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Investigating Gravity Waves in Polar Mesospheric Clouds Using Tomographic Reconstructions of AIM Satellite Imagery

V. P. Hart Utah Valley University, [email protected]

M. J. Taylor Utah State University, [email protected]

T. E. Doyle Utah Valley University

Yucheng Zhao Utah State University, [email protected]

Pierre-Dominique Pautet Utah State University, [email protected]

B. L. Carruth

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Recommended Citation Hart, V. P.; Taylor, M. J.; Doyle, T. E.; Zhao, Yucheng; Pautet, Pierre-Dominique; Carruth, B. L.; Rusch, D. W.; and Russell, J. M. III, "Investigating Gravity Waves in Polar Mesospheric Clouds Using Tomographic Reconstructions of AIM Satellite Imagery" (2018). Publications. Paper 27. https://digitalcommons.usu.edu/ail_pubs/27

This Article is brought to you for free and open access by the Atmospheric Imaging Laboratory at DigitalCommons@USU. It has been accepted for inclusion in Publications by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. Authors V. P. Hart, M. J. Taylor, T. E. Doyle, Yucheng Zhao, Pierre-Dominique Pautet, B. L. Carruth, D. W. Rusch, and J. M. Russell III

This article is available at DigitalCommons@USU: https://digitalcommons.usu.edu/ail_pubs/27 1 Investigating Gravity Waves in Polar Mesospheric Clouds Using 2 Tomographic Reconstructions of AIM Satellite Imagery

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4 V. P. Hart1, M. J. Taylor2,3, T. E. Doyle1, Y. Zhao3, P.-D Pautet3, B. L. Carruth4, D. W. Rusch5, 5 and J. M. Russell III6 6 7 1 Department of Physics, Utah Valley University, 800 West University Parkway, MS 179, 8 Orem, Utah 84058, USA 9 2 Department of Physics, Utah State University, 4415 Old Main Hill, Logan, Utah 84322, USA 10 3 Center for Atmospheric and Space Sciences, Utah State University, 4405 Old Main Hill, 11 Logan, Utah 84322, USA 12 4 No current academic affiliation, residence of Logan, Utah, USA 13 5 Laboratory for Atmospheric and Space Physics, University of Colorado, 1234 Innovation 14 Drive, Boulder, Colorado 80303, USA 15 6 Center for Atmospheric Sciences, Hampton University, 100 East Queen Street, Hampton, 16 Virginia 23668, USA 17 18 Corresponding author: Vern Hart ([email protected]) 19

20 Key Points: 21 • First application of tomography for studying polar mesospheric cloud structures imaged 22 by the CIPS instrument on the NASA AIM satellite. 23 • Used an intensity-weighted centroid profile and PMC surface maps to determine gravity 24 wave-induced altitude variability in the PMC layer. 25 • New tomographic analyses reveal a spatial anti-correlation between albedo and wave- 26 induced altitude, consistent with current theories. 27 28 29 Abstract

30 This research presents the first application of tomographic techniques for investigating gravity 31 wave structures in Polar Mesospheric Clouds (PMCs) imaged by the Cloud Imaging and Particle 32 Size (CIPS) instrument on the NASA AIM satellite. Albedo data comprising consecutive PMC 33 scenes were used to tomographically reconstruct a 3D layer using the Partially Constrained 34 Algebraic Reconstruction Technique (PCART) algorithm and a previously developed “fanning” 35 technique [Hart et al., 2012]. For this pilot study, a large region (760 x 148 km) of the PMC 36 layer (altitude ~83 km) was sampled with a ~2 km horizontal resolution and an intensity 37 weighted centroid technique was developed to create novel 2D surface maps, characterizing the 38 individual gravity waves as well as their altitude variability. Spectral analysis of seven selected 39 wave events observed during the Northern Hemisphere 2007 PMC season exhibited dominant 40 horizontal wavelengths of ~60-90 km, consistent with previous studies [Chandran et al., 2009; 41 Taylor et al., 2011]. These tomographic analyses have enabled a broad range of new 42 investigations. For example, a clear spatial anti-correlation was observed between the PMC 43 albedo and wave-induced altitude changes; with higher-albedo structures aligning well with 44 wave troughs, while low-intensity regions aligned with wave crests. This result appears to be 45 consistent with current theories of PMC development in the mesopause region. This new 46 tomographic imaging technique also provides valuable wave amplitude information enabling 47 further mesospheric gravity wave investigations, including quantitative analysis of their 48 hemispheric and inter-annual characteristics and variations.

