The detection and characterization of ice clouds was carried out using data from the SEVIRI on board MSG-3 (Meteosat-10) satellite, which is operated by EUMETSAT. MSG-3 is located at 0° longitude in geostationary orbit, approximately 36 000 km above the Earth's surface . SEVIRI provides spectral information across 11 spectral channels, with a temporal resolution of 15 min and a spatial resolution of approximately 3 × 3 km² at the sub-satellite point (SSP) .

Our primary objective is to investigate the behavior of potential contrails above different surface types, and times of the day. These clouds can be visually detected using the Dust/RGB (Red, Green, Blue) composite, which combines data from the MSG/SEVIRI IR8.7, IR10.8 and IR12.0 channels. In this product, the contrails appear as long bluish and reddish lines and are visually distinguished to other cloud types (see Fig. ). Previous studies such as , , and , also successfully utilized the Dust/RGB composite to detect contrails. In this study, using this composite, with the aid of the Satpy Python library and the EUMETSAT RGB recipes (https://eumetrain.org/manualguides/rgb-recipes, last access: 15 April 2025)), we identified specific days during which we could visually detect geographic regions above Europe and parts of the North Atlantic Ocean where persistent contrails were present.

In summary, the study area extends from 30° W to 15° E of longitude and 25 to 55° N of latitude covering data from 6 different days: 30 January 2023; 13 June 2023; 25 September 2023; 30 January 2024; 17 February 2024; and 28 May 2024. The geostationary grid has been re-projected onto a regular grid with a spatial resolution of 0.04°.

In the present study, the OCA product is used for the physical characterization of the detected ice clouds.

The OCA algorithm uses the Optimal Estimation (OE) method along with spectral measurements simultaneously to retrieve the cloud state parameters .

The OCA product is available at a 15 min frequency and at the full earth scanning area in GRIB format . It contains single-layer as well as multi-layer cloud situations and the product is structured in layers numbered in a top-down notation: the first layer (named Layer-One) is the highest layer (closest to the top of the atmosphere) and the second layer (named Layer-Two) is the lower layer, which only exists when the pixel has multi-layer cloud conditions . It should be noted that for the multi-layer cloud scenes, the upper layer is assumed to be an ice cloud and the lower layer a liquid water cloud.

For the present study, we will focus only on pixels characterized as ice or multi-layered clouds (cloud phase) and will use both COT and CTP for the two layers and CER only for the ice cloud. An additional parameter is CTH, which is not included in the OCA product. As we are using a US Standard atmosphere for the construction of the LUTs (see Sect. ), the same profile has been used to linearly interpolate CTP in the pressure vertical grid, and consequently the altitude vertical grid, of the US Standard atmosphere . The uncertainty related to the use of a calculated CTH is presented in Sect. .

LUTs of thin to semi-transparent high-altitude ice clouds are constructed using the libRadtran software . Apart for the range of the parameters, which should be verified by users of these tables, the method here is applicable to naturally occurring cirrus clouds as well as to contrails. In this work, we perform the validation on all ice clouds that are selected by a cloud top pressure filter.

The libRadtran RT library (version 2.0.5) is used to construct LUTs of TOA irradiances for the SW (reflected solar radiation) and LW (emitted thermal radiation) spectral regions, separately. The RT simulations were performed with the one-dimensional (1-D) DIScrete ORdinate Radiative Transfer (DISORT) solver , which is included in the libRadtran software package. Using a 1-D solver means that the ice clouds are assumed to be horizontally uniform.

The spectra for both the SW and LW wavelength regions are simulated under three different scene scenarios:

Ice cloud above ocean surface,

In the SW spectral region, the spectra are simulated from 250 up to 5000 nm, while in the LW wavelength region, from 2500 up to 98 000 nm.

For the LW spectral region and an ice cloud above land and ocean surfaces, the molecular absorption is considered by using the fine resolution REPTRAN parameterization from . For an ice cloud above a liquid water cloud, the same molecular absorption is used but at medium resolution.

Six examples of libRadtran input files (i.e., one in the SW and one in the LW for the three scene scenarios) are provided on the Zenodo platform at 10.5281/zenodo.14859250 .

