2.1 Spectral channel selection

To fulfil the demands of making the TIR imager a tool for cloud and surface characterization, observations at different wavelengths were realized. A synchronously rotating filter wheel, providing six slots for spectral filters (each 25 mm in diameter), is mounted between the lens and the detector. To match images of different channels, when measuring on a fast-flying aircraft, the measurement frequency needs to be fast. Therefore, the whole filter wheel rotates with a frequency of 100 Hz. With six channels, this results in a frame rate of about 15 Hz, meaning that a full filter-wheel spin to separately acquire six single images (one with each of the six filters) takes 0.06 s. Four of the six filter-wheel slots are equipped with band-pass and low-pass filters, which are adapted to the channels (centre wavelength) popular among satellite instruments such as MODIS, MSI, VIIRS, and AVHRR. The applied filter–channel assembly is summarized in Table 2, listing their respective spectral range and space-borne sensor equivalents. The mean maximum transmissivity 𝒯 of the single filters is in the range between 0.8 and 0.9 (Table 2). The smaller the wavelength range of the filter, the smaller the signal reaching the detector, which increases the measurement uncertainty. For some applications, broadband measurements, which provide a higher accuracy are sufficient, e.g. for sea surface temperature or cloud top altitude retrievals. Therefore, two of the filter slots provide redundant broadband measurements (7.7 to 12 µm, channels 1 and 4 in Table 2) but are fitted with an optically transparent window to match the optical paths of the other channels.

Table 2List of all VELOX channels. The wavelength ranges (λ) of the narrow-band channels are determined by the centre wavelength of the particular filter and its half width. The third column lists the mean maximum transmissivity 𝒯_max of the channel filters. According to the wavelength ranges, equivalent MODIS, MSI, VIIRS, and AVHRR bands and centre wavelengths are listed.

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Chylek et al. (2006) showed that in the wavelength range between 8.5 and 10 µm the imaginary part of the refractive index of liquid water and ice is rather equal but shows significantly different slopes at wavelengths between 11 and 12 µm. Therefore, channels 2 and 4 of the VELOX system are used to discriminate between liquid water and ice in clouds; they can also be used to derive the cloud effective radius or the liquid water path (Iwabuchi et al., 2016; Someya and Imasu, 2018) by applying the split-window method (McMillin, 1980; Brogniez et al., 2003; Heidinger and Pavalonis, 2009).

The two remaining filters (channels 3 and 6) serve to discriminate ocean, snow, and ice surfaces in Arctic regions. Hori et al. (2006) have shown that the emissivity of snow and ice is rather equal at 10.6 µm but differs significantly at wavelengths close to 12 µm. Furthermore, those differences at wavelengths close to 12 µm are a function of the particular type of snow and ice (e.g. variable grain size).

The non-imaging nadir-pointing infrared thermometer has a smaller FOV and a lower sensitivity than the TIR imager (compare Table 1). However, the sensor calibration is more stable, does not need to be cooled, and, therefore, is well suited to serve as a reference for the TIR imager. The spectral window of the infrared thermometer covers the spectral channel 3 of the TIR imager (compare Table 2), which allows for a measurement comparison between the two instruments and cross-calibration checks.

2.2 Airborne operation and installation on HALO

VELOX is currently mounted in the belly pod of HALO, outside the aircraft's pressurized cabin. To operate the sensors under constant environmental conditions and minimize thermal effects on the sensor sensitivity, the TIR imager and the infrared thermometer are installed in a temperature- and pressure-controlled housing. Humidity inside the housing is minimized by purging the inner air volume with nitrogen gas before each flight. However, the temperature control is only unidirectional, using the instrument's heat production and additional heaters but no Peltier cooling system. To monitor the remaining changes of the environmental conditions inside the chamber, six temperature sensors, an air-pressure sensor, and a humidity sensor are installed, measuring with 1 Hz and relative uncertainties of ±0.1 ^∘C, ±2.5 hPa, and ±2 %, respectively.

Figure 1 shows a technical sketch with an inside view of the single instruments. This cylindrical housing was manufactured mainly out of aluminium and stainless steel and is 44 cm tall with a diameter of 25.5 cm. The entire setup has a weight of approximately 20 kg.

Figure 1Schematic of the cylindrical housing of VELOX. Only the main components of the system are labelled.

