Cloud geometry from oxygen-A-band observations through an aircraft side window

During the ACRIDICON-CHUVA (Aerosol, Cloud, Precipitation, and Radiation Interactions and Dynamics of Convective Cloud Systems–Cloud Processes of the Main Precipitation Systems in Brazil: A Contribution to Cloud Resolving Modeling and to the GPM (Global Precipitation Measurement)) aircraft campaign in September 2014 over the Amazon, among other topics, aerosol effects on the development of cloud microphysical profiles during the burning season were studied. Hyperspectral remote sensing with the imaging spectrometer specMACS provided cloud microphysical information for sun-illuminated cloud sides. In order to derive profiles of phase or effective radius from cloud side observations, vertical location information is indispensable. For this purpose, spectral measurements of cloud-sidereflected radiation in the oxygen A absorption band collected by specMACS were used to determine absorption path length between cloud sides and the instrument aboard the aircraft. From these data, horizontal distance and eventually vertical height were derived. It is shown that, depending on aircraft altitude and sensor viewing direction, an unambiguous relationship of absorption and distance exists and can be used to retrieve cloud geometrical parameters. A comparison to distance and height information from stereo image analysis (using data of an independent camera) demonstrates the efficiency of the approach. Uncertainty estimates due to method, instrument and environmental factors are provided. The main sources of uncertainty are unknown in cloud absorption path contributions due to complex 3-D geometry or unknown microphysical properties, variable surface albedo and aerosol distribution. A systematic difference of 3.8 km between the stereo and spectral method is found which can be attributed to 3-D geometry effects not considered in the method’s simplified cloud model. If this offset is considered, typical differences found are 1.6 km for distance and 230 m for vertical position at a typical distance around 20 km between sensor and convective cloud elements of typically 1–10 km horizontal and vertical extent.

brightness temperature is interpreted as cloud top temperature which can be converted to a height if the temperature profile is known (e.g. Smith and Platt, 1978). More complex thermal techniques also relax the black body assumption to derive cloud heights for semi-transparent cloud layers from two or more thermal channel's observation differences (split window techniques, CO2 slicing, e.g.: Chahine, 1974;Menzel et al., 2008).
In addition to simple vertical cloud extent, other aspects of cloud geometry strongly affect passive remote sensing of cloud 5 microphysical properties through illumination effects, e.g., shadows or bright cloud slopes (Varnai and Marshak, 2002;Varnai and Marshak, 2007;Vant-Hull et al., 2007;Liang and Di Girolamo, 2013;Grosvenor and Wood, 2014).
Especially on higher spatial resolution effects caused by geometry variation are of important influence .
A method based on high resolution cloud reflectivity measurements in the solar spectral range is the so-called cloud side 10 remote sensing approach, proposed by Martins et al. (2011) and Zinner et al. (2008) for the retrieval of cloud microphysical properties (particle size and phase) along the vertical profile of convective clouds. For this approach, Ewald et al. (2018) shows that cloud surface orientation can explain most of the observable variation of cloud reflectivity due to three-dimensional radiative transfer. If cloud surface orientation would be known, it could be considered for an important improvement of all passive cloud remote sensing methods. For cloud side observations, this is also demonstrated in Ewald et al. (2015) using a 15 scanning cloud radar to reconstruct cloud geometry.
For the cloud side retrieval of convective microphysics profiles, a localisation of each observation to a vertical position is obviously indispensable (e.g. for thermodynamic phase in Jäkel et al. (2017) or effective radius in Ewald et al. (2018)).
Originally Martins et al. (2011) suggested to use a thermal cloud side imager to obtain the necessary information. Cloud radar aided localisation as in Ewald et al. (2015) is also possible within its sensitivity limitations. Both methods depend on additional Figure 1. Illumination and observation geometry for cloud side remote sensing. A sensor mounted on an aircraft at height z observes a cloud side at distance xi − x0. Solar radiation enters the atmosphere at a solar zenith angle θ0 to the cloud where it gets scattered and reaches the sensor at sensor zenith angle θ. Dependent on cloud distance, radiation within the oxygen absorption band gets absorbed on this path according to the path length and increasing atmospheric density with decreasing height. This 2D illustration shows a situation with the solar illumination in line with the sensor viewing direction (relative sensor azimuth 0 • ). In this study relative sensor azimuth ± 45 • , solar zenith 0 < θ0 < 30 • , and sensor zenith angles 40 • (below horizon) < θ0 < 100 • (above horizon) will be considered.
