The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS; ) was an infrared Fourier-transform spectrometer (FTS) aboard the ESA satellite Envisat. It measured the spectral range from 685 to 2410 cm-1, with a spectral resolution of up to 0.025 cm-1. We employ here the reduced (or optimized) spectral resolution of 0.0625 cm-1 that was used in the majority of its operational years. Similarly, we employ the vertical sampling of ≈1.5 km in the upper troposphere–lower stratosphere (UTLS), which was mostly used from 2005 till the end of operation in 2012 (RR27/nominal mode). We assume for the synthetic simulation of MIPAS measurements a horizontal sampling of 420 km that was used in the period from 2005–2012 and the vertical field of view, which has a full width at half maximum of roughly 0.06∘ (equivalent to about 3 km vertically; e.g., ).

The Gimballed Limb Observer for Radiance Imaging in the Atmosphere (GLORIA; ) is an airborne imaging Fourier-transform spectrometer capable of acquiring more than 6000 interferograms with its 128×48 detector pixels used in less than 2 s. This enables it to measure a full atmospheric profile at once. The horizontal dimension across the line of sight is currently only used to increase the signal-to-noise ratio by averaging but could be exploited as well, e.g., for imaging small-scale cloud structures. The interferogram acquisition time can be adjusted between fast measurements with coarse spectral resolution and slow measurements with a high spectral resolution over the effective spectral range from 780 to 1400 cm-1 . The spectral sampling is configurable between 0.625 cm-1 (roughly 2 s acquisition time) and 0.0625 cm-1 (roughly 10 s acquisition time). The effective spectral resolution is roughly a factor of 2 worse than the sampling due to the employed Norton–Beer apodization . A unique feature of GLORIA is its capability to point the instrument towards different directions relative to the aircraft heading. This allows for the measurement of air masses at an angle between 45∘ and ≈132∘ with respect to the flight direction. By constantly panning the instrument over the available angles, the same air masses are measured from multiple directions, which enables the tomographic reconstruction of three-dimensional structures . In addition to the IR instrument, there is also a standard camera with three channels (red/green/blue) operating in the visible range that observes a much wider field of view.

GLORIA has been operated successfully during multiple campaigns on both the German HALO research aircraft and the Russian M-55 Geophysica. The measurements discussed later were taken on 18 September 2017 during the Wave-driven ISentropic Exchange (WISE) campaign based in Shannon, Ireland.

The Imaging IR Limb Sounder (IRLS) is a concept for an Earth-observing satellite instrument that was originally proposed for the ESA's seventh Earth Explorer program. It is, effectively, a GLORIA-like instrument in space with a fixed viewing direction backwards compared to its flight direction. This configuration also allows for the tomographic 3-D reconstruction of the measured atmosphere. While the PREMIER IRLS offered higher spectral resolutions, we focus here on the spatial capabilities and thus assume a spectral sampling of 1.25 cm-1 and 15 horizontal measurement tracks covering ±3.5∘, as well as an along-track sampling of 50 km. For the vertical sampling, we assume a pixel pitch of 0.014∘, which corresponds roughly to a vertical sampling of ≈700 m in the troposphere. These capabilities are in line with those of the GLORIA instrument and thus certainly achievable. They correspond to the “dynamics mode”, which was envisioned to be used for about half of the instrument measurement time; its primary purpose was a high spatial resolution to reveal processes associated with mixing and convective outflow in the UTLS, as well as three-dimensionally resolving gravity waves to determine momentum fluxes driving global circulation systems .

The Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP; ) is a nadir-viewing lidar on the CALIPSO satellite, which is part of NASA's A-Train. CALIOP provides high-resolution vertical profiles of cloud and aerosol properties, with a vertical resolution of 60 m below 20.2 km and 180 m above and an along-track resolution of 5 km. We used cloud extinction data from the L2CPro V3.01 product files of the full month of December 2009 to generate test cases of realistic 2-D cloud scenes for the limb-viewing geometry using a radiative transfer model (see Sect. ). In addition to the given extinction values, we also used a data set for which we reduced the supplied extinction values by an order of magnitude. This allows us to explore the sensitivity of limb sounders with respect to clouds that are thinner than those present in CALIOP level 2 products.