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The TIR imager and the infrared thermometer view through the downward-looking side of the cylinder, in which transparent windows are integrated. As a trade-off between stability and potential effects on the measurement, two separate germanium windows of 0.5 cm thickness were chosen. The windows provide a high mean transmissivity 𝒯 of 0.9395 for the wavelength range between 7.7 and 12 µm. Both sides of the window are covered with an anti-reflection coating to minimize transmission losses and specular reflections inside the housing. In addition, the window plane is tilted by 5^∘ with respect to the TIR imager and infrared thermometer viewing axis. This avoids a direct mirroring of the cold detector itself. The remaining reflections are mostly driven by the thermal emission of the imager optics and are imprinted as a homogeneous offset in the measured radiation field. By knowing the temperature of the instrument's optic and the reflection coefficient of the window, these offsets can be removed (see Sect. 3.2.5).

The window is directly exposed to the air flow around the aircraft and cools down significantly more compared to the atmosphere inside of the VELOX cylinder. Condensation or icing on the inside of the window is avoided by several means. The purging with nitrogen gas reduces the absolute humidity to less than 2 g m⁻³. Furthermore, three heating elements are installed, and three fans generate a continuous airflow over the windows.

3.1 Geometric characterization

The geometric characterization of the VELOX system addresses two main issues: (i) the relative pixel orientation (sensor zenith and azimuth angles) and size (ground or cloud top related) as a function of aircraft attitude and altitude, including the relative position of the field of view (FOV) of the infrared thermometer within the images of the TIR imager and (ii) the matching procedure of images with different filters.

3.2 Radiometric calibrations and corrections

Each pixel of the TIR imager provides a digital number, which is proportional to detected photon counts per unit time. During EUREC⁴A, the imager was operated with a frame rate of 100 Hz and an integration time of 70 µs, for which the thermal influence of the spectral filters can still be well corrected for. To convert the digital counts into radiance I^↑ (in units of W m⁻² nm⁻¹ sr⁻¹) or brightness temperature T_B (here given in units of degrees Celsius, while T_B differences are given in units of kelvin), several calibration and correction processes are applied. This includes a radiometric calibration, non-uniform corrections of the detector, extended radiometric cross-calibrations, bad-pixel corrections, and corrections of the influence of the window in the case of airborne application in the tubular mounting. Figure 2 shows an example measurement, acquired during EUREC⁴A. Each step of the calibration and correction process is displayed in a single panel and is separately discussed step by step in the subsequent sections.

Figure 2Illustration of the post-processing steps using a 2D VELOX image acquired with the broadband channel (7.7–12 µm) during the EUREC⁴A flight on 13 February 2020 at 11:37:30 UTC.

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3.2.5 Correction of window influence during airborne operation

For the airborne operation of VELOX in the tubular mounting, the effects of the window additionally need to be corrected. In this case, the observations are affected by transmission, absorption/emission, and reflection off/on the window surface. Transmission losses reduce the raw signal, while emission from the window and reflection on the inside of the window will increase it. Typically, the window is cooled down by the outer environment, which leads to a difference between the emission by the window (low temperature) and the reflected emission by the imager lens (higher temperature).

The radiance $I_{\mathrm{meas}}^{\uparrow }$ at flight altitude, which impinges on the outside of the window, will be mostly transmitted, and the remaining fraction will be reflected or absorbed. Re-emission of absorbed radiation by the window occurs due to its own temperature T_win. The resulting radiance $I_{\mathrm{meas}}^{\uparrow }$ behind the window is then composed of the transmitted radiation and the emitted radiation by one side of the window but also by reflected radiation, originating from the imager's lens emitted with its own temperature T_lens. According to this, the following equation is applied for the correction of the measured signal:

$$\begin{array}{}\text{(1)}& I_{\mathrm{cor}}^{\uparrow }={\displaystyle \frac{I_{\mathrm{meas}}^{\uparrow }-{\mathit{ϵ}}_{\mathrm{win}}\cdot I_{\mathrm{win}}\left(T_{\mathrm{win}}\right)-{\mathit{ϵ}}_{\mathrm{lens}}\cdot I_{\mathrm{lens}}\left(T_{\mathrm{lens}}\right)\cdot {\mathcal{R}}_{\mathrm{win}}}{{\mathcal{T}}_{\mathrm{win}}}},\end{array}$$