The derivation of distance from the absorption along the light path of reflected light in the oxygen A-band was originally proposed by Yamamoto and Wark (1961) for satellite application. Wu (1985), Fischer and Grassl (1991) and  discussed the theory behind the approach in detail. Recently Yang et al. (2013) nicely summarize different approaches to the retrieval of cloud height and cloud thickness at the same time by combination of measurements of the DISCOVR EPIC sensors in the oxygen A-and B-bands. Merlin et al. (2016) suggest to derive both parameters from a combination of oxygen-A 5 measurements at different angles. Depending on cloud type and the choice of spectral information used, an accuracy between 50 and a few hundred metres is found. We adapt the method to cloud sides and near horizontal light paths between sensor and clouds for the specMACS sensor. In contrast to other approaches, as e.g. a stereo image analysis, this method is not limited to a few features of high contrast, but provides distance over large continuous parts of the available data.
Nevertheless data from a manual stereo distance analysis by Jäkel et al. (2017) for a number of ACRIDICON-CHUVA 10 cloud cases is used for comparison to the absorption path derived distance. Stereo techniques were first applied to clouds from operational geostationary and polar-orbiting satellites (Hasler, 1981;Muller et al., 2007). For high spatial resolution groundbased stereo-camera systems Seiz et al. (2007) and Beekmans et al. (2016) estimate typical distance biases in the order of a few 100 m or a few percent of the distance. Opposed to the usual use of two pictures synchronously taken from two fixed cameras, Jäkel et al. (2017) used consecutive pictures from one and the same camera onboard the moving HALO aircraft.

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Distance determination for the ACRIDICON-CHUVA cloud side observations is presented in the following. A detailed analysis of uncertainty is conducted for the oxygen-A method applied to our sensor setup and an uncertainty estimate product is provided as part of the method. Geometrical heights obtained this way are compared to stereo analysis results. . DISORT simulation of oxygen-A band using on REPTRAN medium resolution (0.2 nm, red line) and reduced to specMACS spectral response (black line, sampling 1.6 nm, FWHM = 2.8 nm). Colored dots label specMACS channels used in this work.
2 Distance retrieval from oxygen A-band absorption path 2.1 Measurements and modelling of spectral radiance Through a side window of the German HALO (High Altitude LOng range) aircraft reflected sunlight around the oxygen Aband was measured by the imaging cloud spectrometer specMACS during the ACRIDICON-CHUVA campaign (Fig. 1). It has a spectral resolution of 2.5-4 nm below 1000 nm and 7.5-12 nm above 1000 nm wavelength. Data was collected at a spectral 5 sampling of 1.6 nm and a spectral bandwidth of 2.8 nm (FWHM) in the region of the oxygen A-band (Ewald et al., 2016). Ewald et al. (2016) characterised spectral channel positions as well as the spectral filter function width in detail. Figure 2 shows the spectral shape of the oxygen A-band in reflectivity at specMACS sampling together with a simulation at higher resolution. These simulated spectra, as well as all radiative transfer calculations necessary for the setup of the method were done with the libRadtran package (Mayer and Kylling, 2005;Emde et al., 2016). The measurement setup shown in 10 Fig. 1 with a sideward viewing sensor, near horizontal absorption paths, and nearly vertical convective cloud sides can not be represented in a one-dimensional plane-parallel standard setup. Thus, the 3D radiative transfer model MYSTIC (Monte Carlo code for the physically correct tracing of photons in the atmosphere Mayer et al., 2009) was applied. Spectral gas absorption was considered using the REPresentative wavelength radiative TRANsfer method (REPTRAN) by Gasteiger et al. (2014). REPTRAN is based on line-by-line calculations. Radiances are approximated as a weighted mean at representative 15 wavelengths. As mentioned above, Figure 2 shows the spectral region of the oxygen-A band at different spectral resolutions.