For pressure and temperature in the cloud scene simulations based on CALIOP data and as a priori in all retrievals, ERA-Interim data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF; ) were employed. The model data are available in 6 h time steps with the T255/L60 resolution, which corresponds to a horizontal sampling of ≈80 km. Quadrilinear interpolation is used for resampling the model onto the needed grids, whereby pressure is interpolated in log space. The horizontal wind speeds and diabatic heating rates from the ECMWF ERA-Interim data were also used for the calculation of backward trajectories using the Chemical Lagrangian Model of the Stratosphere (CLaMS) model introduced in the next section.

As CALIOP only provides vertical 2-D slices, we turned towards simulations generated by the Chemical Lagrangian Model of the Stratosphere (CLaMS; ) for providing realistic 3-D cloud structures. The CLaMS-ICE module includes a double-moment bulk microphysics scheme for modeling cirrus clouds i.e., ice water content and ice crystal number;. The box model runs in a forward direction on backward trajectories (24 h) started from points on a regular grid with user-defined resolution and extent in longitude, latitude, and pressure space. A resolution 0.25∘ in the horizontal and 0.5 km in the vertical domain is used for resolving finer cirrus structures compared to the original ERA-Interim resolution. For initialization, cloud ice water content and specific humidity from ERA-Interim are spatially interpolated to the CLaMS-ICE starting point of each individual trajectory.

The trajectories are calculated on hybrid potential temperature coordinates, which allows transport processes to be resolved in the troposphere that are influenced by the orography and transport processes in the stratosphere, where adiabatic horizontal transport dominates.

To reduce the computational effort of the radiative transfer model, we transform the ice water content and radius information supplied by the CLaMS-ICE module to a simple extinction coefficient by the formula of : E=A⋅I⋅R-1, with E being extinction in km-1 at 804 nm, A=1500 mm3g-1, I the ice water content in gm-3, and R the radius of particles in µm.

This paper employs the JUelich RApid Spectral Simulation Code version 2 (JURASSIC2), which is a radiative transfer code optimized for large-scale and tomographic simulations and retrievals . It includes capabilities from computing spectrally resolved radiances line by line to using spectrally averaged lookup tables for extremely fast computations. The algorithmic adjoint model allows for its efficient use in retrieval schemes (employing the JUelich Tomographic Inversion Library; JUTIL) and data assimilation in general. JURASSIC2 has been exemplarily used for the analysis of CRISTA-NF data e.g.,, for the study of clouds and aerosol using MIPAS data e.g.,, for the operational processing for the GLORIA instrument e.g.,, and for studies on the aerosol layer in the Asian Summer Monsoon .

In this study, the emissivity growth approximation e.g., is used in combination with precalculated lookup tables of optical path (also called optical depth or thickness) in relation to temperature, pressure, and volume mixing ratio to quickly compute radiances and derivatives with respect to temperature in a discrete representation of the atmosphere. The tables were computed using a line-by-line model convolved with the respective instrument line shapes, which for FTSs mostly depend on the interferogram length and apodization employed.

JURASSIC2 is also used to compute lines of sight and tangent points in this study using a simple refraction scheme by .

Simulations with JURASSIC2 for MIPAS-like and IRLS spectra employed the trace gases CCl4, CFC-11, H2O, HNO3, and O3 with climatological values . A ray-tracing step length of 5 km was employed. For both MIPAS-like and IRLS measurements, the spectral samples from 787.50 to 796.25 cm-1 and from 831.25 to 835.00 cm-1 were used, albeit with different spectral sampling for each instrument of 0.0625 and 1.25 cm-1, respectively, and a strong Norton–Beer apodization . We simulated synthetic MIPAS-like and IRLS radiances for all CALIOP extinctions of December 2009 and these microwindows.

