crystals\nmixed into the evolving contrail do not efficiently slow down the sublimation of the ice crystals in the\ndownward travelling wing vortex, and that cirrus can dissolve an embedded contrail after few hours by\naggregation of ice crystals. The changes in the radiative properties of subvisible and visible cirrus\nresulting from the above-described changes of cloud microphysics after the release of a contrail of\nmean optical depth of 0.34 (median 0.24, modal 0.1) into the cloud will increase the resulting optical\ndepth of the modified cirrus (see Figure 1), but with yet unknown radiative impact. “\n“stronger”, I am interpreting a greater potential climate impact (as you define it), which I interpret as\na positive RF. I am less clear over “weaker” – weaker than what? Is it a cooling impact? Or a less\nwarming impact than clear sky conditions/subvisible conditions? As per above, it seems as if adding\noptical thickness to an already optically thick cloud (which is ‘cooling’) as the negative forcing of the\nnatural cloud, is made ‘more negative’ which then becomes a negative RF effect (as per the definition\nof RF, i.e. something interfering with the pre-industrial radiation balance).\nReply: Former Figure 4 was completely revised according to the criticism by all three reviewers. The\nnow Figure 1 and accompanying text is now put to the front of the results section. Concerning the\ncategories ‘stronger impact’ and ‘weaker impact’ we refer to the general text at the beginning of this\ndocument.\nL227-232. Same comment over “stronger” and “weaker”. I’m not sure how much value this figure is\nadding, and if short of space, might be relegated to the SI.\nReply: See response above and introductory text. The figure itself was simplified and modified, following\nalso a recommendation of Reviewer 1.\nL234. Interesting statement. I don’t disagree from the analysis presented, but this offers quite a\ndifferent perspective of the ‘big hits’ terminology (of which I remain unconvinced).\nReply: The paragraph containing this statement has been removed, see also our replies to the next\npoints.\nL235 I disagree. I think that suggesting this is premature. What is more to the point is that all this needs\nto be better understood before formulating strategies (which may turn out to be pointless). L236 says\nthis better.\nReply: As said above, this statement has been removed. However, we kept the recommendation to\ninclude cirrus clouds in rerouting strategies, see also our final remark below.\nL238 “should help minimizing trade-off effects…” I think this is subtly wrong. I think accounting for all\nthis reduces risks of doing the wrong thing. At the moment, given the authors’ results, the outcome of\nre-routing has just become far more uncertain.\nReply: As already stated, this sentence has been removed.\nL234-248. This all makes sense, but it would be nice to have a stronger recommendation as to what\nresearch would firm this up (ERF vs occurrence conditions). Can this be accounted for/studied in global\nmodels or can some hybrid observational/radiative transfer study be undertaken?\nReply: Agreed, see our response below.\nL242-248. This seems like people-pleasing. We do not know - and this paper adds to the evidence –\nthat re-routing is either a sensible or viable option for mitigating aviation’s impacts on climate. As they\nsay, “get off the fence”! More seriously, simply reiterate the importance of these findings for re-routing\nproposals.\nReply: Very good suggestion! We removed the entire paragraph on the rerouting and kept only the final\nstatement (lines 325 – 328): “This topic needs to be further analysed and verified in terms of their\nradiative impact for consideration of the potential impact of contrail avoidance strategies including\nflight rerouting. Finally, ice-supersaturation only is by far not a reliable, stand-alone criterion for\n12\nassessing contrail-cirrus climate effects. Instead, we need to include pre-existing cirrus clouds and their\ninteractions with contrail-cirrus into all our considerations.”