The initial output files of the RT simulations in the SW and LW spectral regions contain the wavelength, the output altitude, the direct beam irradiance with respect to the horizontal plane, the diffuse down irradiance and the diffuse up irradiance. These variables are integrated over the total simulation wavelength range separately in the SW and LW wavelength regions to estimate the TOA downward and upward solar/thermal-infrared irradiances (Fdown and Fup, respectively).

RF_sol and RF_tir of ice clouds are defined as the difference in fluxes between the ice cloud (Fic) and ice cloud-free (Ficf) atmosphere at the TOA: 1RF=Fic-Ficf=Fdown-Fupic-Fdown-Fupicf

Then, the net RF is a summation between RF_sol and RF_tir . It should be noted that negative RF values indicate cooling, while positive ones correspond to warming.

In the SW wavelength range, the LUTs store the TOA Fdown, Fup, and RF_sol as a function of the following parameters:

the Solar Zenith Angle (SZA), COT and CER for an ice cloud above ocean surface,

The LUTs in the LW store the TOA Fdown, Fup, and RF_tir by varying the following parameters:

the SST, CTH, COT, and CER for an ice cloud above ocean surface,

To save computational time, RT simulations have been performed for all IGBP surface types in the SW spectrum but not in the LW spectrum. In the SW spectrum, there are 17 different LUTs, each corresponding to simulations for the 17 different IGBP surface types. The only IGBP surface type not included in these simulations is type 17 (ocean water). For this type, the LUTs correspond to the scenario of an ice cloud above an ocean surface. In the LW, RT simulations were conducted for 8 specific IGBP surface types (i.e., evergreen needle forest, closed shrubs, open shrubs, woody savanna, grassland, urban, antarctic snow, and desert). The other IGBP surface types were mapped to the existing ones based on their similar or closely related emissivity responses.

The LUTs are all stored in a single NetCDF file and are available on the Zenodo platform at 10.5281/zenodo.14859250 .

The reader should note that the RF values stored in the different LUTs depend on at least three parameters (e.g., SW wavelength range and the scene scenario of ice cloud above ocean) and up to five parameters (e.g., LW wavelength range and the scene scenario of ice cloud above a liquid water cloud). It is complex to illustrate every single dependency of RF with respect to each input parameter. Therefore, we have chosen to demonstrate some of these dependencies in Figs.  and .

Figure  presents an example of the variation of RF_sol for an ice cloud above ocean as a function of COT, SZA (different plots), and CER (different lines in every plot). In the SW wavelength range, RF is negative, corresponding to a cooling effect of the climate at the TOA due to cloud reflectivity. As observed, RF_sol increases in magnitude as the ice cloud becomes optically thicker (larger COT values). Additionally, the size of the ice crystals (i.e., CER) becomes significant for optically thick clouds. Finally, as we can see, the SZA also plays an important role in the simulations, resulting in larger absolute RF_sol values for a SZA value equal to 0°.

Similar to Fig. , Fig.  demonstrates the variation of RF_tir for an ice cloud above the ocean as a function of COT, SST (different plots), and CER (different lines in every plot). Here, we observe that RF_tir changes rapidly for small values of COT, specifically in the range from 0 to 10. However, RF_tir saturates when the cloud reaches a certain optical thickness (approximately a COT equal to 10). The influence of SST on the RF increases as the cloud becomes optically thicker. Additionally, when SST and COT increases, and consequently the infra-red radiation is trapped between surface and ice cloud, RF_tir becomes larger. Finally, CER does not have as large an effect as it does on RF_tir in the SW wavelength range.

Table  provides a summary of all the parameter used in RT simulations with their respective symbol, unit, and range of values.

As will be seen in Sect. , an important input for the LW RT simulations is the surface temperature, called skin temperature (SKT), in the geographic area of interest for each selected day. SKT maps are downloaded from the Meteorological Archival and Retrieval System (MARS) archive for the forecast stream (fc) of the European Center for Medium-Range Weather Forecasts (ECMWF) for the 6 selected days. The data are re-gridded on a regular grid with a spatial resolution equal to 0.04°, covering the geographic domain of this study (see Fig. ). The data are based on the 00:00:00 and 12:00:00 UTC analysis, each covering the subsequent 12 h forecast period in a time resolution of 1 h. For MSG/SEVIRI observations falling between two time steps, linear interpolation is performed between the two successive time steps to assign SKT maps to those observations.