The REPTRAN medium resolution (about 0.2 nm in this spectral range) was found to provide sufficient accuracy compared to higher spectral resolution and will be used in the following. At this resolution still part of the detail of the absorption band is visible. Details like the two absorption minima at 761 and 763 nm are not resolved at specMACS resolution (black line in Fig. 2). Still a number of channels can be used to provide a valid measurement of absorption band depth. Five specMACS channels between 745 and 754 nm (green dots) will be used as reference measurement not affected by oxygen absorption and three channels inside the absorption band between 759 and 765 as a measure of absorption (red dots).

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After the solar radiation is reflected by clouds the absorption path through the atmosphere mainly depends on the distance and the observation zenith angle θ. While θ 0 , θ and the general oxygen distribution in the atmosphere are known, cloud distance can be derived from the absorption signal within some limitations. Fischer and Grassl (1991) propose a cloud height derivation based on a spectral measurement around the oxygen A-band with a resolution on the order of 1 nm, but also demonstrate that lower spectral resolution of several nanometers could be sufficient. Technically, they use the relation of cloud distance and a 10 radiance ratio composed from one measurement next to the oxygen absorption region and one within the absorption band. In the following we describe our implementation of this approach and the expected sources of error and uncertainty.

Sensitivities
The impact of a range of sources of uncertainty is investigated using radiative transfer simulations in the following. Already Fischer and Grassl (1991) emphasise the importance of a knowledge of the spatial distribution of scattering coefficient or cloud 15 optical thickness. Both influence the in-cloud photon absorption path and thus the cloud reflectance within the absorption band.
We plan to derive distance only for optically thick clouds and thus expect to be in a saturation regime for reflected radiances which would minimise errors due to unknown optical thickness. The unknown 3D distribution of the scattering coefficient (related to cloud microphysics) still could strongly affect the method -influence of liquid water content (LWC), cloud particle size and cloud extent are tested. Neglected detail of the aerosol distribution could have similar effects. Surface albedo and 20 pressure profile variations are tested as well as the impact of the spectral calibration accuracy of the used spectrometer. Figure 1 shows the setup for the 3D Monte Carlo simulations in this section. The horizontal cloud extent in the following is ∆x = 2km, cloud liquid water content is at a homogeneous 0.5 g/m 3 , and effective radius at constant 10 µm. Example oxygen-A spectra are shown in Fig. 3. The dependence of the absorption band depth on distance (Fig. 3a) will be utilised to retrieve cloud distance -and together with observation zenith angle θ -will provide cloud vertical position. In the following 25 "distance" is always the horizontal distance between sensor and cloud (as opposed to the line-of-sight distance).
All spectra in Figure 3 are normalised to the minimum value at the 762 nm channel in order to visualise the band depth.
As introduced above, the absorption signal is reduced to a radiance ratio similar to Wu (1985) and Fischer and Grassl (1991).
Following their considerations and the fact that specMACS lacks spectral resolution compared to more specialised sensors, we average all three channels available within the oxygen band (red dots) and five channels next to it (green dots). We define the (1) The larger the absorption, the smaller the ratio is. Fig. 3 gives the values of R O2A related to the shown absorption band depths.
Although spectral position and spectral filter functions have been characterised by Ewald et al. (2016), some remaining uncertainty has to be assigned to this calibration: An accuracy of the spectral position of about 0.1 nm and an uncertainty of the spectral width of 0.2 nm can be assumed (Ewald et al., 2016). As a test of the impact, a variation of bandwidth of ± 0.2 nm is applied. It yields small differences of around 1% in the observed radiance ratio as shown in Figure 3b. 5 Absorption path length depends on sensor zenith angle θ, as it controls the total absorber amount to be passed after scattering by the cloud in combination with the observer height (Fig. 3c). Changes of solar zenith angle and relative azimuth angles have a much smaller effect on the path length (Fig. 3d,e). Using aircraft orientation data these parameters can be characterised with sufficient accuracy.