A practical method for identifying a radiance measurement of a cloud is the so-called cloud index (CI), first introduced by . The CI is a color ratio, defined as the ratio between the radiance averaged over a spectral region with a strong emission feature, such as the CO2 Q branch at 12.6 µm, and the radiance averaged over an atmospheric window, such as the one located at 12 µm. It is a dimensionless quantity with a slight dependence on latitude and season. For given tangent point altitudes, one can derive specific thresholds that separate cloudy measurements from others. Typical CI values in cloudy conditions are between 1.1 and 6 . The lowest detectable extinction from a space-based limb emission measurement within the atmospheric window at 833 cm-1 is of the order of 2×10-5 km-1 . For IR limb emission measurements the clouds are termed optically thick when the CI profile at and below cloud altitude runs into saturation, which occurs for extinctions of 5×10-2 km-1 and higher . Here, we employ altitude-dependent thresholds of to determine if an index indicates a cloud. For optically thin conditions, the CI correlates well with extinction and the integrated volume density or area density path along the limb path . The latter differentiation depends on the particle radius range, where larger median radii, typical of ice clouds, correlate with the area density. Although the CI approach is an effective and computational cheap detection mechanism for thin and thick clouds, its information content is limited when retrieving cloud information below the cloud top, as clouds affect the CI of clear air below, and hence, the cloud detection thresholds are not effective in distinguishing clear air from cloud below the cloud top.

The cloud index is also sensitive to an increased aerosol load such as that caused by, e.g., volcanic eruptions, wild fires, or dust storms. The highly sensitive altitude-dependent CI thresholds will certainly also detect enhanced aerosol levels. Using additional detection and classification methods e.g., can provide a distinction between ice clouds and aerosols with a different spectral signature. The synthetic studies below disregard aerosols for simplicity's sake.

This section describes two different approaches to the spatial detection of ice clouds from measured infrared limb spectra. The first approach builds on the CI method e.g.,, which can detect the presence of a cloud in a measured spectrum. Previous satellite instruments, such as MIPAS-Envisat , have a comparatively coarse measurement pattern, where individual lines of sight of measured spectra do not usefully intersect (at least in the most common operation modes). Figure  shows the lines of sight of measurements of a MIPAS-like instrument and the assumed IRLS. At lower altitudes, the lines of sight of MIPAS do not overlap at all in the tangent layer. In contrast, the IRLS has a very fine measurement grid, where many lines of sight overlap to the extent that the lines of sight of the immediately neighboring measurements of one altitude overlap at their tangent point altitude. This overlap of the IRLS lines of sight allows for the application of tomographic methods e.g., and even requires them to utilize the instrument to its full capacity.

The first proposed spatial detection method is a two-dimensional evolution of the CI method, described in Sect. . The cloud detection is improved by taking into account not only the tangent point of a measurement but instead the full extent of and overlap within the tangent point layer. This extension already allows for the exploitation of the increased sampling density of IRLS-like instruments.

In addition, a much more computationally involved method is proposed in Sect. . This method deduces the atmospheric extinction values of clouds in a tomographic nonlinear inversion that has so far been mostly used to derive temperature and trace gas concentrations.

In a first step, we compare the cloud indices as gained from MIPAS-like and IRLS spectra. Figure b shows the CI for the simulated spectra based on an exemplary CALIOP cross section and the MIPAS measurement grid and spectral resolution. The simulated radiances were generated using the grid defined by the CALIOP L2 data shown in Fig. a. The “pixels” corresponding to MIPAS measurements in Fig. b are very coarse compared to the fine structure of the clouds contained in the CALIOP data due to the much sparser horizontal sampling density of the MIPAS instrument. Figure c shows the IRLS simulations. The increased spatial sampling density results in a much finer sampling of the clouds, but the bow-like artifacts due to the optically thick atmospheric conditions become apparent. These are also given in the synthetic MIPAS data but are barely discernible due to the coarse measurement grid. Figures d–f show the same situation but with CALIOP extinction reduced by a factor of 10. These numerical experiments shift the focus to very thin clouds that may not be present in the original data set.