where $I_{\mathrm{cor}}^{\uparrow }$ is the corrected signal, using $I_{\mathrm{meas}}^{\uparrow }$ as input for the measured signal. The specific absorption/emission is given by ϵ, the reflection by ℛ, and the transmission by 𝒯. The subscripts denote the two coefficients of the window (win) and the imager's lens (lens). The spectral ϵ, ℛ, and 𝒯 of the window as provided by the manufacturer and validated by cross-calibrations with a black body are shown in Fig. 3. Overall, the germanium window has a high average transmissivity of 93.95 % in the wavelength range from 7.7 to 12 µm. The spectral behaviour of the reflection coefficient is rather constant over the entire range with about 5 % on average, while the absorption/emission coefficient is almost negligible for the VELOX channels 2 and 3 but affects longer wavelengths (up to 10 % for channels 5 and 6). The emission coefficient of the lens is 0.15. Although this value seems to be quite large, it results in a rather low contribution to the composed signal (≈0.75 %), because it only corresponds to the radiation emitted by the lens. For the application of Eq. (1), the window parameters were integrated for the filter response function of the selected spectral channel.

Figure 3Spectral transmission, reflection, and absorption/emission coefficients of the germanium window for the wavelength range covered by the TIR imager. Included are in addition the response functions (transmission coefficients, dashed–dotted lines) of the four narrow-band channels.

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The window temperature is observed by a PT-100 temperature sensor attached to a part of the window that is not covered by the imager's FOV. It is displayed as a colour-coded time series for the single flights in Fig. 4a. The temperature of the lens is measured internally by the imager and is displayed in Fig. 4b. Both show a dependence on flight altitude and environmental temperature, which has a significant time lag. For the first 2 h of each flight, the airflow around HALO continues cooling down VELOX. However, once HALO has reached a stable flight altitude, the temperature changes remain small. The measurements thus benefit from maintaining a constant flight altitude.

Figure 4Time series of (a) the window temperature and (b) the temperature of the imager optics acquired during different EUREC⁴A research flights.

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3.3 Sensitivity and stability

A typical measure for the accuracy of measurements in the TIR wavelength range is the noise equivalent temperature difference (NETD). For the standalone TIR imager, the manufacturer reports the NETD to be 40 mK. For the full setup, including spectral filters and the window, the NETD was estimated for each channel by measurements in front of a black body. The measurements are started after a 2 h spinup time to guarantee a stabilized filter and instrument operating temperature. Afterwards, 64 subsequent images at 10 ^∘C, 128 subsequent images at 20 ^∘C, and 64 subsequent images at 30 ^∘C were recorded. The difference between the average counts per pixel measured at 30 and 10 ^∘C divided by 20 gives a count-response file per kelvin. From the 128 images measured at 20 ^∘C, the standard deviation of each pixel is calculated, leading to a temporal noise file. Dividing the temporal noise file by the response file, averaging over all pixels, and multiplying it by 1000 gives the NETD in millikelvin. The acquired NETDs are 48 mK for the two broadband channels (channels 1 and 4), 347 mK for channel 2, 605 mK for channel 3, 473 mK for channel 5, and 442 mK for channel 6. Due to the use of the spectral filters, the detector receives less radiation but is limited by the same thermal noise, leading to the partly large NETDs. However, as long as the image values provide a significant contrast, the acquired thermal signal allows us to resolve spatial structures of the target.

To quantify the absolute accuracy, 5 min image sequences were recorded, each using a different black body temperature setting (5 K steps, −10 to 35 ^∘C). Figure 5 shows box-and-whisker plots calculated from the mean measured brightness temperature of each single image for all six channels. On average, the measured brightness temperature matches well with the black-body-generated temperature values. Furthermore, a comparison of the single sections reveals that the standard deviation is rather independent of the target temperature (no temperature-dependent trend in the boxes and whiskers).

Figure 5Box-and-whisker plots for each of the six channels of the TIR imager. Each panel, (a) to (f), shows the deviations of the measured brightness temperature (T_VELOX) of the single channels from the different black body temperature settings (T_BB). The box encloses the interquartile range, defined at the 25th and 75th percentiles. The whiskers extend out to 1.5 times on either side of the 25th and 75th percentiles.

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Averaged over the whole time series including all 10 black body temperature settings, a standard deviation of 0.016 K is derived for both broadband channels. For the four other channels, the standard deviations are larger, with 0.14 K for channel 2, 0.23 K for channel 3, 0.17 K for channel 5, and 0.16 K for channel 6. However, considering the 25th and 75th percentiles only, the deviations are in the range of ±0.01 K for the two broadband channels, ±0.09 K for channel 2, ±0.15 K for channel 3, ±0.11 K for channel 5, and ±0.1 K for channel 6.