Other characteristics of atmosphere and surface situation are not as accessible. Higher surface pressure would lead to an 10 increase of oxygen absorption and a decrease in R O2A at a given height. It is obvious in Fig. 3f that this influence is small for the observed range of surface pressure during the ACRIDICON-CHUVA campaign (995 -1015 hPa). Surface albedo can also influence the absorption band depth due to multiple scattering between surface and atmosphere. Longer absorption pathes are generated for larger surface albedo (Fig. 3g). Aerosol concentration along the path influences the path length in a similar way: The higher the aerosol content, the longer the path due to multiple scattering, and the smaller R O2A (Fig. 3h).

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The spatial distribution of scatterers in clouds influences the in-cloud path lengths. Wu (1985) or Fischer and Grassl (1991) point out that the spatial distribution of the scattering coefficient as well as the optical thickness of the cloud layer are critical for their retrievals of cloud height for a wide range of optical thick and thin clouds. In case of cloud side remote sensing of convective cloud microphysics the task is simplified. The object of interest is a dense vertical cloud with a horizontal spatial extent of the order of kilometres. A liquid water content of 0.5 g/m 3 (typical for ACRIDICON-CHUVA Wendisch et al., 2016) 20 and an extent of just 1000 m already leads to large (horizontal) optical thickness values in the order of 50 and above. Wu (1985) shows that these circumstances minimise uncertainties. Figures 3i, j and k show the effect of varying characteristics of the cloud on the absorption band depth: LWC, particle size and horizontal extent are varied. Cloud extent does not cause any important uncertainty, influence of droplet size is also small. Unknown LWC leads to a larger potential uncertainty especially for low water content.
25 Figure 3m demonstrates the effect of a deviation of the general cloud geometry from the idealised "cloud wall". Absorption band results are simulated for a large spherical cloud here. A cloud sphere with diameter of 2 km is placed at fixed 10 km horizontal distance. In order to vary the angle of the cloud surface relative to the horizon without changes of sensor elevation angle or distance, its vertical and horizontal position is changed (vertically and with respect to distance to sphere center).
θ cloud = 90 • is comparable to the reflected radiance from a vertical cloud surface as shown in the other displays before. The 30 surface tilts away from the vertical towards the cloud top until it reaches a horizontal surface with θ cloud = 0 • . The more horizontal the cloud surface is, the more likely short photon pathes between sun, cloud and sensor become. A retrieval based on the assumption of vertical cloud sides would provide a negative distance bias. An important consequence of this last test is the limitation of the method developed in the next section to cloud sides. Cloud top areas as well as horizontal cloud formations, like stratocumulus decks, should be excluded. It can be expected that an average deviation from the assumption of vertical cloud sides will lead to a systematic effect.

Lookup-table
The retrieval of sensor-cloud distance will be realised through forward simulations describing the relation of absorption ratio R O2A and distance. As mentioned before, the geometry of the observation situation requires 3D radiative transfer simulations.

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As these are very time consuming, strong constraints apply to the affordable computational effort. This leads to the simplification of convective cloud geometry to vertical "cloud walls". Consideration of different or more typical cloud side inclination would be possible in principal -e.g., a cloud surface slightly tilting away from the vertical. However, already at this stage, the derivation method is based on extensive time consuming 3D radiative transfer simulation. Unfortunately the implementation of tilted cloud slopes into an orthogonal x-y-z simulation grid would increase the computational effort to the point of futility, 10 because calculations on a much finer spatial grid would become necessary.
The horizontal distance and the observation geometry (sensor height, sensor zenith angle, solar zenith angle) define the dimensions of a lookup table. All other sensitivities will be neglected and have to be considered as source of uncertainty to be quantified: either because parameters can not be constrained at all (LWC, r eff , cloud horizontal extent, local aerosol and albedo situation), or uncertainties introduced are so much smaller than the above mentioned that the expensive extension of the lookup 15 table with another free parameter seems unnecessary (surface pressure, solar azimuth angle). A detailed uncertainty analysis is provided later.
To generate a lookup table forward simulations are set up for the selected environmental parameters listed in Table 1.
Observation zenith angle θ are discretized in steps of 2 • between 41 • (below horizon) and 99 • (above horizon), cloud distances at 17 values of increasing distance between 0.5 and 60 km, and flight altitudes in steps of 1 km between 2 and 11 km. The 20 cloud for these simulations has the dimensions ∆x = 2km (in viewing azimuth direction), ∆y = ∞ (perpendicular to viewing azimuth angle) and ∆z = 12km (between surface and 12 km height).