\nIN CONCLUSION\nI think that the findings are of great importance and significance, but I am uncomfortable with their\nsimplistic treatment of “potential climate impact”. This seems relatively clear, based on prior work\nwith RT models/GCM calculations with RT, that clear sky conditions will net warm. Similarly, this may\nbe the case for sub-visible cirrus with low OD. For persistent contrails forming contrail cirrus clouds\nwithin pre-existing cirrus, which seems to be the majority of incidence of persistent contrails from this\nstudy, then without much more information, we don’t know what the outcome of this will be. This\nshould be stated much more clearly, and provide a recommendation for further work, given that the\nauthors’ findings suggest that we should have an increased concern over what was already known to\nbe a huge uncertainty – formation of persistent contrails within pre-existing cirrus. The title of the\narticle says it all!\nReply to all comments on the concluding section (lines 234 to 248 and Conclusions):\nThe entire concluding section was rewritten, taking up the points raised by all reviewers. Please refer\nto the revised manuscript, starting on line 317.\nSummary of the manuscript:\n“Contrails inside cirrus clouds predominate with uncertain climate impact” by Petzold et al. examines\nthe potential occurrence of contrails, short-lived or persistent, as a function of humidity and ambient\ncirrus occurrence. Contrails form when the Schmidt-Appleton criterion is met and nominally can persist\nin ice-supersaturated regions (ISSR) where RH > 100%. Recent research shows that contrails can also\nice\npersist when RH > 90%, giving rise to a larger range of humidities and, hence, a greater number of\nice\nregions (43% more) of potential contrail coverage. Those regions are designated as potential contrail-\ncirrus regions (PCCRs). Results are presented for both ISSRs and PCCRs.\nThe motivation for the study is that a certain class of tropospheric conditions could be eliminated from\nany aircraft rerouting system that might be established to minimize contrail effects. That particular\nclass of conditions is defined as the presence of thick cirrus clouds at planned flight levels. For this\nclass, the radiative forcing induced by the development of contrail cirrus clouds is assumed to be small,\nor negligible enough to be ignored. Ergo, there is no need to reroute the flight because of contrail\neffects.\nThe analysis uses 7 years of IAGOS aircraft RH measurements matched with interpolated ERA 5 to\nice\ndetermine the ambient cloud conditions at flight level. A threshold of ERA5 CIWC > 0.001 ppmv is used\nto differentiate between clear and cloudy conditions. To further classify the cloud conditions, a cloud\noptical depth (OD) of 0.03, equivalent to CIWC = 1.0 ppmv, was used as the threshold differentiating\nsub-visible from thick cirrus for a given cloudy datapoint. Thus, any preexisting cirrus with cloud OD >\n0.03 is assumed to be thick cirrus. Radiative forcing (RF) as a function of cloud OD is characterized using\na plot of RF as a function of cirrus OD provided by Ref 11. The plot reproduced from Ref 11 indicates\nthat RF increases with cloud OD up to a value of ~0.85 then drops precipitously for greater cirrus ODs\nto negative values for OD > 1.0.\nThe results of the analysis show that for the 4 regions examined, only 20% (ISSRs) - 30% (PCCRS) of the\nair masses can support contrail cirrus formation. Of these, roughly 64% of the contrails have a weaker\nimpact on RF (climate) and the remaining 36% have a stronger impact. The overall effects vary\nregionally and seasonally, with minima over SE Asia and maximum effects during spring and winter.\nThe results lead to the recommendation that any plan to adjust flight levels should include model\npredictions of cirrus locations, so that planes could fly in areas with thick cirrus and height adjustments\nwould only be needed for clear areas and those with sub visible cirrus. The results also suggest that\n~90% of contrails form within thick cirrus over SE Asia, it would probably be of little benefit to\nundertake any flight rerouting.\nReview:\nThe uncertainty in radiative forcing by contrails is high, leading to low confidence in our understanding\nof this somewhat small component of the climate change equation. Rerouting aircraft to avoid forming\ncontrail cirrus is probably the most straightforward solution to minimizing contrail effects. However, it\ninvolves expenditure of more fuel and would further complicate air traffic control procedures. Thus,\nminimizing the number of possible aircraft reroutes by eliminating suspect air masses is a worthy\neffort. Thus, the goal of this study is of interest to the aviation and climate communities.