The results of the convex hull CI algorithm are exemplarily depicted in Figs.  and . Figure  shows the results for the MIPAS instrument, while Fig.  shows the result for the IRLS instrument. For MIPAS, no obvious differences between CI and the convex hull CI are apparent. The minor visible discrepancies can be attributed to the difference between the tangent point grid of the CI and the rectilinear grid on which the convex hull CI algorithm operates. In contrast, a noticeable improvement can be seen for the IRLS measurements. The convex hull CI algorithm reduces the bow-like structures around thin clouds. Especially the comparatively small structures at 38∘ N have a much reduced size, more aligned with the true structure as shown by the extinction contour. But a deficit is also apparent. Below thick clouds, no actual measurement information is present, and the CI is (wrongly) attributed to the tangent point location. This will still cause an overestimation of cloud presence.

This section presents some results of the extinction retrieval. Figure  shows the extinction retrieved for the same extinction distribution derived from CALIOP data for MIPAS and IRLS data for one of the 440 processed cross sections. Both retrievals were set up identically with the difference that Fig. b used simulated MIPAS measurements and a coarser horizontal retrieval grid (≈160 km) and Fig. c used simulated IRLS measurements. The MIPAS-based retrieval is both horizontally and vertically coarser in comparison to the IRLS retrieval as required by the different measurement grid. The results are generally more accurate than the picture provided by the CI in Fig.  as even for the coarse MIPAS measurement grid, the overlap of measurements at higher altitudes can be used to constrain the location of thin clouds better. The retrieval using the IRLS measurement specification in Fig. c offers a much better resolved result. The finer spatial sampling and the reduced field of view allow us to see below clouds with clear-sky conditions, as with the equatorial high cirrus cloud. We also encountered similar conditions with our airborne instruments GLORIA (see below) and CRISTA-NF . The location of clouds, expressed in increased values of extinction, is more precise and much closer to the actual extinction distribution compared to the CI-based methods. Some artifacts remain below thick clouds, where, due to their opacity, no or nearly no measurement information is present. As such, the values below 9 km at 20∘ S are not reliable. On the other hand, the weak structures at and above 15 km are well reproduced. Obviously, the retrieval works better for optically thin conditions.

This section aims to quantify the performance of the 2-D convex hull CI and the 2-D tomographic extinction retrieval algorithms with respect to cloud top height estimation. We focus here on the capabilities of the IRLS instrument. Figure  shows an exemplary CALIOP orbit with detected cloud extent according to the CALIOP extinctions (extinction larger than 10-4 km-1), cloud index (CI), convex hull cloud index (convex hull CI), and tomographic extinction retrieval (extinction larger than 3×10-4 km-1). A slightly larger threshold is employed here, as the smoothing by the regularization extends the rather large extinctions vertically, and a smaller threshold would thus lead to a systematic overestimation of cloud extent. One can immediately see that all methods typically agree within about 1 km, with larger errors occurring at the border of extended cloud regions.

Table  shows the numerical results for the cloud top height derived by the three algorithms for 440 semi-randomly selected CALIOP orbits (we arbitrarily picked 1 month of data). Using unmodified CALIOP extinctions, the CI shows a positive bias of 1.08 km with a standard deviation of 2.29 km. There are two major sources for a high bias. First, the field of view of the instrument causes an overestimation of cloud top altitude, especially for thicker clouds e.g.,. Second, and more importantly, the cloud is horizontally extended, causing cloud detection events beside the actual cloud, where no cloud is in the original data e.g.,. The second effect mainly causes the large variance in the results. As expected, the convex hull CI algorithm significantly reduces this bias, whereby the tomographic extinction retrieval even seems to be superior. Both are capable of reducing the impact of “horizontal cloud lengthening”. For thinner clouds, the situation improves all around. Using clouds that are an order of magnitude thinner, here, the CI shows a bias of only 0.66 km. For optically thinner clouds the general cloud top height overestimation is reduced or even turns into an underestimation , and the horizontal cloud lengthening is also reduced (Fig. ). The bias of the convex hull CI algorithm and the tomographic extinction retrieval are both on the order of 160 m, whereby the extinction retrieval has a reduced standard deviation compared to the convex hull algorithm.