For combinations of these parameters reflected radiances are simulated using libRadtran/MYSTIC with REPTRAN medium.
Eight simulated specMACS channels (as labelled in Fig. 3) contribute to the ratio R O2A as defined in Eq. 1.    of polynomial functions p θ,θ0 , one for each sun and sensor geometry, allows for an effective retrieval using these functions to derive distance d = p θ,θ0 (R O2A ). Although the impact of Monte Carlo uncertainty is much reduced through the fitting, it still results in a contribution to the uncertainty to be considered.
With given values of solar zenith angle θ 0 , sensor zenith angle θ and flight altitude this set of polynomial functions provides a distance retrieval for each R O2A measurement. Distance can be retrieved for situations with solar zenith angle between 3 10 and about 60 • . The allowed relative azimuth between sun and sensor view is limited to 45 • . Distance derivation for larger azimuth differences is strongly affected by 3D effects (e.g. shadows). By filtering out cloud tops, which are always more or less horizontal, the impact of non-vertical cloud surfaces will be minimised. Table 1 summarises observed ranges for several environmental parameters during ACRIDICON-CHUVA. As these are either 15 not known or not represented in the forward simulations, they lead to uncertainty for the retrieval based on the oxygen-A ratio R O2A (= R for simplicity in the following). Using these parameter ranges together with sensitivity tests as shown in Fig.3 uncertainties for the ratio are derived. A maximum spread for R O2A can be derived from the observed values, e.g. for pressure R min − R max = R(1005 hPa) − R(997 hPa). In specific observation situations even more extreme local values could be present.

Uncertainty budget
Assuming that R min and R max at least limit the range including 95% of all possible values in a Gaussian error distribution, we can simplify our error estimation. A standard deviation value might then be defined as describing the uncertainty in a specific observation situation due to environmental parameters. If it is further assumed that all uncertainties in Table 1 are independent, we can use error propagation and take the square root of the total of all squared contributions to find an overall uncertainty estimate for the ratio R O2A of about σ R = 2.8%.
These environmental uncertainties are combined with the mentioned Monte Carlo uncertainties and sensor calibration ac-10 curacy (spectral and radiometric) to provide a total error budget. For three different observation altitudes Figure 5 shows an example of the resulting uncertainty budget for derived distance from all sources apart from 3D effects (which are limited by suited filtering of the observation scenes). The shape of these maps with respect to distance and elevation angle is caused by the general cloud/observer geometry. At low altitudes most cloud sides can be observed looking upward, while for high altitudes they are observed looking downward. Relative uncertainties of distance become large (>15%) for distances smaller than 5 km 15 and for viewing zenith angles close to or above the horizon at 90 • . The reasons are the unknown cloud parameters and albedo: If the sought distance signal on absorption is weak, either due to small cloud distance, or due to a shortage of absorbing oxygen (e.g. more horizontal compared to more downward looking observation geometries), the impact of these unknown boundary conditions is stronger. Effects of aerosol situation, Monte Carlo statistics, and sensor accuracy are much smaller. Only at low altitudes the higher aerosol content in these layers has larger impact.
Uncertainties of more than 10% might be too large for most applications of distance measurement.This is also true for the application to cloud side remote sensing intended here (Jäkel et al., 2017;Ewald et al., 2018). The geometrical setup of our application, the vertical localisation of cloud microphysical observations from a flying aircraft, fortunately improves the 5 situation: Relative uncertainty of 10% in horizontal distance maps onto the same relative uncertainty in altitude difference using the observation elevation angle. However, the distance affected this way is only the altitude difference between the point on the cloud and the observer, i.e., the flight altitude. For a cloud altitude of 7500 m and a flight altitude of 5000 m, a relative uncertainty of 10% in distance translates into an altitude uncertainty of only 250 m, or 3%. In the next step height retrieval and connected uncertainty budget will be systematically compared to independent measurements of height.