To assess the validity of using a single atmospheric vertical temperature profile, radiative transfer simulations were performed for selected pixels by using real vertical temperature profiles instead of the LUTs in a number of randomly selected pixels (see Sect. ). For this purpose, we downloaded hourly ERA5 vertical temperature profiles from the ECMWF's MARS archive for the analysis stream re-gridded onto a regular grid with a spatial resolution of 0.04°. The temperature profiles are temporally interpolated into the MSG/SEVIRI observation time by using linear interpolation between the analysis data at the previous and next hour.

Using a representative land use dataset for the geographic area of interest is essential because it affects the RT simulations in the LW wavelength range through the surface aldedo and emissivity. We utilize the Terra and Aqua combined Moderate-Resolution Imaging Spectroradiometer (MODIS) Land Cover Type (MCD12Q1) Version 6.1 data for the most recent available year, 2022. The MCD12Q1 data are provided as tiles approximately 1000 × 1000 km² using a sinusoidal grid. The data are re-projected on a regular grid with a spatial resolution of 0.04° in the geographic domain of interest (see Fig. ) with the aid of Satpy Python library .

In this study, we employ the IGBP global vegetation classification scheme, which identifies 17 different land cover classes. It should be noted that in the case of pixels being covered by multiple IGBP classes, we assign the land cover value with the largest percentage coverage to that pixel, with a special treatment for water. We first discriminate whether the pixel is covered by water for more than half of its fine-scale MODIS pixels, in which case it is assigned the water class. Else, we consider all non-water classes for the majority choice.

The CERES instruments aboard Terra measure the Earths' total radiation budget . This type of satellite observations are essential for assessing the radiative effect of clouds.

The Single Scan Footprint (SSF) TOA/Surface Fluxes and Clouds product contains instantaneous CERES observations for a single scanner instrument . The data used in this study combine CERES observations with scene and cloud properties from MODIS on Terra and Aqua satellite.

In this study, we use TOA SW and LW fluxes from CERES Terra-Flight Model 1 (FM1) and Aqua FM3 Edition 4A SSF to validate the TOA SW and LW flux maps of high-altitude ice-clouds derived using the Rapid Contrail-RF Estimation Approach (see Sect. ).

First, as described in Sect. , we use the MSG/SEVIRI Dust/RGB composite to identify specific days during which persistent contrails could be visually detected. It should be noted that contrails with COT values lower than 0.05 are undetectable when using imaging instruments aboard geostationary satellites . For these particular days, the OCA product is re-gridded onto a regular grid with a spatial resolution equal to 0.04°, covering the study area, which expands from 30° W to 15° E longitude and 25 to 55° N latitude. The necessary additional data, including SKT data (see Sect. ) and the surface type (see Sect. ), are also resampled onto the same regular grid with the same spatial resolution as the re-gridded OCA product. As a result, the generated maps contain pixels with information on the cloud phase (cloud-free, liquid, ice, or multi-layered clouds), CTP, COT, CER, SKT, and surface type.

For each pixel characterized as an ice or multi-layered cloud, we first determine which LUT should be used among the three scene scenarios by utilizing the surface type information (land or ocean) and the OCA cloud phase (ice or multi-layered). Once the choice of LUT is made, a multi-dimensional interpolation of the simulated RF_sol and RF_tir values from the LUT at the actual values of the cloud and environmental parameters for each pixel (SZA, COT, SKT etc.) is performed.

The dimensions of the interpolation are determined by the number of parameters on which RF_sol and RF_tir depend in each LUT. For instance, for an ice cloud above ocean and within the SW wavelength range, a 3-dimensional interpolation is performed with the simulated RF_sol being a function of COT, CER, and SZA parameters. For the same scene within the LW wavelength range, a 4-dimensional interpolation is necessary, where simulated RF_tir is a function of COT, SST, CTH, and CER parameters.

The final output of this approach is the construction of RF_sol and RF_tir, as well as Fsol and Ftir maps of the detected ice clouds.