49 Keywords: Aeronomy of Ice in the Mesosphere (AIM), Cloud Imaging and Particle Size (CIPS) 50 experiment, Algebraic Tomography, Atmospheric Gravity Waves, ANGWIN

51 52 1 Introduction

53 Polar Mesospheric Clouds (PMCs), originally known as Noctilucent clouds (NLCs), are the 54 highest, driest, coldest, and rarest clouds on Earth. Ever since the first NLC sightings in the 55 summertime twilight skies over Northern Europe [Leslie, 1885; Backhouse, 1885; Jesse, 56 1885], their extreme altitude and the unusual conditions under which they occur continue to 57 inspire and challenge new observations, theory, and modeling studies. 58 It is now well established that PMCs are formed by water-ice nucleation primarily onto 59 cosmic dust [e.g., Hervig et al., 2009] in the tenuous summer mesopause region (altitude 60 ~85 km) where the summertime temperatures can fall below 130-150 K [Gadsden and 61 Schroder, 1989; Bailey et al., 2009]. The anomalously cold mesopause temperatures provide 62 a conducive environment for the formation of microscopic ice crystals that nucleate and 63 grow to detectable sizes (few 10’s of nm), over periods of typically several hours to a few 64 days [Gadsden, 1982; Jensen and Thomas, 1988; Rapp et al., 2002; Rapp and Thomas, 2006; 65 Baumgarten et al., 2008; Hervig et al., 2009; Cho and Rottger, 1997; Merkel et al., 2009]. 66 Atmospheric gravity waves (GWs) play two key roles in the formation, visibility, and 67 structure observed in PMCs. The first is through their ability to transport large amounts of 68 energy and momentum upwards from copious tropospheric sources. On a global scale the 69 resultant deposition of GW momentum flux acts to close the mesospheric jets and drives a 70 residual meridional inter-hemispheric circulation [Lindzen, 1973; Holton, 1983; Garcia et 71 al., 1985; McIntyre, 2001], resulting in strong upwelling in the summer polar region. 72 Consequent strong adiabatic cooling creates the remarkably cold summer mesopause region 73 at polar latitudes [Fritts et al., 2003; Lȕbken, 1999, Fritts and Alexander, 2003]. The second 74 role of GWs is their local effect on the PMC particles acting to alter their sedimentation, 75 growth, and sublimation via wave-induced vertical displacement and by impressing their 76 characteristic spatial structures onto the cloud field [Witt, 1962; Klostermeyer, 2001; Chu et 77 al., 2003; Rusch et al., 2009; Chandran et al., 2010]. 78 From the ground, these ‘night shining’ mesospheric ice clouds often appear as a 79 geographically extensive, thin (few km) visual cloud layer seen at twilight by strong 80 forward scattering of sunlight off the ice particles. They are frequently characterized by a 81 variety of spatially periodic wave structures. Indeed, observations over the past ~120 years 82 have established a standard NLC classification with large-scale ‘bands’ and small-scale 83 ‘billows’ as two of the primary categories for describing the clouds’ appearance [Witt, 1962; 84 Fogle and Haurwitz, 1969; Taylor et al., 1984; Gadsden and Schroder, 1989; Gadsden and 85 Parviainen, 1995]. 86 Observations, mainly from the northern hemisphere, have provided important 87 information on the most commonly occurring wave structures in the mesopause region 88 during the summer. This has enabled high-quality investigations of their spatial properties, 89 dynamics, and associated instability processes at high-latitudes [Fogle and Haurwitz, 1969; 90 Gadsden and Schroder, 1989; Taylor et al., 2011; Fritts et al., 1993; Dalin et al., 2004; 91 Pautet et al., 2011; Fritts et al., 2014]. For example, Type II bands are signatures of 92 extensive propagating small to medium-scale gravity waves exhibiting horizontal 93 wavelengths of ~10->100 km, with lifetimes of up to several hours. In contrast, Type III 94 billow events are spatially limited, exhibit short horizontal wavelengths (typically 5-10 km), 95 and are signatures of transient convective or dynamical instabilities generated in situ by 96 strong wind and temperature gradients [Gadsden and Schroder, 1989; Fritts et al., 1993; 97 2014]. 