\nThe premise is logical: contrails forming in a clear sky or in sub visible cirrus should have greater\nradiative impacts than those forming in thick cirrus. Persistent contrail development in already thick\n14\ncirrus adds little to either the LW or SW impact of the existing cirrus because of the small change in OD\nfor optically thick cirrus clouds. Yet, there are some shortcomings in how this premise is addressed.\n1) The first issue is that the authors looked to no later than 2010 (ref 29) for information about contrail\ncloud overlap. There are observations of persistent contrail coverage available for 2006 and 2012\n(Duda et al., 2013; 2019).\nDuda et al. (2013) combined contrail analyses of 1 year of Northern Hemisphere Aqua MODIS data\nwith MODIS cloud retrievals (Minnis et al. (2011). Using these, Bedka et al. (2013) differentiated\nbetween contrails over/within ice clouds (cirrus) and contrails detected in clear skies or over low-level\nwater clouds. Passive satellite retrievals have difficulty detecting cirrus with OD < 0.05. The hit rates\nfor clouds having OD < 0.1 are around 50% (Trepte et al., 2019). Thus, the clear category would include\nboth clear and subvisible clouds and the ice clouds would be thick according to the definition used\nhere. With that in mind, Bedka et al. (2013) found that contrails were detected with ice clouds\npredominating in 33% of the cases, compared to 46% with low liquid water clouds, and 17% in clear\nskies. Seasonal variations are superimposed on those averages. There are likely a few more percent\ncontrails having ice cloud concurrence as ~20% of clouds classified as water were likely to consist of\nnon-opaque cirrus over lower liquid water clouds and a few more water clouds were misclassified as\nice than ice clouds misclassified as water (Sun-Mack et al., 2024). Nevertheless, the observed fraction\nof weaker impact conditions (33% coincidence with ice clouds) is significantly smaller than the 64%\ncomputed here. Perhaps, the selection of CIWC = 0.001 ppmv as the cloud threshold produces too\nmany clouds. It is not all that different from 0.000 ppmv in frequency. This would be consistent with\nReference 57, which indicates that ERA5 generates too much ice cloud in the upper troposphere\nrelative to CALIPSO.\nReply: The selected CIWC threshold of 0.001 ppmv is based on a large set of in-situ observations of total\nwater and gas-phase water from in total 24 field campaigns and validated by analysing the RH\nice\ndistributions from IAGOS for various CIWC thresholds; see ‘Methods’ section. Since the selected\nthreshold is based on in-situ observations, we believe it is justified. Furthermore, we combine clear sky\n(CIWC < 0.001 ppmv) and subvisible cirrus (0.001 ppmv  CIWC < 1.0 ppmv) to one category when\ndiscussing potential climate impacts. In that respect, the details of the selected threshold have no\nimpact on our conclusions.\nMore influential on the results seems to be the visibility threshold and the selected area. On request by\nReviewer 1 we combined the former regions 1 – 3 into one single region for Northern Midlatitudes and\nrecalculated our analysis. Now we find a contrail-cirrus overlap of 55% to 60% for a CIWC visibility\nthreshold of 1.0 ppmv and 46% to 52% for a threshold of 2 ppmv. It looks like the cloud visibility\nthreshold of 2 ppmv developed from Sassen et al. (1992) is closer to the T criteria used for the analysis\n11\nby Bedka et al..\nWe discuss the results for contrail - cirrus overlap; see line 247 – 254: “The above-mentioned study on\nproperties of linear contrails using MODIS data reports 33% of contrails formed in areas already\ncovered by clouds. The applied method distinguishes contrails from other cirrus by their linear shape\nand relatively large 11–12 µm brightness temperature difference. We apply a combination of in-situ\nbased criteria such as the fulfilment of SAC, exceedance of RH threshold for PCCR, and exceedance of\nice\nERA5 CIWC to an on-flight-level dataset and obtain a fraction of 46% (PCCR, CIWC = 2.0 ppmv).\nvis vis\nTaking into account that about ~20% of clouds classified in the MODIS analysis as water were likely to\nconsist of non-opaque cirrus over lower liquid water clouds and a few more water clouds were\nmisclassified as ice than ice clouds misclassified as water, the agreement between the two studies is\nreasonable.”