4.1 Brightness temperature

Figure 6 displays time series of the averaged brightness temperature of the central 10×10 pixels (black) measured with the different channels of VELOX along the flight track on 13 February 2020. The highest values of the particular brightness temperature along the time series are related to cloud-free areas below HALO, indicating the detection of the brightness temperature of the ocean surface. All lower values are related to observations of the colder clouds.

Figure 6Time series of brightness temperature observed by the central 10×10 pixels of the thermal imager during the EUREC⁴A flight on 13 February 2020. Each panel, (a) to (f), displays the brightness temperature observed by the use of the different channels (black) and the corresponding cloud-free simulations (red).

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Cloud-free simulations (red; see Appendix A) are used to validate the brightness temperature measurements for cloud-free areas. It can be nicely seen that the highest brightness temperature values along the flight track match the cloud-free simulations.

Figure 7 shows the correlation between the cloud-free simulations and the maximum brightness temperature values classified by a maximum envelope fit for all six channels. The maximum envelope fit is based on the time series of the averaged brightness temperature of the central 10×10 spatial pixels. The time series is divided into sections of 60 s, which was found to be the best setting for trade wind clouds. For each section, the maximum brightness temperature is used to build the envelope by setting all measurements to this maximum value. If a 60 s sequence is fully covered by clouds, the maximum values of the previous cloud-free sequence are used for the envelope. This is justified because temperature changes of the ocean surface can be assumed to be spatially (temporally) weaker compared to the effect of clouds. A 60 s sequence is defined fully cloudy, if its maximum brightness temperature is reduced by more than 3 % compared to the previous sequence. It should be noted that while this approach works well for the trade wind cumuli observed during EUREC⁴A, it may fail for scenes covered by extensive stratiform clouds.

Figure 7Correlation between the cloud-free simulations and the maximum brightness temperature values displayed in Fig. 6, which represent cloud-free measurements over the warm ocean.

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The correlation R between the maximum envelope fit and the simulations is 0.84 (Pearson correlation). Tests have shown that the measurement uncertainties have a minor influence on these differences. Although the NETD varies significantly between the single channels, the spread of the deviations observed with the different channels shows a similar pattern. The reason for the observed differences is mainly linked to the spatial–temporal resolution of the simulations, which is limited by the frequency of dropsonde releases (between one sonde per 5 min and per 1 h). Within such a period, the simulations remain constant, while in reality, the atmosphere might change continuously. Excluding flight sections with low dropsonde density (e.g. 11:30 to 13:30 UTC in Fig. 6) removes the largest differences, which supports this assumption. However, none of the six channels show a significant deviation from the general correlation. This indicates that the wavelength-dependent window transmissivity is well captured by the correction.

Figure 8 shows a series of 2D images of brightness temperature acquired by the broadband channel (channel 1, 7.7 –12 µm) of VELOX during the EUREC⁴A flight on 5 February 2020. With HALO flying at 10 km altitude, the images cover an area of 6.4 km×5.1 km with a spatial resolution of 10 m×10 m, both with respect to the surface. The images show the contrast between the warm ocean in red colours and the colder clouds in blue colours and highlight that VELOX is capable of resolving cloud structures with sizes well below 100 m. This is especially beneficial for observations in the trade wind region, where Schnitt et al. (2017) reported that 70 % of all observed clouds have a horizontal extension smaller than 2 km, which is further quantified for the present measurements from EUREC⁴A by Mieslinger et al. (2021).

VELOX measures with a frequency of 100 Hz. Therefore, each sequence of six channels is repeated after 0.06 s, which translates into a flight distance of approximately 13 m for a typical flight speed of 220 m s⁻¹. This means that subsequent images acquired with the same filter overlap as illustrated in Fig. 8a and b. This overlap depends on the flight speed and the distance to the target. For the example shown in Fig. 8a and b, almost no shift of the scene is visible because 99.5 % of the scene is covered in both images. Therefore, Fig. 8c shows the acquired scene 1 s later. Here, the shift becomes visible, but 91 % of the image overlaps with Fig. 8a.

This overlap opens additional options for analysing the VELOX images. Subsequent images with sufficient overlap provide a sequence of observations at different angular directions. Such image sequences have potential for stereoscopic 3D reconstruction of clouds (Kölling et al., 2019) and the investigation of 3D radiative effects in the TIR wavelength range. It further allows the study of the small-scale geometry of shallow cumulus and dynamic processes at cloud edges, where the transition from water vapour to cloud droplets and entrainment take place.