Merging the different datasets, as explained in Sect. , will generate RF and fluxes maps of both natural and aviation-induced clouds. To emulate the detection of potential persistent contrails, among naturally occurring and contrail clouds, we apply a filtering method based on the ice clouds' CTP value similar to the approach described in . This procedure does not allow for an impact study of aviation but is sufficient to validate our method.

The rationale behind this approach is that most of commercial airplanes fly at altitudes ranging from 8 to 12 km, which corresponds to a mean pressure level of 250 hPa. However, for a persistent contrail or a contrail cirrus to form, specific atmospheric conditions are required, mainly the presence of an ISSR. On average, these ISSRs are typically found at slightly higher pressure levels, around 300 hPa. Combining both information, we implement a CTP filter at 300 hPa in our analysis, meaning that clouds above 300 hPa may contain persistent contrails or contrail cirrus. It should be noted that this approach provides a rough and approximate filtering compared to better approaches, such as manually labeling remote sensing images , or contrail detection algorithms based on machine learning .

The detection and characterization of potential contrails are conducted for each selected day by zooming on smaller geographic regions within our spatial domain of interest, based on the presence of a large number of potential contrails. This choice significantly reduces the computational time for Sect. , , and , while allowing us to sample pixels over land or ocean on the different days. Figure  presents the selected longitude and latitude ranges for each day, while Table  provides a summary.

Figure  presents an example of the DUST/RGB composite from SEVIRI/MSG, focusing on the geographic region over France and the Bay of Biscay for 25 September 2023, from 06:00:00 to 07:15:00 UTC. It should be noted that, for the sake of visual clarity, Figs. , , and  demonstrate only a part of the zoomed geographic region where potential contrails are observed. At 06:00:00 UTC, a dense ice cloud is observed, surrounded by line-shaped ice clouds over the northern Bay of Biscay and France. As time progresses, the dense ice cloud mass disperses, while at the same time, we observe the formation of several line-shaped ice clouds around it.

As it is demonstrated in Fig. , the OCA algorithm successfully detects the dense ice cloud at 06:00:00 UTC as a mixture of ice and multi-layered clouds. Interestingly, as time progresses, most of the formed line-shaped potential contrails are characterized as clouds by the OCA algorithm. We observe that many ice clouds are identified as clouds only in their central parts, while their thinner edges often remain undetected. We speculate that this is due to the spatial resolution of SEVIRI/MSG observations, which is 3 × 3 km² at the SSP.

As presented in Sect. , the application of a CTP filter distinguishes natural cirrus clouds from potential contrails. In the following section, we proceed with the generation of RF maps based on this distinction. Table  summarizes the average number of pixels characterized as ice and multi-layered clouds for each selected day per observation, as well as the percentage of these pixels having potential contrails. The day with the largest number of potential contrail pixels is 17 February 2024, followed by 30 January 2024.

From this section onward, the focus is exclusively on potential contrail clouds: a net RF value was assigned to the pixels characterized as ice or multi-layered clouds that passed the distinguishing filter between low- and high-altitude ice clouds, the latter representing potential contrails in this work.

The net RF is calculated as the sum of RF_sol + RF_tir. As discussed in Sect. , the presence of an ice cloud is most commonly expected to result in cooling in the SW wavelength region (negative RF values) and warming in the LW wavelength region (positive RF values).

Figure  presents maps of potential contrails net RF for the same geographic region as in Figs.  and  on 25 September 2023, from 06:00:00 to 07:15:00 UTC. For this sequence of observation times, the detected potential contrails exhibit a positive radiative effect, indicating that the overall effect was warming during these early morning hours. At 06:00 UTC, the long, thin ice cloud mostly located above the Atlantic exhibits the strongest warming effect compared to other ice clouds during the rest of the time period, likely due to the still nighttime conditions in this region. As daytime progresses and the sun rises, the warming effect of the potential contrails diminishes, indicating that the shortwave cooling effect becomes more pronounced.