\nobtained values.\nSpangenberg et al. (2013; S13) computed RF for all of the contrails. The resulting mean values support\nthe premise of this paper. Indeed, one could look at those averages and come to the same conclusion\nas the results of this paper: Flying in an atmosphere with preexisting visible cirrus will cause less RF\nthan flying in other conditions. In fact, the observations actually quantify the differences. S13 found\nthat the net unit contrail RF during the daytime (~13:30 LT) was 3.9 Wm-2 for clear skies and 1.3 Wm-\n2 for contrails in the same column as ambient cirrus clouds. That is a factor of 3 decrease, a change\nthat would support the use of the sub visible threshold. Yet, the LW RFs for clear and cloudy scenes\nare 18.5 and 11.7 Wm-2, respectively, a difference of only 36%. That LW difference is the same at night\nwhen no SW RF occurs to balance the LW RF.\nReply: Thank you very much for pointing us to that highly valuable reference. We added the following\nparagraph on lines 46 to 54: “The analysis of linear contrail occurrence over the Northern hemisphere\nin MODIS data for the year 2006 revealed, that contrails were detected within an environment with ice\nclouds in 33% of the cases, compared to 46% with low liquid water clouds, and 17% in clear skies. The\nsame data set yields that the net contrail radiative forcing (RF), i.e., the sum of short-wave and long-\nwave RF, during daytime (~13:30 LT) is 3.9 Wm-2 for clear sky and 1.3 Wm-2 for contrails in a column\nalready filled with visible cirrus clouds. During night, when no shortwave RF occurs, the longwave RF\nfor clear and cloudy scenes is 16.9 and 11.0 Wm-2, respectively. Thus, daytime net contrail RF is\nincreased by a factor of 3 while nighttime longwave RF still is increased by a factor of 1.5 for contrails\nformed in clear sky or subvisible cirrus, compared to those having formed inside, above or below pre-\nexisting cirrus.“\nThese findings were used as justification for our categorisation as “warming” and “ambiguous” in the\ndescription of our methodology, described from line 134 to line 159. We refer the reviewer to the\nmanuscript because this section is too long to be included here. The justification itself can be found on\nlines 156 – 159: “The net warming of Cases 1 and 2 and the minor net warming of Case 3 are confirmed\nby MODIS observations, whereas a model study speculates that ignoring the impact of cirrus on contrail\nformation may possibly underestimate the cooling of the contrail perturbations within optically thicker\nclouds (Case 4).”\n2) The premise of this paper seems too limited in scope. One would expect that a contrail developing\nabove or below a thick cirrus would also have a similar impact as a contrail imbedded in the cirrus since\nthe ice cloud OD added to the total column is nearly the same in both cases. Perhaps, that is implied\nhere somehow.\nReply: The focus on our study is on the fraction of contrail-cirrus forming inside pre-existing clouds,\ndetermined from in-situ observations of relative humidity with respect to ice. Given the nature of in-\nsitu sampling by aircraft, we can only collect information along the flight path but have no access to\ninformation about cloudiness etc. above or below flight altitude. The reviewer states correctly that a\ncontrail developing above or below a pre-existing cloud also has a different radiative impact than a\ncontrail forming in a clear sky column, we cannot investigate these effects in our study.\nWe added the following paragraph at the beginning of the main text to clarify the scope our study\nwhich starts on line 37: “Uncertainties of the climate effects of contrail-cirrus are largely related to the\nunanswered question of the extent to which contrails form inside cirrus clouds, how they influence cirrus\ncloud coverage and optical depth, and what are the radiative implications. However, it is obvious that\ncontrail-cirrus formed in clear sky or in or above pre-existing subvisible cirrus clouds have a stronger\n16\nradiative effect than contrail-cirrus embedded in pre-existing visible cirrus, because the difference in\nthe optical contrast with and without contrail is much larger.”