98 Ground-based optical, rocket-borne, and more recently, active lidar soundings of these 99 clouds have provided a wealth of information on their evolution, particle size, wave 100 dynamics, and altitude structure essential for quantifying their variability [Semeter et al., 101 1997; Rapp et al., 2002; Chu et al., 2003]. They have also established the remarkably 102 consistent and stable altitude of the NLCs in the upper mesosphere over the past century, 103 occurring at a mean height of 83 ± 2.5 km [Jesse, 1896; Stȍrmer, 1933; Paton, 1964; Taylor 104 et al., 1984; Gadsden and Taylor, 1994; von Zahn et al., 1998; Chu et al., 2004; Collins et 105 al., 2009; Thayer et al., 2003; Baumgarten et al., 2009; Gerding et al., 2007]. However, 106 most of these measurements are from isolated sites and are naturally limited by the 107 prevailing weather conditions [Gadsden and Schroder, 1989]. In contrast, space-based 108 observations of PMCs have revolutionized our understanding of their global-scale spatial 109 and temporal variability. 110 The earliest space-based human observations began with Soyuz 9 [Vasil'yev et al., 1987] 111 and were later conducted from Skylab [Packer et al., 1977]. Such observations continue 112 today from the International Space Station 113 [www.nasa.gov/mission_pages/aim/multimedia/ISS031-E-116058.html]. The earliest 114 satellite measurements by the OGO-6 satellite [Donahue et al., 1972], and by the Solar 115 Mesosphere Explorer (SME) satellite [Thomas et al., 1984] established the near continuous 116 presence of a PMC layer in the perpetually sunlit summer polar regions over the Arctic 117 (May–August) and Antarctic (November–February) [Jensen et al., 1988; Thomas, 1991; 118 Evans et al., 1995; Carbary et al., 2000; von Savigny et al., 2004; Bailey et al., 2005; 119 Russell et al., 2007; 2008]. 120 The first satellite image measurements of the PMC layer were obtained by the WINDII 121 limb viewing interferometer aboard the Upper Atmosphere Research Satellite (UARS), 122 which recorded patchy structures in the cloud layer as observed in the Earth's limb at ~83 123 km [Evans et al., 1995]. Subsequent measurements by the Ultraviolet and Visible Imaging 124 and Spectrographic Imaging (UVISI) instrument on the Mid-Course Space Experiment 125 (MSX) satellite provided the first evidence of large-scale “transpolar wave structures” in the 126 PMCs as imaged in the earth's sub-limb, exhibiting horizontal wavelengths of 500-1000 km 127 over both the northern and southern summer polar regions [Carbary et al., 2000]. Ensuing 128 analyses of these data also revealed smaller-scale structures with horizontal wavelengths 129 <100 km, typical of the band-type waves frequently observed in ground-based NLC imagery 130 [Carbary et al., 2003; Gadsden and Schroder, 1989; Dalin et al., 2004; Pautet et al., 2011]. 131 The Optical Spectrograph and Infrared Imaging System (OSIRIS) on the Odin satellite 132 (launched in 2001) has been used to collect atmospheric limb-scans from 7-107 km altitudes 133 over the spectral range 275-810 nm [Gattinger et al., 2009]. These line-of-sight brightness 134 measurements provide accurate multiple-angle views of the PMC layer suitable for 135 tomographic imaging studies. Degenstein et al. [2003] initially used the near infrared data to 136 investigate the feasibility of retrieving structure from a series of limb images using a 137 likelihood expectation maximization algorithm and succeeded in mapping volume emission 138 rates of the oxygen infrared atmospheric (OIRA) band [Degenstein et al., 2004]. Most 139 recently, Hultgren et al. [2013] have utilized OSIRIS in a special “tomographic mode” 140 focusing the line-of-sight scans over a restricted altitude range (~73-88 km), thereby 141 increasing the number of scans through the PMC layer. Using 180 orbits of ultraviolet (<310 142 nm) data obtained during the northern hemisphere summers of 2010 and 2011, they 143 successfully retrieved two-dimensional distributions of volume emission rate as a function 144 of altitude and horizontal range through the PMC region. This novel tomographic study 145 demonstrated new capabilities for investigating the vertical structure and particle size 146 composition of PMCs [Hultgren et al., 2013; 2014]. 