HIPÓTESIS

The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is an infrared limb sounder with a Fourier Transform Spec-trometer (FTS) developed for deployment on an aircraft (Friedl-Vallon et al., 2014; Riese et al., 2014). GLORIA combines a classical Michelson interferometer with a 2-D detector array. It measures the infrared ra-diation in the spectral range from 780 cm⁻¹ to 1400 cm⁻¹ (Figure 3.2), which is emitted by particles and trace species in the atmosphere. The interferometer spectrally resolves this radiation to reveal characteristic molecular emission bands. The 2-D detector array consists of 256× 256 pixels, out of which 48 horizontal× 128 vertical pixels are used to de-crease the read-out time. GLORIA provides more than 6 000 simulta-neous limb-views with elevation angles ranging from −3.3° to slightly upwards. Thereby, an altitude range from 4 km up to flight altitude around 15 km is covered. To increase the signal-to-noise ratio, all pixels of one detector-row are added to superpixels. Even though this co-adding reduces the horizontal resolution of trace gas and temperature retrievals in flight direction slightly, it improves the measurement quality drastically. Further, one has to keep in mind, that the horizontal resolu-tion across flight direcresolu-tion is much worse than in flight direcresolu-tion, which means the slight reduction in flight direction does not change the infor-mation content gained from these measurements. The horizontal point spread function (PSF) of these superpixels is 1.5°, which corresponds to 6.7 km at an altitude of 10 km.

GLORIA’s line of sight (LOS) aims towards the horizon - also called limb of the Earth - on the right side of the aircraft. These straight LOSs get a parabolic shape when plotted in a cartesian coordinate system with x-axis following the Earth’s surface (Figure 3.3 a). The point of the LOS which is closest to the earth surface is called tangent point. Due to the exponentially declining density of the atmosphere with altitude, most

3.2 GLORIA 41

Figure 3.2: Infrared spectra measured by GLORIA on 25 January 2016 at 10:14 UTC. Shown are co-added spectra of the 128 superpixels. The spec-tral ranges used for the retrievals in this thesis (see Table 3.4) are highlighted in grey.

radiation along the LOS is emitted at lower altitudes and, thus, around this tangent point. Moreover, for geometrical reasons, a comparatively long part of the LOS samples altitudes close to the tangent point, while higher atmospheric layers are passed only briefly. As a consequence, limb sounders are in general more sensitive to changes in the atmo-sphere around the tangent point. The temperature weighting function in Figure 3.3 b, which is a measure for the amount of measured radiation originating from a certain point in space, demonstrates this nicely. The horizontal resolution of limb sounders along LOS can be calculated from the full width at half maximum (FWHM) of this temperature weighting function. For conventional limb sounders this resolution along LOS is on the order of 200 km to 300 km (Riese, 1994; von Clarmann et al., 2009;

Ungermann et al., 2012).

GLORIA is operated in two different modes: The chemistry mode, which has a high spectral sampling of 0.0625 cm⁻¹, and the dynamics mode with a coarser spectral sampling of only 0.625 cm⁻¹. The coarser

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Figure 3.3: In Panel (a) a simple schematic of the limb sounding geometry is given. The airplane is flying orthogonally into the paper plane. Images taken under 90° azimuth cover the dark grey area with LOSs. The respective tangent points (bright coloured dots) increase in distance with decreasing altitude. The tangent points of forward and rearward looking images (light grey and pale coloured dots) are closer to the flight path. The LOS, which are straight lines in reality, have a parabolic shape in this plot due to the transformation into a cartesian coordinate system with x-axis following the earth surface. Panel (b) shows the weighting function along three different LOSs indicating the con-tribution of the respective part of the atmosphere to the observed signal. In panels (c) and (d) the principles of LAT and FAT with the GLORIA instrument are depicted, respectively. Shown are top views in bird perspective onto the flight path. The dots again indicate the tangent points and are coloured ac-cording to their altitude. Each grey sector indicates one horizontal scan from 45° (right forward) to 135° (right backward). The lighter the grey, the later in time are these measurements taken. Figure from Krisch et al. (2018).

3.2 GLORIA 43

spectral sampling leads to a faster interferogram acquisition and accord-ingly an improved spatial sampling in flight direction (at 10 km altitude 0.45 km instead of 2.25 km). The horizontal resolution in flight direc-tion, is not dominated by the spatial sampling but by the point spread function (PSF) of the detector and is on the order of several kilometres for both measurement modes depending on the tangent-point altitude.

The improved spatial sampling of the dynamics mode is used to scan the atmosphere horizontally in steps of 4° from 45° (right forward) to 135° (right backward) with respect to the aircraft’s heading (Figure 3.3 c).

In this way, the same volume of air is measured under different angles, which allows for tomographic retrievals (Natterer, 2001). With this con-cept the horizontal resolution can be improved by up to an order of magnitude. The exact values of the spatial resolutions in all directions, depend on the specific measurement pattern and retrieval set-up and are discussed separately for each presented retrieval in the respective chapters.

Measuring emitted radiation from all 360° around the volume, for instance, by flying a hexagon, is called full angle tomography (FAT, Figure 3.3 d). In contrast to FAT, limited angle tomography (LAT, Fig-ure 3.3 c) does not measFig-ure the volume from all sides but only from a limited set of angles. Due to the horizontal scanning capabilities of the GLORIA instrument, this is already possible on a linear flight path. How-ever, LAT inversion problems are in general seriously ill-posed (Natterer, 2001). Well-posed problems in the mathematical term are defined to have a unique and continuous solution (Hadamard, 1902). If a problem does not have a solution or the solution is not unique or not a contin-uous function of the input parameters, the problem is called ill-posed.

Problems with multiple solutions can often be converted to well-posed problems through adding a priori knowledge in form of regularisation terms.

Using FAT allows for the 3-D reconstruction of a cylindrical volume.

The diameter of this volume depends on the flight path and is usually on the order of 400 km. The volume which can be reconstructed with LAT is given by the tangent point distribution. Tangent points of forward or backward looking measurements are closer to the flight path then those

with an azimuth angle of 90° (see Figure 3.3 a). At higher altitudes, the tangent points are closer together and thus the horizontal resolution across flight track is higher. At the same time the horizontal extent of the tangent point covered area is smaller at higher altitudes. In the verti-cal, the volume covered by tangent points has a banana-like shape with increasing distance to the flight path and increasing horizontal extent with decreasing altitude. At 10 km altitude, the horizontal extent of the measurement volume across flight track is on the order of 150 km.

Using LAT, all overlapping measurements of an air parcel are taken less than 15 min apart. In contrast, the acquisition time of the full angle tomogram acquired on the 25 January 2016 above Iceland was 125 min.

Thus, LAT is more suitable for measurements of transient gravity waves and gravity waves in a fast changing background wind, whereas for FAT steady gravity waves with a ground-based phase speed of approximately 0 are needed. Further advantages and disadvantages of FAT and LAT for gravity wave measurements are discussed in Chapter 5, where the sensitivity of both measurement methods to gravity waves is studied in detail.