Comparison to stereo derived distance and height
In order to check the validity of distance and height measurements derived from the oxygen-A band, we compare this data from the specMACS imager to completely independent stereo cloud distance estimates from a 2-D camera system. specMACS observes at a pushbroom geometry to the side, while stereo-matching depends on the tracking of the same image features for different angular position on 2D pictures. The camera used for the latter is a GoPro Hero (manufactured by GoPro, Inc.,

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USA, HD3+3660-023 Full-HD, hereafter GoPro) which was fixed to a side window next to the specMACS sensor during ACRIDICON-CHUVA. It collected RGB images of 1920x1080 pixels size with a total field-of-view of about 90 • x60 • at a frame rate of 30 Hz. The cloud sides observed by specMACS were visible in the 2D imagery due to GoPro's much wider field-of-view along and across-track. In order to compare results for cloud distance from both systems, an accurate temporal and geometrical matching of the data sets is necessary. Automation of this matching is tedious, in particular because mounting With these values and our analysis shown in Figure 5 it seems likely that oxygen-A retrievals produce similar values for clouds up to 10 km distance. For more distant clouds (and especially for distances above horizon and for strong 3-D effects) the uncertainty of oxygen-A retrieval uncertainties are larger than these values. However, for distances above 10 km stereo methods uncertainties are most likely increasing too, as camera projection uncertainties in these methods lead to distance 15 dependent uncertainty contributions. Figure 6 shows a comparison of oxygen-A derived distances and stereo derivations from Jäkel et al. (2017) for an example case. A systematic comparison to several hundred stereo derived positions is shown in Figure   7.
One minute of specMACS data at 745.5 nm wavelength from ACRIDICON-CHUVA flight AC18 on 28-09-2014 around 18:51 UTC at an altitude of 9.1 km is shown in Figure 6a. Data was collected by specMACS along the time axis with a 32 • 20 spatial field-of-view across track (dark current calibration at around 18:51:10 UTC). The sensor is looking sideward centred at 5 • below horizon with respect to the aircraft orientation (here 85 • sensor zenith angle). The solar zenith angle was 37.5 • and the relative azimuth angle 177 • . That means, the sun was almost exactly in the back of the observing sensor. Figure 6b shows the oxygen-A ratio R O2A for this case. Obviously the measured ratio is strongly depending on distance. While nearby clouds at low sensor zenith angle show large values, corresponding to short absorption path lengths, distant clouds towards horizon 25 show much smaller R O2A values due to much larger absorption path lengths. Cloud tops have the tendency to display shorter absorption paths and larger ratios due to 3D effects. In a similar way flat horizontal surfaces display shorter absorption pathes than vertical cloud parts. Likely reason is the 3D cloud surface orientation effect as deomstrated in Fig. 3m. Shadows are rare at this solar illumination and they are only casted on the lower cloud parts (e.g. central cloud element at 75 • sensor zenith angle).
If present, they display relatively long absorption paths and smaller ratios than the rest of the cloud, because these parts are 30 only illuminated by indirect, scattered light. Using the method described in Section 2.2 values of R O2A can now be attributed to distances depending on observation zenith angle . Then distances are translated into vertical height values, using the flight altitude (here 9.1 km) and observation zenith angle (Fig. 6d).   Figure 6c range from 13.7 to 24.1 km. The related oxygen-A distances are somewhat lower between 10 and below 20 km distance. For the reasons mentioned earlier, the 5 difference between the derived cloud heights from stereo and oxygen-A data in Figure 6d is less striking.
The systematic analysis in Figure 7a reveals that the tendency to underestimate stereo distances is typical for many cases.
From 27 cloud scenes 519 stereo points were identified within specMACS data. 233 of these are not considered for quantitative comparison (grey points, removed manually) , because they are located very close to cloud tops (e.g. the top two points in Fig. 6), they are located at angles more than 15 • below horizon (four lowest points in Fig. 6), cloud geometry observed was a 10 horizontal cloud deck and not a cloud side, or they are located in cloud shadows. The 286 coloured points in Figure 7a remain for analysis. Data points from the above example show up in a bright turquoise colour close to the centre of the figure. 27 different colors stand for the 27 cloud scenes analysed.