147 The NASA Aeronomy of Ice in the Mesosphere (AIM) satellite (launched in 2007) is the 148 first satellite mission with the primary objective of studying PMCs and their variability 149 [Russell et al., 2009]. The Cloud Imaging and Particle Size (CIPS) instrument onboard AIM 150 comprises four wide-field UV imagers that map the PMC field with high spatial and 151 temporal resolution. As the satellite traverses over the summer polar region, it provides 152 unprecedented observations of the PMC layer and the embedded mesospheric gravity wave 153 structure [Rusch et al., 2009; McClintock et al., 2009; Lumpe et al., 2013]. These data have 154 enabled several novel investigations of the broad spectrum of gravity waves present over the 155 summer polar regions. Early CIPS data were utilized to investigate the characteristics of the 156 frequently observed small-scale (horizontal wavelength < 100 km) gravity waves in the high 157 Arctic and their relationship to those generally observed in lower-latitude NLCs [Chandran 158 et al., 2009; Taylor et al., 2011]. Chandran et al. [2010] and more recently Zhao et al. 159 [2015] have utilized several seasons of CIPS data to investigate the spectrum of larger scale 160 gravity waves (horizontal wavelengths up to 800 km) and their inter-seasonal and inter- 161 hemispheric similarities and differences. 162 This paper presents the first results of applying tomographic techniques to the CIPS 163 imagery to investigate the potential of the extensive AIM data set (2017 marks 10 years of 164 continuous measurements in the northern and southern polar summer mesosphere) to 165 quantify horizontal and vertical wave structures and amplitudes in the PMC field, and their 166 variability induced by the ever-present gravity waves. 167 168 2 PMC Reconstructions 169 2.1 Tomography 170 Tomographic data are acquired as a signal is emitted by, projected through, or reflected 171 from a surface and measured by a sensor or camera. As the number of available sensors 172 increases, more viewing angles become available which enhances the quality and accuracy 173 of reconstructions. Sparse tomography is a process in which an imaging region is 174 reconstructed using non-ideal projections. Such data are often limited by the geometry of 175 the imaging region, allowing for a restricted range of viewing angles while offering a 176 limited number of viewing locations. This reduces the amount of data available for 177 processing and can degrade image quality. 178 Large-scale tomographic measurements, such as those commonly used in atmospheric 179 imaging, are naturally limited in their range of viewing angles and result in a sparse ray 180 distribution. Despite these limitations, tomography has proven to be a powerful imaging tool 181 for a variety of atmospheric phenomena (e.g., airglow, aurora, and ionospheric disturbances) 182 [Bernhardt et al., 1998; Bernhardt et al., 2006; Pryse et al., 2003; Kamalabadi et al., 2002; 183 Kamalabadi et al., 1999; Semeter et al., 1997; Semeter et al., 1999; Hart et al., 2012; 184 Nygren et al., 2000]. This can be attributed primarily to a specific class of algorithms, 185 known as matrix methods, which have been developed and implemented for yielding 186 practical solutions to ill-conditioned imaging problems. 187 In matrix tomography, the low density of the projected rays necessitates the use of a 188 quantized representation. A grid is overlayed on the imaged object to produce a discrete 189 structure through division into pixels, as shown in Figure 1 a). This quantization of the 190 imaging region and the corresponding projections gives rise to a linear description and a 191 matrix formalism. A single projection 푝 is equal to the product of the weighting factor 푤, 192 which quantifies the effect of a pixel on a ray, and the pixel 푓 through which the ray is 193 projected: 푝 = 푤푓. (1) 푡ℎ 푡ℎ 194 In this study, the weight 푤푚푛 of the 푛 pixel in the 푚 projection is defined as the area 195 of intersection between the pixel and the two rays constituting the projection (see Figure 1).