As the overestimation of the horizontal extent of clouds strongly affects the cloud top altitude comparison, we examined more closely how well the shape of the cloud top is reproduced. In a first step the true cloud top is determined from CALIOP extinctions. Using the tomographic extinction retrieval grid, all cloud top grid boxes plus all boxes within two squares' distance (Manhattan norm, ±1 km vertically, ±50 km horizontally) are selected for comparison. The results are collected in Table . The table shows an increase for correctly identified cloudy pixels for the three methods, with the conventional CI being worst and the tomographic extinction retrieval being best. False positives decrease accordingly. However, there is a slight increase for false negatives, which is caused by horizontally small clouds that are filtered away by the convex hull CI as the CI is pushed below the threshold and for which the tomographic extinction retrieval determines an extinction below the threshold (potentially due to slightly smearing out the cloud). This is confirmed by the numbers for the scaled extinction test cases, for which the number of false negatives increases across the board.

This section describes the result for the convex hull algorithm CI for the CLaMS-ICE-model-based simulations that allow for the simulation of the across-track coverage of the IRLS instrument in contrast to the CALIOP-based simulations that allow for only a simulation of the center track.

Figure  shows horizontal cross sections at several pressure levels through the extinctions derived from the 3-D CLaMS-ICE ice water content simulation. The center of the simulated IRLS measurements follows the 19∘ W meridian. Actual satellite measurements of the instrument will not follow a perfect polar orbit, but for the simulations, the difference is negligible and simplifies the simulation setup. One can see a cloud field on the left-hand side on lower altitudes and a second cloud field on the right-hand side at different altitudes. At higher latitudes, the two cloud fields merge. This situation gives a nice across-track variation over the images of the IRLS that can be examined in the following.

This variation can be seen better in Fig.  that shows the CLaMS-ICE extinction as “images” as the IRLS would see them. Each “pixel” of the picture corresponds to one pixel of the IRLS, but the horizontal coverage is slightly larger by 2 pixels. The IRLS would take roughly twice as many images of the situation than depicted here. The depicted images cover the latitudes from 39.1 to 64.6∘ N. The simulation ends shortly beyond these latitudes. The images show a two-layered structure on the left-hand side between 42.7 and 51.9∘ N. Northward of 46.4∘ N, one can see the second cloud structure to the right, first with rather faint extinctions and then higher ones until the two structures join around 61∘ N.

The measurements of the individual tracks can be treated individually as singular cross sections and may be assembled in a second step. As MIPAS only measured a single track, no MIPAS simulations are shown here for comparison as the results will not be different from those of Sect. .

The computation of the conventional CI and the application of the cloud index threshold are depicted in Fig. a and b. Similar to the simulations of Sect. , the cloud extent is overestimated to the sides of the clouds and below. The result of the convex hull CI algorithm is shown in Fig. c and d. One can see again that the new algorithm follows the true extinction more closely. In the case of the central track (Fig. e), it becomes apparent that the chosen value for extinction of 10-3 km-1 is not the true detection limit as the faint cloud structure in the center track below that limit is also detected by the CI.

The individual tracks can then be assembled into a three-dimensional view on the cloud structure. Figure a shows a three-dimensional representation of the true extinction distribution. The zonal extent is limited by the measurement coverage of the IRLS. One can see the across-track and along-track variation as well as the vertical structure. The result of the convex hull CI algorithm is presented in Fig. b. The three-dimensional results agree similarly to the cross sections discussed before. The cloud extent is slightly overestimated horizontally, and the vertical structure of the cloud is lost; the bottom of the cloud is often located lower than in the actual extinction structure. Also, the very small spot of a cloud to the south was not detected.