An overall daily view of the RF effect of potential contrails is provided in Fig. . Over the geographic region of interest and for the 6 selected days, the net RF values of the detected ice or multi-layered cloud pixels have been multiplied by the coverage area per pixel, summed and then divided by the total coverage area for all the pixels. We refer to this summation as the total RF_ice. Additionally, summing up only the potential contrail pixels will provide us the total RF_contrail. For the example day of 25 September 2023 (Fig. c), the total net RF values of the potential contrails range from -3.71 W m⁻² (12:00 UTC) to 3.90 W m⁻² (23:30 UTC). As it is expected, for all the selected days, the maximum total net RF_contrail appears during nighttime due to the absence of SW cooling, while the minimum RF_contrail value occurs during daytime and close to each midday. Even though the largest number of potential contrail pixels is found during 17 February 2024, we observe that the absolute maximum RF_contrail values are observed during 13 June 2023 (see Table ). This is due to the increased incoming solar radiation during the warmer months in the Northern Hemisphere compared to the colder months. Additionally, the contribution of the LW RF to the total RF for the detected ice and multi-layered clouds, and potential contrail pixels is presented in each subplot in Fig. . It is observed that, for each case, the LW consistently contributes positively to the total RF throughout the day, with small fluctuations observed across different cases.

The core component of the Rapid Contrail-RF Estimation Approach is the construction of the ice cloud RF LUTs and their merging with the re-gridded geostationary maps (see Sect. ). As presented in Sect. , the atmospheric temperature vertical profile used in the RT simulations remains constant and corresponds to the U.S. Standard Atmosphere.

To assess the validity of this choice and estimate the uncertainty associated with using a single constant temperature vertical profile, randomly selected pixels from the zoomed geographic regions of each day-containing potential contrails above land, ocean, and liquid water clouds (i.e., multi-layered)-covering day- and night-time conditions were chosen as the sample of this investigation.

For these selected pixels, RT simulations were performed using the ERA5 vertical temperature profile from ECMWF (see Sect. ) as the input atmospheric profile. These profiles were also used to estimate CTH and wCTH (only in the presence of a liquid water cloud). Additionally, for each pixel, the actual CER and COT values from the OCA product were used, along with the real SZA. In the presence of a liquid water cloud, we use the wCOT value from the OCA product.

In Fig. , for each scene scenario, we present the comparison results between the RF values coming from the LUTs (RF_USstandard) and the RF values calculated by using the actual atmospheric and cloud conditions (RF_ERA5) per selected pixel in the SW and LW wavelength ranges, separately. As it can be seen, for all the scene scenarios in the SW wavelength range, overall good agreement is found with the correlation coefficient (R) ranging from 0.97 to 1.00 and slope (s) from 0.93 to 0.97, with the exception of a few comparison points. Table  provides some statistics for the two different methodologies followed in this Section per wavelength and scene scenario. In the SW wavelength range, the use of LUTs instead of real-time RT simulations per pixel can lead to RMS error percentage equal to 6.30 %, 7.32 %, and 17.56 % above land, ocean, and liquid water cloud, respectively. The comparisons in the LW wavelength range (see Fig. ) reveal an overall good agreement with correlation coefficient values being around 1.00 and slope values in the range of 0.95–0.97. In contrast to the comparison in the SW, in the LW, we observe that a larger number of points appears to be scattered around the 1:1 line. This finding means that the RT simulations in the LW wavelength range are more sensitive in the choice of the atmospheric temperature vertical profile. The use of LUTs in the LW wavelength range leads to RMS error values of the same order of magnitude for the three scene scenarios. When focusing on the SW and LW RMS error percentage, we find that the largest values for both wavelength ranges are observed for the scene scenario of an ice cloud above a liquid water cloud (multi-layered).

To explain the scattered points around the 1:1 line in the subplots of Fig. , we focus on the points with an RMS error value larger than the mean RMS error value plus two times the standard deviation of the RMS error. For these points, we first investigated whether there is a correlation between the large discrepancies in the two RF datasets and the differences between the values of each actual cloud parameter and the closest values used during the multi-dimensional interpolations in the LUTs. The comparison results depicted no correlation.

Additionally, for these points, we examine the corresponding ECMWF vertical profiles used in the RTM simulations. Figure  illustrates the temperature and humidity of the US Standard profile, along with the median profile of the ECMWF vertical profiles, as well as the coverage of these profiles. We observe that the coverage of the ECMWF vertical profiles demonstrates different values for surface temperatures but their median profile agrees very well with the US Standard atmospheric profile. In contrast, the humidity ECMWF vertical profiles depict a large difference at the surface compared to the US Standard profile.