196 The total projection 푝푚 is given by the sum of the weights of each intersected pixel. The 197 total measured signal along a given angle resulting from an interaction with 푁 pixels can be 198 expressed as the following sum: 푁 푝 = ∑ 푤푛푓푛. (2) 푛=1 199 The projection of the 푚푡ℎ ray through the imaging region is then given by: 푁

푝푚 = ∑ 푤푚푛푓푛. (3) 푛=1 200 These projected rays constitute a vector which contains the combined contribution of each 201 pixel. The resulting system of equations can be expressed as a matrix:

푤 푤 푤 ⋯ 푤 푓1 푝 11 12 13 1푁 1 푓 푝 푤21 푤22 푤23 ⋯ 푤2푁 2 2 푤 푤 푤 ⋯ 푤 푝 (4) 31 32 33 3푁 푓3 = 3 . ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮ [푤푀1 푤푀2 푤푀3 ⋯ 푤푀푁] [푝 ] [푓푁] 푀 202 This matrix equation is difficult to solve in practical applications. The primary reason 203 being that most imaging geometries produce underdetermined systems for which no unique 204 solution exists. Additionally, arrays with large numbers of elements can make accurate 205 approximations difficult. Finding sufficiently accurate solutions to this system is the 206 primary objective of sparse tomography. The most common approach utilizes a set of 207 tomographic methods known as algebraic reconstruction techniques (ARTs). ARTs are a set 208 of correction algorithms in which an initial image is gradually improved as successive 209 iterations are carried out. An initial approximation of the object’s structure is provided to 210 the algorithm as a vector and a correction factor is iteratively added. This correction term is 211 calculated by comparing the tomographic projections of the previous image in the iteration 212 with the measured projections. 213 Various ART algorithms have been developed, including constrained or totally 214 constrained ART (TCART), multiplicative ART (MART), the simultaneous iterative 215 reconstruction technique (SIRT), simultaneous ART (SART), and memory ART. These 216 various ART algorithms have been successfully implemented in prior studies [Bender et al., 217 2011; Tsai et al., 2002; Padmanabhan et al., 2009; Vecherin et al., 2007; Hobiger et al., 218 2008]. The performance of each algorithm was tested using synthetic data and the resulting 219 images exhibited a high degree of similarity. We ultimately selected to use PCART because 220 it was slightly more consistent, though in most cases the difference was small (particularly 221 for multiplicative ART which performed well). 222 The PCART algorithm is given by [Kak and Slaney, 2001]: 𝑖 (푝푚 − 푝푚)푤푚푛 푓푚푛 = 푓푚−1,푛 + 휆 , (5) 푁푚 푡ℎ 푡ℎ 223 where 푓푚푛 is the discrete value of the reconstructed image for the 푚 ray and the 푛 pixel.

224 The addition of a correction factor to previous image values (푓푚−1,푛) provides the iterative

225 step. Elements of the weighting matrix are given by 푤푚푛 and convergence of the corrections

226 can be controlled by the relaxation parameter λ. The measured projections correspond to 푝푚 𝑖 푡ℎ 227 and the computed projections to 푝푚. The 푁푚 term is the total weight of the 푚 ray and can 228 be expressed as the sum of each individual weighting factor for the 푁 pixels in the imaging 229 area: 푁