\nWe finish the Method section with a\n“Final note on data interpretation\nGiven the nature of in-situ sampling by aircraft, we can only collect information along the flight path\nbut have no access to information about cloudiness etc. above or below flight altitude. Knowing that a\ncontrail developing above or below a pre-existing cloud also has a different radiative impact than a\ncontrail forming in a clear sky column, we cannot investigate these effects in our study. Thus, the\nreported fractions of contrail-cirrus inside clouds should be taken as a lower limit of the contrail-cirrus\ninteracting with pre-existing cloudiness.”\n3) The somewhat vague notion of weaker and stronger impacts is not particularly satisfying. Given the\nobserved RF results, what average difference in RF is considered to be enough to separate weak and\nstrong impacts? Is the use of cloud OD > 0.03 as a thick cirrus optimal? Is the characterization\n“thick”warranted or should visible be used always. Normally one would consider a cirrus cloud to be\nthick when the emissivity approaches unity or the change in emissivity with unit optical depth is\nrelatively small, typically when OD is between 3 and 6. While it is true that adding a contrail to sub\nvisible cirrus will have nearly the same impact as adding a contrail to a clear-sky, there could still be\nsignificant contrail RF impacts when the extant cirrus has an OD < 1.5 (e.g., Meerkötter et al.1999).\nHong and Liu (2015) show that a large portion of ice clouds observed by CALIPSO have ODs between\n0.05 and 1.5, while the mode of the total distribution is OD = 1.2. Thus, there will be a range of\nsignificant RFs that could be produced by contrails. Determining the optimal cirrus OD threshold would\nrequire a sensitivity study and possibly consideration of low-level clouds.\nThis need for quantification is more apparent when considering that the weaker impacts constitute\nalmost 100% of persistent contrail diagnoses in SE Asia. That suggests that overall RF should be smaller\nin that region compared to North America or Europe. The RF results from S13 suggest otherwise.\nThey suggest that over the SE Asia flight corridors are much like their USA and European counterparts,\nand even greater at night.\nReply: The main outcome of our study is the quantification of the clear-sky to subvisible cirrus areal\nfraction close to ice-saturation which allow for the existence of long-living contrail-cirrus. However,\ngiven our data set, we cannot quantify the RF threshold between weak and strong climate impact.\nInstead, we moved to warming and ambiguous climate impacts as qualitative descriptions.\nNevertheless, the radiative impacts need to be studied. Thanks to the clear comments by all reviewers,\nwe put this statement prominently into our conclusions (lines 317 to 328) since this is one of the major\noutcomes of our study:\n“The results of our study suggest that conditions necessary for the formation of contrail-cirrus are most\noften fulfilled in regions that are already covered by visible cirrus, which reduces their warming impact\nor even turns it into a cooling effect. Those of a stronger warming significance, however, form under\nonly limited circumstances in clear sky and subvisible cirrus. Unfortunately, our knowledge on the\nradiative effects of contrail-cirrus embedded in subvisible, visible and optically thick clouds, and\nfeedback mechanisms between contrail and cirrus ice particles is highly limited. There will be a range\nof radiative forcings that could be produced by embedded contrail-cirrus, and the quantification of the\nclimate impacts would require a sensitivity study and possibly consideration of low-level clouds.\nof the potential impact of contrail avoidance strategies including flight rerouting. Finally, ice-\nsupersaturation only is by far not a reliable, stand-alone criterion for assessing contrail-cirrus climate\neffects. Instead, we need to include pre-existing cirrus clouds and their interactions with contrail-cirrus\ninto all our considerations.”\nOther comments\nIt should be noted that the RF results in Fig. 4 are based on a single set of conditions, noon at SZA = 50\ndeg?. There is no consideration for the ERF at night, which is all warming. The results for other angular\nconditions, latitudes, and backgrounds will be highly variable.