Figure 8The 2D fields of brightness temperature measured at a flight altitude of approximately 10 km with the VELOX broadband channel between 7.7 and 12 µm during the EUREC⁴A field campaign on 5 February 2020 at (a) 11:25:30.00 UTC, (b) 11:25:30.06 UTC, and (c) 11:25:31.00 UTC.

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To combine different spectral channels, the successive images need to match pixelwise. This requires accounting for the horizontal shift between the images. This shift is estimated from the aircraft speed and the projected pixel size, while the latter depends on the distance between the surface/cloud and the aircraft (see Sect. 3.1).

For combining with traditional push-broom imagers (specMACS; Ewald et al., 2016) or nadir-pointing active remote sensing (WALES, HAMP; Wirth et al., 2009; Mech et al., 2014; Konow et al., 2019), the VELOX data were converted into a push-broom-like data set by extracting the central swath of each image along the flight path.

Figure 9 shows a push-broom image of brightness temperature measured at channel 1 for a 5 min time period on 5 February 2020. The scene covers the single images, which are shown in Fig. 8 and marked here by a black rectangle. Comparing the real 2D images with the push-broom-like images may indicate if fast-moving clouds are distorted in the push-broom view, which might have consequences for determining the cloud fraction from push-broom images (Konow et al., 2021).

Figure 9The 2D time series of measured brightness temperature at a flight altitude of approximately 10 km using the centre swath line of the VELOX broadband channel (7.7 to 12 µm). The data were acquired during the EUREC⁴A field campaign on 5 February 2020 between 11:22:00 and 11:27:00 UTC. The black rectangle marks the measured area displayed in Fig. 8. Adapted from Konow et al. (2021).

Further applications for such a combination between VELOX and specMACS are cloud retrievals that are based on measurements in the solar and thermal wavelength range and the investigation of the differential surface warming due to simultaneous cloud shadowing and cloud base emission.

4.2 Cloud cover

If the contrast between cloud top temperature and surface temperature is sufficiently high, TIR images are suitable for determining a cloud mask and to estimate the cloud fraction of a scene. In the case of measurements above open ocean, the cloud mask can be determined by a threshold method. During EUREC⁴A, the ocean had a rather uniform horizontal temperature distribution at about 27±1 ^∘C and provides a good background to identify even small and thin clouds. Even a slightly colder brightness temperature can identify a cloud. However, due to atmospheric absorption and emission, the brightness temperature of the ocean surface measured at the flight altitude of about 10 km is lower than the real ocean skin temperature. As the atmospheric conditions along the flight track can change, this needs to be considered when deriving the cloud mask by simple threshold methods. For example, for the flight on 9 February 2020, the measured brightness temperature of the cloud-free ocean varied between 19 and 21 ^∘C (at 10 km flight altitude). Figure 10a shows the corresponding time series. To account for such fluctuations of the background brightness temperature, the envelope method described in Sect. 4.1 is applied to continuously adapt the cloud mask algorithm to changes in the atmosphere and ocean conditions by the maximum measured brightness temperature in the surroundings of the particular point of interest. As illustrated in Fig. 10a, the envelope reflects the circular flight pattern typically flown during EUREC⁴A. This could be processed further assuming that spatial differences in sea surface temperatures along a circle were/are larger than temporal variations over the course of a flight. For the cloud mask algorithm, the difference between the measured brightness temperature and the envelope is calculated.

The reference level for measurements over cloud-free ocean is constant for the entire flight (Fig. 10b). Thus, a single threshold decides if a cloud was present or not. To account for the fuzzy nature of cloud edges, four different thresholds of 0.5, 1.0, 1.5, and 2.0 K were applied. For the flight shown in Fig. 10, this approach results in a total cloud fraction of 29.4 %, 18.3 %, 15.3 %, and 13.5 % depending on the selected threshold.

Furthermore, the four thresholds were combined into a cloud mask. If the largest threshold of 2 K is exceeded, the measurement is denoted as “most likely cloudy”, and if only the lowest threshold of 0.5 K is exceeded, the measurement is denoted as “probably cloudy”. The state “cloud free” is classified when no threshold is reached, and “unknown” is classified when the cloud mask algorithm fails, e.g. due to condensation on the window. For the flight shown in Fig. 10, the combined cloud mask identifies 13.6 % of the data as most likely cloudy, 17.9 % as probably cloudy, and 68.5 % as cloud free.