푁푚 = ∑ 푤푚푛. (6) 푛=1 230 The limitations of atmospheric tomography require an initialization of the algorithm, 231 which is iteratively corrected. We previously used the PCART algorithm to reconstruct 232 mesospheric airglow wave signatures [Hart et al., 2012]. In that study, the algorithm was 233 well tested using synthetically generated profiles and a range of different initializations 234 (e.g., binary, Gaussian, and Chapman functions) [Hart et al., 2012]. Both the Chapman and 235 Gaussian functions performed well, but the Gaussian profile was ultimately selected due to 236 its frequent use in the literature to quantify the airglow emission layer profiles (peak height 237 and fullwidth at half maximum (FWHM) thickness) as observed by limb viewing satellites 238 [e.g., Zhao et al., 2005]. 239 PMCs naturally occur in a well-defined, relatively thin continuous cloud layer with a 240 typical mean altitude centered around 83 km. Lidar measurements now provide excellent 241 observations of the optical thickness of this layer (typically 1-3 km) and local variability in 242 altitude induced by gravity waves and other perturbations [von Zahn et al., 1998; Chu et al., 243 2003, 2004; Collins et al., 2009; Thayer et al., 2003; Gerding et al., 2007]. The choice of an 244 initialization is determined by the shape of the structures being imaged. As PMCs reside in 245 thin localized layers, a narrow Gaussian band was selected to represent the expected shape

246 of the reconstructed PMCs. This Gaussian profile was used as the initial term (푓푚−1,푛) in the 247 PCART algorithm and was successively modified with each iteration. It was centered at 83 248 km with a FWHM of 4 km, providing good extension over an ~8 km altitude range 249 encompassing the PMC layer. During reconstruction, this initial profile successfully 250 converged to a width of ~2-3 km, consistent with prior PMC observations. We used 251 Gaussian profiles of varying sizes along with Chapman and box functions to prevent the 252 initialization from biasing reconstructed images. The results of synthetic testing showed 253 these reconstructions became more accurate as the initialization more closely approximated 254 the physical shape of the layer being imaged. This provided a rationale for a Gaussian 255 initialization, as LIDAR data have confirmed the shape of such layers. As part of our 256 analyses we have also utilized a novel ‘fanning’ technique that was introduced in our 257 airglow study to generate the 3D PMC volume retrievals [Hart et al., 2012]. This method is 258 illustrated in Figure 1 and described in the following sections. 259 260 2.2 Imaging Configuration 261 AIM was launched into a sun-synchronous 600 km altitude circular orbit. The CIPS 262 experiment uses four intensified cameras filtered to observe UV emissions at 265 nm. The 263 four cameras are aimed towards the nadir and are tilted to observe the forward, aft, port, and 264 starboard directions, such that their fields of view overlap slightly. Together, these four 265 cameras comprise a wide-angle imager with a field of view spanning 120o along track and 266 80o across track, resulting in an ~2000 x 1000 km field of view at the PMC layer altitude 267 [Rusch et al., 2009; McClintock et al., 2009]. 268 Snapshot images (~0.75 s exposure) were acquired by each of the four cameras 269 simultaneously at 43 second intervals along the polar track with a nadir pixel resolution of 2 270 km, that reduces to ~5 km at the edges of the forward and aft cameras. When merged 271 together, these four images create a “bowtie” shaped map of the PMC layer which is often 272 referred to as a “scene” [Rusch et al., 2009]. Figure 2 shows the utilization of several 273 consecutive scenes for the tomographic reconstruction (discussed in more detail below). 274 CIPS data comprising the scene information are routinely combined together to form an 275 ~1000 km wide by up to 8000 km long composite image of the PMC layer over the summer 276 polar region. This is a standard CIPS level 2 data product, which is available at 277 http://lasp.colorado.edu/aim/index.html and provides measurements of the cloud presence, 278 spatial morphology, and microphysical parameters, re-binned to a uniform pixel resolution of 25 279 km2. However, for this initial tomographic investigation, we have utilized the original, 280 higher-resolution CIPS bowtie scenes [Chandran et al., 2009; Rusch et al., 2009], which are 281 not a standard AIM/CIPS data product but can be made available upon request. 282 Similar studies conducted with OSIRIS data from the Odin satellite have established the 283 required preprocessing of images for tomographic inversion. Specifically, cloud radiance 284 must be separated from background radiation due to molecular Rayleigh scattering and 285 instrumental effects [Hultgren et al., 2014]. This process was implemented with the CIPS 286 imagery as each scene was first flat-fielded and then normalized to albedo units. The flat 287 fielding involved two main processes as described in detail by Rusch et al. [2009]: a) 288 correction for Rayleigh scattered sunlight from the atmosphere observed by CIPS at 289 different viewing angles due to its wide field of view, and b) compensation for the strong 290 forward scattering behavior when viewing the PMC ice particles at small scattering angles 291 as CIPS encounters each sunrise and sunset. The layer was also assumed to be optically thin 292 and tenuous. As a result, multiple-scattering and diffusion were ignored in the tomographic 293 reconstruction process. 294 The forward scattering correction was well modeled by a phase function comprising a 295 Gaussian distribution of spherical water-ice particles with a mode radius of 60 nm and a 296 width of 12 nm (applicable to bright PMCs as reported herein). The cloud albedo, defined as 297 the ratio of the scattered radiance (after the background correction) to the incoming solar 298 irradiance averaged over the band pass of the CIPS instrument, was then normalized to a 299 90° solar scattering angle [McClintock et al., 2009]. For our pilot tomographic analysis, data 300 from five consecutive scenes were combined to create a “common PMC volume” sampled 301 by CIPS as the satellite transited overhead. This process comprised two parts as illustrated 302 in Figures 1 and 2. 303 Figure 2 shows the five flat-fielded scenes displaced vertically (for illustrative