\nReply: Tis information has been added to the text connected to the description of Figure 4. We added\nthe following sentence (lines 145 to 148): “Since only a single set of conditions, (noon at solar zenith\nangle at 50° North) was used and the results for other angular conditions, latitudes, and backgrounds\nwill be highly variable, the figure only serves as a descriptive sketch. The radiative effects of contrail-\ncirrus developing in the various environments are categorised in the context of radiative effects of the\nembedded contrail-cirrus in addition to the radiative effects of the unperturbed clouds.”\nLine 331 red curve is for 0.01, not 0.05. Purple curve is for 0.05 in Fig. &a.\nReply: Thank you, corrected.\nDespite the issues and reservations described above, not to mention the uncertainties in current model\nrepresentations of RHice and clouds, the authors have laid the groundwork for a reasonable method\nto define cirrus cloud conditions that could theoretically be used to reduce the magnitude of flight\nrerouting in a future contrail avoidance system.\nReferences cited in the response to the Reviewers\nBedka, S. T., Minnis, P., Duda, D. P., Chee, T. L., and Palikonda, R.: Properties of linear contrails\nin the Northern Hemisphere derived from 2006 Aqua MODIS observations, Geophysical\nResearch Letters, 40, 772-777, 10.1029/2012gl054363, 2013.\nBickel, M., Ponater, M., Burkhardt, U., Righi, M., Hendricks, J., and Jöckel, P.: Contrail Cirrus\nClimate Impact: From Radiative Forcing to Surface Temperature Change, Journal of Climate, 38,\n1895-1912, 10.1175/jcli-d-24-0245.1, 2025.\nPrather, M. J., Gettelman, A., and Penner, J. E.: Trade-offs in aviation impacts on climate favour\nnon-CO2 mitigation, Nature, 8, 10.1038/s41586-025-09198-2, 2025.\nSingh, D. K., Sanyal, S., and Wuebbles, D. J.: Understanding the role of contrails and contrail\ncirrus in climate change: a global perspective, Atmospheric Chemistry and Physics, 24, 9219-\n9262, 10.5194/acp-24-9219-2024, 2024.\nSpangenberg, D. A., Minnis, P., Bedka, S. T., Palikonda, R., Duda, D. P., and Rose, F. G.: Contrail\nradiative forcing over the Northern Hemisphere from 2006 Aqua MODIS data, Geophysical\nResearch Letters, 40, 595-600, 10.1002/grl.50168, 2013.\nimpact of cirrus cloud properties on contrail formation, Atmospheric Chemistry and Physics,\n22, 8819-8842, 10.5194/acp-22-8819-2022, 2022.\nZhang, W. Y., Van Weverberg, K., Morcrette, C. J., Feng, W. H., Furtado, K., Field, P. R., Chen, C.\nC., Gettelman, A., Forster, P. M., Marsh, D. R., and Rap, A.: Impact of host climate model on\ncontrail cirrus effective radiative forcing estimates, Atmospheric Chemistry and Physics,\n25, 473-489, 10.5194/acp-25-473-2025, 2025.\nResponses to ®nal reviewer’s remarks are marked in green. The annotated manuscript is\nadded to this document.\nReviewer #1 (Remarks to the Author):\nThe authors have carefully revised their manuscript according to the comments provided\nby three reviewers. The paper is now very straigh(cid:1)orward to read and conveys a clear\nmessage. The use of Figure 1 for illustra(cid:2)ng the conceptual expecta(cid:2)on is good.\nGoing through the manuscript, I found it diYcult to reconcile the informa(cid:2)on provided in\nFigures 3 and 5, which are clearly showing di(cid:3)erent combina(cid:2)ons of the same numbers.\nWhile all became clear a(cid:4)er inspec(cid:2)ng Table 1, I would try to avoid similar confusion with\nreaders by omi(cid:5)ng Figure 5 from the paper.\nOverall, this is great and important work that sheds some light on an understudied\nphenomenon. I am happy to see this published.\nReply: Thank you very much for the very posi(cid:1)ve feedback, we very much appreciate that.\nThe idea behind showing these two diVerent ®gures is that\n1. in Figure 3, we focus on the separa(cid:1)on of no contrail forma(cid:1)on, short-lived contrails,\nand long-lived contrails, dis(cid:1)nguished in each case according to clear-sky and in-cloud\ncondi(cid:1)ons,\n2. in Figure 5, we focus on the climate eVect according to our conceptual analysis and\nsplit up in areas of no impact, ambiguous impact and warming impact.