The group of points filtered out is not only responsible for most of the larger deviations, but also shows the large error estimates provided directly by the oxygen-A retrieval. Apparently we filtered the correct points, difficult to retrieve for different reasons, before quantitative analysis. The remaining points line up along the 1:1 line with a noticeable offset for a majority of 5 the points. The oxygen-A method seems to underestimate distance. If a linear polynomial fit is applied to all remaining points, an almost perfectly parallel line with a slope parameter of 0.97 and an offset of 3.76 km is found. These parameters do not strongly depend on the point filtering applied.
After careful analysis of other possible sources, we conclude that this offset of about 3.8 km towards shorter distances in the oxygen-A method is mainly caused by the strength of the typical 3D effects not considered in the retrieval. Order of magnitude 10 and sign of the effect is consistent with the sensitivity tests using a cloud sphere in Figure 3m. A constant offset would be a consequence of systematically shortened absorption pathes due to the dominating geometry in the observed cloud scene. As a consequence, for the cloud height derivation in these ACRIDICON-CHUVA flights a simple distance offset correction of 3.8 km to all distances derived from oxygen-A data seems reasonable. This approach will not produce bias-free results for each individual scene as cloud geometry and viewing perspective vary between scenes. Figure 7a shows groups of coloured points 15 (different cloud scenes) with different offsets. Still for these a partial bias will remain. Mostly in the order of 1-2 km. For other cloud types the approach would have to be adapted (e.g. more horizontal cloud layers) or different observer perspective (e.g. ground-based). Without auxilliary means of distance determination, this "calibration" step could be achieved from a small set of 3D forward radiative transfer simulation results for synthetic cloud cases, e.g., from cloud resolving modelling. This possibility and our conclusions regarding the role of 3D effects are illustrated in the discussion and conclusion section. As last step of this method, distance has to be translated into cloud height using the flight altitude and the sensor zenith angle.

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As pointed out before, differences are diminished during this step due to the fact that only the vertical difference between cloud and flight altitude is affected by the uncertainties. This becomes obvious in Figure 7b. After offset correction, the comparisons points closely line up along the 1:1 line. 86% of all height value comparisons coincide within the uncertainty expectations, which implies that real uncertainties for the cloud height might even be smaller than the error budget predicted. The remaining standard deviation assuming a Gaussian distribution for the difference between stereo and oxygen-A derived distances is 490 30 m. The number is strongly influenced by a few large "non-Gaussian" outliers. The median absolute difference value, the typical difference of a single point, is 11% (1.6 km) for distance and 4% (230 m) for height.
The instrumentation of the ACRIDICON-CHUVA HALO campaign lacked a method to provide cloud localisation important for the application of cloud remote sensing data. Thus, a method was presented to derive cloud distance and vertical position of cloud elements from sideward viewing observations in the oxygen-A band using data from the specMACS imaging spectrometer. A distance derivation from cloud side reflected radiance was presented. Using this method, a straight forward possibility is 5 provided to assign a position in space to all products derived from the same sensor. First main goal is the provision of a height value to generate cloud particle size or phase profiles averaged over whole convective clouds or cloud ensembles, a second goal the provision of a cloud surface orientation to be used to reduce the impact of 3D radiative effects on microphysics retrievals (see Jäkel et al., 2017;Ewald et al., 2018).
Uncertainties of the method have been characterised by radiative transfer experiments. The validity of the derived distance 10 and height values and of their error budget calculations have been corroborated by comparison to a substantial number of stereo derived values from Jäkel et al. (2017). We find an average offset between both data sets of 3.8 km. If this offset is corrected, typical observed differences lie in the range expected from the error budget. Observed differences from the stereo derived values are somewhat larger which could be due to uncertainties in the stereo deviation itself.
For the large offset we simply use as a correction factor we consider 3D cloud geometry itself to be the most likely reason: 15 cloud side geometry is not considered completely correct in the retrieval method due to computational limitations. Starting point of the derivation method is the simplification of cloud geometry into vertical cloud walls. A cloud side tilted away from the vertical towards the horizontal decreases the typical in-cloud oxygen absorption path contributions compared to a vertical cloud. This is especially noticeable approaching (horizontal) cloud tops, but is true to some extent for most real, not perfectly vertical cloud sides. On average over all cloud situations and distances, the value of the reduction of absorption path for the 20 observed convective cloud fields with respect to the simulated absorption path is surprisingly constant around 3.8 km. Other candidates for the observed offset are albedo or aerosol missmatches with respect to the lookup table values (table 1). However our sensitivity tests which lead to the shown uncertainty bars in Figure 7 point to impacts below 10% uncertainty for most data points. The stability and size of the effect over a large number of flight situations and cloud geometries and the consistency with the expectation that non-vertical cloud surfaces would have just this effect, point to the 3D geometry as the reason for this result.