Overall, in the SW wavelength range, the use of a standard profile in the construction of the LUTs lead to mean bias percentage of about 2.05 %, 1.01 %, and 4.29 % for a contrail above land, ocean, and liquid water cloud, respectively. In the LW wavelength range, the mean percent errors equal to 2.64 %, 2.93 %, and 5.95 % for a contrail above land, ocean, and liquid water cloud, respectively.

The micro-physical properties of the ice crystals, which are part of the ice clouds, play a crucial role in their single scattering properties and, consequently, the RF of these clouds . Here, we assess the impact related to the choice of ice cloud parameterization in the RT simulations. The parameterization determines how the ice water content and CER are translated into optical properties. Since the ice crystal shape is an unknown parameter, we have selected the parameterization by , assuming the ice crystal habit to be a column composed of 8 elements with a moderate degree of roughness, as this is the habit most frequently observed for thin ice clouds and contrails . According to the same study, 60 % of cirrus clouds are a mixture of ice crystals with severe roughness, while 40 % a mixture of smoothed ones. Similarly to , we have chosen a moderate degree of roughness for the simulations included in the LUTs.

For this sensitivity study, we performed a small subset of RT simulations in the SW and LW wavelength ranges, varying the choice of ice cloud parameterization. We selected all the available ice crystal shapes from the parameterization by . In addition, we included the parameterization by , and by , which is operationally applied in the ECMWF Integrated Forecasting System (IFS) and assumes ice crystals as pristine hexagonal columns. The simulations are always performed for an ice cloud with a COT equal to 0.5 to maximize its semi-transparency and, subsequently, the effect of cloud microphysics. We have chosen three different SZA values (10, 40, and 70°), a CER of 20 µm, and a CTH of 10 km. For these simulations, the ice cloud is located above an ocean surface characterized by three different SST values (273, 293, and 303 K).

Figure  presents RF_sol as a function of various ice crystal habits based on the parameterization of (i.e., column with 8 elements, droxtal, hollow bullet rosette, hollow column, plate, plate with 10 elements, plate with 5 elements, solid bullet rosette, and solid column) and their degrees of roughness (smooth, moderate, and severe) for three different SZAs. The ice crystal habit of an hexagonal column by is included as well. Additionally, the figure presents the relative differences in RF_sol compared to the selected ice crystal shape and degree of roughness for the construction of the LUTs. As observed, the choice of ice crystal habit and roughness degree can result in large differences, which can be up to 60 % (e.g., the case for SZA = 10° for smooth plates of 10 elements) in the SW wavelength range. In addition, the parameterization of , which assumes a pristine hexagonal column results in differences up to approximately 20 % for the case of a small SZA. For the three SZA scenarios, RF_sol of the selected ice crystal shape and roughness appears to have the lowest values compared to other ice crystal shapes and degrees of roughness.

Figure  presents RF_tir as a function of the same ice crystal habits and roughness degrees for three different SST scenarios, along with their relative differences. In contrast to the shortwave range, the differences in the LW (RF_tir) are much smaller, not exceeding 12 %.

From the sensitivity tests, we conclude that ice crystal habit and roughness can lead to significant differences in RT simulations in the SW wavelength region, while these factors play a less significant role in the LW wavelength region. When investigating the simulated upward and downward irradiance at TOA in the SW wavelength region, we find that the largest differences between the selected ice crystal shape and roughness (i.e., column of 8 elements with moderate roughness) and a plate of 10 elements with a smooth degree of roughness (i.e., largest differences in RF_sol) occur in the following wavelength ranges: 1122–1135, 1346–1471, 1800–1954, and 2486–2752 nm. Similarly, in the LW wavelength, the simulated spectrum is affected the most by the choice of the ice crystal shape and roughness in the following wavelength ranges: 3487–4171, 4645–5502, and 8113–9153 nm.