\nSince we s(cid:1)ll believe in the visual strength of Figure 5, we want to keep it. To avoid confusion,\nwe clari®ed the diVerent purposes of Figs. 3 and 5 by rephrasing the sentence describing Fig.5,\nstar(cid:1)ng on line 282. It reads now:\n“ The results summarised in Figure 5 and presented numerically in Table 1, middle column,\nhighlight the expected climate impact. This informa(cid:1)on supplements that given in Figure 3\nwhich focuses on the environmental condi(cid:1)ons of contrail-cirrus occurrence. …”\nReviewer #2 (Remarks to the Author):\nThe authors have responded comprehensively and thoroughly to all three reviews and I\nrecommend publica(cid:2)on as soon as possible of the ground-breaking paper.\nI would only suggest one (cid:2)ny modi®ca(cid:2)on, where the authors have (I think) possibly\nmisunderstood my point. My comment was \"L30 please insert “present day” a(cid:4)er 60%,\nsince the propor(cid:2)on depends en(cid:2)rely on recent growth rates of avia(cid:2)on (there is a\nmisconcep(cid:2)on that this is somehow a ®xed propor(cid:2)on).\"\nThe authors replied: We changed the sentence to “With an ERF of 60 mW m-2 contrail-\ncirrus is es(cid:2)mated to be the largest non-CO2 ERF contribu(cid:2)ng 60% (present-day knowledge)\nto the avia(cid:2)on net total ERF of 100 mW m-2”.\nI was not referring to \"present-day knowledge\" (and propor(cid:2)ons, thereof) of avia(cid:2)on ERF\nassessments but rather that the propor(cid:2)on of non-CO2 forcing to the total is a func(cid:2)on of\nthe history of CO2 emissions and the complexi(cid:2)es of C cycle CO2 accumula(cid:2)on (and\nsubsequent ERF) and the simpler linear response of SLCFs of ERF to emissions (in general).\nThis can be seen in Figure 2c of Klower et al. (2021) h(cid:6)ps://doi.org/10.1088/1748-\n9326/ac286e (RH bars), where di(cid:3)erent growth rate scenarios result in di(cid:3)erent\npropor(cid:2)ons of response (it's actually dT but that ma(cid:6)ers li(cid:6)le to the point being made).\nThe authors of not need to add a reference or anything like that, I only point out to clarify\nand they can very simply ®x this by removing the work \"knowledge\".\nOtherwise, great job!\nReply: Thank you very much for the highly encouraging feedback. The modi®ca(cid:1)on was\nimplemented as suggested by removing the word “knowledge” on line 30.\nReviewer #3 (Remarks to the Author):\nThe authors have sa(cid:2)sfactorily answered my concerns and altered the paper accordingly.\nThus, would recommend publica(cid:2)on in its current form.\nReply: Thank you very much for the very posi(cid:1)ve feedback."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have carefully revised their manuscript according to the comments provided by three reviewers. The paper is now very straightforward to read and conveys a clear message. The use of Figure 1 for illustrating the conceptual expectation is good.\nGoing through the manuscript, I found it difficult to reconcile the information provided in Figures 3 and 5, which are clearly showing different combinations of the same numbers. While all became clear after inspecting Table 1, I would try to avoid similar confusion with readers by omitting Figure 5 from the paper.\nOverall, this is great and important work that sheds some light on an understudied phenomenon. I am happy to see this published.", "reviewer_2": "The authors have responded comprehensively and thoroughly to all three reviews and I recommend publication as soon as possible of the ground-breaking paper.\nI would only suggest one tiny modification, where the authors have (I think) possibly misunderstood my point. My comment was \"L30 please insert “present day” after 60%, since the proportion depends entirely on recent growth rates of aviation (there is a misconception that this is somehow a fixed proportion).\"\nThe authors replied: We changed the sentence to “With an ERF of 60 mW m-2 contrail-cirrus is estimated to be the largest non-CO2 ERF contributing 60% (present-day knowledge) to the aviation net total ERF of 100 mW m-2”.\nI was not referring to \"present-day knowledge\" (and proportions, thereof) of aviation ERF assessments but rather that the proportion of non-CO2 forcing to the total is a function of the history of CO2 emissions and the complexities of C cycle CO2 accumulation (and subsequent ERF) and the simpler linear response of SLCFs of ERF to emissions (in general). This can be seen in Figure 2c of Klower et al. (2021) https://doi.org/10.1088/1748-9326/ac286e (RH bars), where different growth rate scenarios result in different proportions of response (it's actually dT but that matters little to the point being made).