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Nonetheless, variation between cloud scenes (different colors) could also be due to albedo or aerosol variations. The method presented uses a constant offset for compensation. For the given ACRIDICON-CHUVA cases' typical observation perspectives and hence the dominant cloud surface orientation observed, this is found by comparison to stereo values. In the future, this limitation might be overcome by a method using "vertical cloud wall" results as presented as first guess, allowing for a first approximate derivation of cloud surface orientation and using forward simulations for varying cloud tilt to iteratively improve 30 results. The computational effort necessary for such an approach exceeds the resources available for this study. Alternatively, a simple "calibration" of the method as presented could also be reached using a small set of selected 3D simulations. A small number a few hundred test results (as in our comparison to stereo points) at a low Monte Carlo accuracy -a high noise levelwould be sufficient to characterise a single typical offset value. It could be provided at a limited computation effort. In Figure 8 an example of the 3D cloud geometry impact on the method is shown for a synthetic cloud observation. For this demonstration an available mid-latitude cumulus case was used. Of course this scene can not be expected to be fully comparable to the tropical cumulus congestus cases during the ACRIDICON-CHUVA campaign. Still it illustrates this possibility and at the same time displays once more a the impact of 3D cloud geometry at the observed order of magnitude. The case is taken from an ICON-LEM (Icosyhedral Nonhydrostatic weather model -Large Eddy Model) run for Germany with a spatial resolution of 5 165 × 165 × 165 m with a two-moment microphysics model package (Heinze et al., 2017). True cloud distances shown in Fig.   8b range between 8 and about 20 km. The application of the oxygen-A band retrieval to these simulations results in deviations of a few hundred metres to a few kilometres from the true distance. As already seen in the comparison of stereo and oxygen-A band values, for the synthetic test the deviation is negative almost erverywhere too (distance derived from oxygen-A is too small). For this case the mean deviation over the whole scene is 2.1 km. As all parameters in this synthetic test case are fixed to 10 the values used in the lookup-table of the method, only remaining candidate source of deviation is the specific 3D geometry of this cloud case. Here the central part of the cloud field systematically tilts away from the vertical with values close to vertical at the cloud lower edge and almost horizontal cloud top for the top line of analysed pixels.
In the future a consideration of such cloud surface orientation caused systematic differences could be possible by including additional forward solutions for arbitrarily tilted cloud surfaces using into the lookup-table with the help of far more extensive 3D radiative transfer simulations and iterative approaches. The overall accuracy of oxygen-A derived heights apart from this cloud geometry impact is comparable to the accuracy of a stereo image based approach for the application to aircraft observations, A clear advantage of the presented absorption method is that it is not limited to individual features of high image contrast 5 (as the stereo method), but provides distance over large continuous areas (apart from cloud tops and shadows). It provides the cloud heights on the sensor coordinate grid which facilitates evaluation of other information on the same grid.
Eventually a full integration of stereo and absorption approach into one method might be a beneficial approach, as advantages of both methods could be combined. At cloud tops and horizontal edges where the oxygen absorption is strongly affected by 3D cloud geometry effects, stereo methods can most easily provide information as image contrast is high. In cloud regions where 10 geometry variation is small, it is impossible to identify points of high contrast for the stereo method, but oxygen absorption still provides reliable information.
The actual specific goals of the presented retrieval are the provision of vertical location for the determination of particle size and phase profiles of convective cloud fields from spectral cloud side remote sensing and the provision of cloud surface orientation for improved microphysics retrievals (Jäkel et al., 2017;Ewald et al., 2018). To this end, oxygen-A band based Author contributions. U. Schwarz developed a first tested the approach and sensitivities in a Master's thesis. Based on his work T. Zinner