To estimate the uncertainty associated with the selection of a specific ice cloud parameterization in the RF_sol and RF_tir maps, we have re-performed the RT simulations for the randomly selected pixels (see Sect.  for only a single day; 25 September 2023). Consequently, the comparison is made between RF_sol and RF_tir obtained in Sect. , where the default ice cloud parameterization was applied, and those generated by employing the same input values for the RT simulations, but differing the choice of ice cloud parameterization. For the comparison, we have used the ice crystal habit and roughness, which exhibits the largest difference with our default settings: plate of 10 elements with a smooth degree of roughness .

Table  summarizes the findings of the above-mentioned comparison. As expected by the sensitivity study, the use of another ice crystal habit and roughness can lead to large differences in the SW and slightly affects the LW wavelength range. For the SW wavelength range and for all the scene scenarios, the mean RF values for columnar and plate ice crystals differ by a negative bias, with the largest bias found for contrails above ocean surfaces (-49.33 W m⁻²).

For the LW wavelength range, the bias values are smaller, with the largest bias being equal to 5.89 W m⁻² for ice clouds above liquid water clouds (i.e., multi-layered).

We should keep in mind that actual measurements of the micro-physical properties of ice crystals in contrail clouds are rare and difficult to obtain. There have been in situ measurements, such as those in , which found that the primary ice crystal habit is aggregates (i.e., the one used in this study), though the presence of other crystal shapes has been reported. Consequently, we used the most common one to optimize the representation of ice crystals. However, applying a single ice crystal shape and roughness for the overall number of potential contrails during different seasons, and above various scenes may not be fully representative.

As mentioned in Sect. , the OCA product provides the CTP. To have the information about CTH, which is used as a parameter in the RT calculations in the LW wavelength range, the US Standard profile is used. More precisely, we linearly interpolate the CTP in the pressure vertical grid, and consequently, the altitude vertical grid, of the US Standard atmospheric profile.

CTH plays an important role in the LW wavelength range, where it is utilized to perform the multi-dimensional interpolation of the simulated RF_tir values from the LUT at the actual values of the cloud and environmental parameters for each pixel. To evaluate the accuracy of using a constant atmospheric profile to estimate the CTH, we have selected the same pixels as in Sect. . For these pixels, ECMWF pressure vertical profiles were used to interpolate linearly the potential contrail CTP in the altitude vertical grid of those profiles. Consequently, this CTH value, named “CTH - ECMWF”, in every selected pixel can be used to re-perform the multi-dimensional interpolation in the parameters and estimate a new RF value in the LW wavelength range.

Figure  presents the comparisons between this new RF value by using the actual CTH and a CTH estimated by the US Standard profile. As we can see, the correlation between them is excellent for the three different scene scenarios, indicating that using a different CTH value does not affect the multi-dimensional interpolation performed in the LUTs to extract the RF_tir. As it is demonstrated in Fig. , for the three different scene scenarios, the CTH values estimated by using a real atmospheric and the US Standard profile depict small differences with a mean bias equal to 0.85 %, -0.60 %, and -1.70 % above land, ocean, and liquid water cloud, respectively. The scatter plots of Fig.  reveal that for the three scene scenarios, CTH estimated by the US Standard profile is systematically lower by 22 %–26 % compared to the CTH estimated by the ECMWF vertical profiles.

TOA upward solar (i.e., SW) and thermal infrared (i.e., LW) fluxes, as observed by the CERES FM1 and FM3 instruments, have been used to validate the first output after merging the datasets in the Rapid Contrail-RF Estimation Approach: the TOA upward SW and LW fluxes referred to as Fup (see Eq. ). This comparison focuses exclusively on pixels identified as potential contrail pixels.

The comparison was conducted using data from the 6 selected days. For each of these days, the closest-in-time MSG/SEVIRI observation was matched with the CERES observations (approximately four per day above the zoomed geographic region of interest) by taking into account the exact acquisition time of the selected MSG/SEVIRI pixels. Since CERES has a larger footprint (approximately 25 km in diameter near nadir) compared to the spatial resolution of the flux maps generated by the Rapid Contrail-RF Estimation Approach, we averaged the potential contrail pixels, which are located inside the CERES footprint. To perform this averaging, we defined an ellipsoid area around the latitude and longitude of CERES field-of-view (FOV) at surface, based on the satellite's height, viewing zenith angle, and the clock angle of CERES FOV at satellite. If this area was covered of potential contrail pixels more than 75 %, we averaged these pixels and compared them with the CERES fluxes in the SW and LW wavelength ranges, separately.