\nThe authors of not need to add a reference or anything like that, I only point out to clarify and they can very simply fix this by removing the work \"knowledge\".\nOtherwise, great job!", "reviewer_3": "The authors have satisfactorily answered my concerns and altered the paper accordingly. Thus, would recommend publication in its current form."}, "author_response": "RESPONSE TO REVIEWERS' COMMENTS\nResponses to ®nal reviewer’s remarks are marked in green. The annotated manuscript is\nadded to this document.\nReviewer #1 (Remarks to the Author):\nThe authors have carefully revised their manuscript according to the comments provided\nby three reviewers. The paper is now very straigh(cid:1)orward to read and conveys a clear\nmessage. The use of Figure 1 for illustra(cid:2)ng the conceptual expecta(cid:2)on is good.\nGoing through the manuscript, I found it diYcult to reconcile the informa(cid:2)on provided in\nFigures 3 and 5, which are clearly showing di(cid:3)erent combina(cid:2)ons of the same numbers.\nWhile all became clear a(cid:4)er inspec(cid:2)ng Table 1, I would try to avoid similar confusion with\nreaders by omi(cid:5)ng Figure 5 from the paper.\nOverall, this is great and important work that sheds some light on an understudied\nphenomenon. I am happy to see this published.\nReply: Thank you very much for the very posi(cid:1)ve feedback, we very much appreciate that.\nThe idea behind showing these two diVerent ®gures is that\n1. in Figure 3, we focus on the separa(cid:1)on of no contrail forma(cid:1)on, short-lived contrails,\nand long-lived contrails, dis(cid:1)nguished in each case according to clear-sky and in-cloud\ncondi(cid:1)ons,\n2. in Figure 5, we focus on the climate eVect according to our conceptual analysis and\nsplit up in areas of no impact, ambiguous impact and warming impact.\nSince we s(cid:1)ll believe in the visual strength of Figure 5, we want to keep it. To avoid confusion,\nwe clari®ed the diVerent purposes of Figs. 3 and 5 by rephrasing the sentence describing Fig.5,\nstar(cid:1)ng on line 282. It reads now:\n“ The results summarised in Figure 5 and presented numerically in Table 1, middle column,\nhighlight the expected climate impact. This informa(cid:1)on supplements that given in Figure 3\nwhich focuses on the environmental condi(cid:1)ons of contrail-cirrus occurrence. …\"\nReviewer #2 (Remarks to the Author):\nThe authors have responded comprehensively and thoroughly to all three reviews and I\nrecommend publica(cid:2)on as soon as possible of the ground-breaking paper.\nI would only suggest one (cid:2)ny modi®ca(cid:2)on, where the authors have (I think) possibly\nmisunderstood my point. My comment was \"L30 please insert “present day” a(cid:4)er 60%,\nsince the propor(cid:2)on depends en(cid:2)rely on recent growth rates of avia(cid:2)on (there is a\nmisconcep(cid:2)on that this is somehow a ®xed propor(cid:2)on).\"\nThe authors replied: We changed the sentence to “With an ERF of 60 mW m-2 contrail-\ncirrus is es(cid:2)mated to be the largest non-CO2 ERF contribu(cid:2)ng 60% (present-day knowledge)\nto the avia(cid:2)on net total ERF of 100 mW m-2”.\nI was not referring to \"present-day knowledge\" (and propor(cid:2)ons, thereof) of avia(cid:2)on ERF\nassessments but rather that the propor(cid:2)on of non-CO2 forcing to the total is a func(cid:2)on of\nthe history of CO2 emissions and the complexi(cid:2)es of C cycle CO2 accumula(cid:2)on (and\nsubsequent ERF) and the simpler linear response of SLCFs of ERF to emissions (in general).\nThis can be seen in Figure 2c of Klower et al. (2021) h(cid:6)ps://doi.org/10.1088/1748-\n9326/ac286e (RH bars), where di(cid:3)erent growth rate scenarios result in di(cid:3)erent\npropor(cid:2)ons of response (it's actually dT but that ma(cid:6)ers li(cid:6)le to the point being made).\nThe authors of not need to add a reference or anything like that, I only point out to clarify\nand they can very simply ®x this by removing the work \"knowledge\".\nOtherwise, great job!\nReply: Thank you very much for the highly encouraging feedback. The modi®ca(cid:1)on was\nimplemented as suggested by removing the word “knowledge” on line 30.\nReviewer #3 (Remarks to the Author):\nThe authors have sa(cid:2)sfactorily answered my concerns and altered the paper accordingly.\nThus, would recommend publica(cid:2)on in its current form.\nReply: Thank you very much for the very posi(cid:1)ve feedback."}]

Decision letter