Figure 10(a) Time series of brightness temperature (black) observed by the central 10×10 pixels of VELOX using channel 1 during the EUREC⁴A flight on 9 February 2020. The maximum envelope fit is illustrated by the red dots. (b) Difference between the measured VELOX brightness temperature and the maximum envelope fit (black). The four thresholds of 0.5, 1, 1.5, and 2.0 K are included by colour-coded lines.

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The maximum envelope as derived from the central 10×10 spatial pixels served as a reference in the cloud mask algorithm described above. Assuming that the envelope value is valid for the full 2D VELOX images, a 2D cloud mask and cloud fraction for each image were derived. Figure 11a shows the brightness temperature of a 2D VELOX image acquired during the EUREC⁴A flight on 9 February 2020, and Fig. 11b shows the derived, combined cloud mask. It is obvious that the cloud mask is also able to detect cloud patches smaller than 100 m in size. By integrating over all pixels in this scene, the cloud cover results in a total amount of 37.2 % most likely cloudy. The percentage of pixels identified as probably cloudy is 32.8 % and illustrates the uncertainty of the cloud mask algorithms, which always suffer from the fact that clouds are a dispersion, whose boundaries are often poorly defined.

Figure 11(a) The 2D field of brightness temperature measured at a flight altitude of approximately 10 km with the VELOX broadband channel between 7.7 and 12 µm during the EUREC⁴A field campaign on 9 February 2020 at 15:05:21 UTC. For the same scene, panel (b) shows the combined cloud mask and panel (c) the retrieved cloud top altitude.

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For EUREC⁴A, time series of the cloud masks and cloud fractions are available for all flights between 24 January and 15 February 2020 (Schäfer et al., 2021a, b), which were partly analysed and compared to other active and passive remote sensing products by Konow et al. (2021). The comparison, based on the most likely cloudy threshold, highlighted the different sensitivities of the instruments to detect clouds, with VELOX always showing slightly larger cloud fractions compared to the other instruments (Konow et al., 2021). This illustrates the capability of VELOX to also detect small cloud patches. This is a benefit compared to most satellite products, which often suffer from detection limits that miss tiny low clouds (Someya and Imasu, 2018).

4.3 Cloud top altitude

The cloud top temperature measured by VELOX is closely linked to the cloud top altitude. This relation is commonly used in cloud top altitude retrievals from satellite observations. Here, a similar approach is used for the images from VELOX and extended by a cross-calibration with nadir-pointing cloud top altitude measurements from WALES (Wirth , 2021). This method allows the extension of the nadir measurements of WALES to 2D maps of cloud top altitudes, which resolve the horizontal structure of shallow cumulus. To apply the cross-calibration, a first guess of cloud top altitude from VELOX is needed. It is derived from the measured brightness temperature of the thermal imager's broadband channel 1. This first guess is necessary since there is no fixed direct relation between cloud top altitude derived from WALES and the VELOX brightness temperature along the flight path. It rather varies in time with the changing influence of the atmosphere. For the first guess, the brightness temperature is combined with atmospheric profiles from dropsondes (George et al., 2021) and radiative transfer simulations of the cloud-free atmosphere. The simulated brightness temperatures are parameterized as a function of the distance to the cloud top and used to invert the measurements.

In a second step this first guess of the VELOX cloud top altitude is cross-calibrated with the WALES cloud top altitude. The cross-calibration uses the cloud mask (most likely cloudy threshold) of VELOX (cloud mask based on the central 10×10 spatial pixels) and WALES. If both instruments detect a cloud, the cross-calibration is applied, which links the first guess of the VELOX cloud top altitude to the WALES cloud top altitude in a linear relationship. At this juncture, the correction of the first guess VELOX cloud top altitude ranges between 100 and 300 m.

Two major reasons for these uncertainties were identified: (i) an increased distance to the next dropsonde leads to uncertainties in the cloud-free simulations and (ii) mismatches in the cloud mask by VELOX and WALES. The latter can be reduced when using the full temporal resolution of VELOX.

Considering the NETD of VELOX, the full approach allows a retrieval of 2D maps of cloud top altitudes with a vertical resolution of 40 m. As an example, Fig. 11c shows the derived cloud top altitude for the cloud scene from 9 February 2020. Cloud top altitudes below 600 m might be nonphysical and are related to very thin clouds or cloud edges. These low cloud top altitudes probably result from a contamination of the signal by the emission of the ocean below.