Figure  presents the outcome of the comparison described above. As seen, there is generally good agreement in the SW and LW wavelength range, with a correlation coefficient (R) of 0.99 and 0.86, respectively.

Table  provides overall statistics for the mean CERES and Rapid Contrail-RF Estimation-estimated upwards TOA fluxes. The bias in the SW wavelength range (1.28 W m⁻²) indicates that the Rapid Contrail-RF Estimation Approach, in general, slightly overestimates the SW fluxes by 1.05 % compared to CERES, while in the LW wavelength range the bias is negative (-16.24 W m⁻²) indicating that our approach underestimates in general the LW fluxes by 9.07 % compared to CERES. Additionally, the higher Rapid Contrail-RF Estimation Approach SW fluxes compared to CERES align with the RF_sol values for the ice cloud microphysics in Sect. . There, it was demonstrated that using column of 8 elements as the ice crystal shape results in the lowest radiative forcing values compared to other ice crystal shapes. Concerning the RMS error, the Rapid Contrail-RF Estimation Approach seems to perform better in estimating LW fluxes than SW ones. However, we observe that in LW wavelength range, the two compared fluxes exhibit the largest scattering, resulting in many points having considerably lower fluxes compared to CERES ones.

Focusing on the mean cirrus optical thickness (COT) values, averaged within the respective CERES footprints and color-coded in Fig. , we observe that in the LW wavelength region, the largest COT values correspond to cases in which the Rapid Contrail-RF Estimation Approach retrieves low fluxes (smaller than 140 W m⁻²), while the CERES fluxes demonstrate larger variability. In the SW wavelength, there is no direct correlation between mean potential contrail optical thickness values and discrepancies between the two datasets.

A direct comparison has been conducted between the outputs of the Rapid Contrail-RF Estimation Approach and the results reported in . In that study, the authors investigated the radiative effects of two contrail cirrus outbreaks over Western Europe using geostationary satellite observations and radiative transfer calculations. Our primary motivation for this specific comparison is the use of a common geostationary satellite and cloud product (a modified OCA product; see below).

The two outbreaks extended over Western Europe on 2 consecutive days, 22 and 23 June 2020. For these days, Dust/RGB images from the MSG/SEVIRI satellite were used to visually demonstrate the two outbreaks. We now describe the methods used by the authors of : radiative transfer simulations were then conducted using ecRad as the radiative transfer code. The required input for ice cloud properties was derived from the OCA product, modified by increasing the COT values by a multiplicative factor of 1.3. The ice crystals were assumed to be pristine hexagonal columns. Atmospheric vertical profiles were obtained from the ECMWF Reanalysis version 5 (ERA5). Consequently, both studies share common components in their methodology but also exhibit important differences.

Figure  shows the net RF values of the contrails during the first outbreak from 09:00 to 22:00 UTC on 22 June 2020, focusing on the same geographic region as in . This figure corresponds to Fig. 2 in . A first qualitative comparison between the two figures clearly reveals the warming effect of contrails over land. However, in our case, at 12:00 UTC, we observe mainly cooling over ocean, whereas in , the ice clouds exhibit both cooling and warming effects. At 18:00 UTC, the pattern is reversed.

We conducted a quantitative comparison to assess the net total power of the SW, LW, and net RF of ice clouds and clouds with CTP above 300 hPa, expressed in terrawatt (TW), over the region of interest from 07:00 UTC on 22 June 2020 to 12:00 UTC on 23 June 2020. We used the online tool WebPlotDigitizer (https://automeris.io/, last access: 28 October 2025) to extract the SW, LW, and net total radiative effect of the both the ice clouds and those located above 300 hPa from Figs. 3b, S6a, and S6b in , which we could then compare directly to our own values. As shown in the comparisons in Fig. , both datasets,total ice clouds and above 300 hPa, exhibit excellent agreement in terms of correlation coefficient values for SW, LW and net total power over the geographic area of interest. However, the Rapid-Contrail Estimation Approach systematically yields smaller values compared to the results of as reflected in the slope values in Fig. .