304 purposes). The scene at time 푡1 is superimposed on a geographic grid, showing its field of 305 view, orientation, and location in the vicinity of the North Pole. As the satellite passed over 306 the PMC layer, images of the same region were sequentially acquired at five different 307 orbital positions. The extended dashed black lines plot the orbital track of the satellite.

308 Subsequent scenes 푡2 − 푡5 (displaced vertically) show the progression of the “common 309 intensity” profile (white line) with time. The resultant profile has a length of 762 km, 310 enabling quantitative investigations of a broad range of gravity wave perturbations evident 311 in the CIPS data. 312 313 314 Figure 1. a) The definition of projections in discrete matrix tomography. b) An illustration 315 of the fanning technique used in this study to acquire projection data from multiple grids 316 within a 3D volume. c) The application of this technique to the AIM imaging configuration 317 using five consecutive observation sites. As the satellite passed over the PMC layer, CIPS 318 acquired albedo images of the same region but from varying angles away from the zenith. 319 320 The extension of the common intensity profile into a “common volume” measurement is 321 illustrated in Figure 1 b), which shows a “fanning” technique that we effectively 322 implemented to investigate gravity waves in the OH emission layer using limited field 323 image data [Hart et al., 2012]. Instead of using a single nadir common profile, a set of 324 intensity profiles were collected. A common volume viewing area was obtained by ‘fanning’ 325 across the PMC layer over a range of angles away from the nadir, as depicted by the red 326 lines in Figure 1 b). Each of the yellow lines in Figure 1 c) represents a 1D albedo profile 327 which were used as projection data in the PCART algorithm. From each 1D projection 328 profile, a 2D image could be reconstructed representing a cross-section of the PMC layer. 329 By combining multiple adjacent cross-sectional images, a 3D PMC layer was established. 330 This process is described as fanning because subsequent 1D albedo profiles were acquired at 331 varying angles increasing away from the nadir, forming the fan-like geometry shown in 332 Figure 1 c). 333

334 335 Figure 2. An illustration of the method used to generate the tomographic projection data. 336 Each of the five consecutive flat-fielded PMC albedo scenes (t1-t5) were acquired at a 337 different time, position, and angle. The common intensity profile (white line) is indicated in 338 each scene. The dashed line shows the track of the AIM satellite. Note the subsequent 339 scenes are displaced vertically for illustrative purposes. These data were acquired from 340 CIPS Orbit 1393, scenes 12-16, taken on day 209 of 2007. 341 342 343 2.3 Synthetic Data and Validation 344 The accuracy of the presented tomographic technique was verified using an artificially generated 345 PMC layer. Known pixel values inside this layer were multiplied by corresponding weighting 346 values of rays within the image grid. This produced synthetic projection data which simulated a 347 physical albedo measurement. These data were then reconstructed and the resulting image was 348 compared with the synthetic layer. This approach provides a ground truth which can be used to 349 assess the accuracy of reconstructed images. The results of this process are shown in Figure 3, 350 which includes the a) synthetic layer and b) corresponding reconstruction. 351

352 353 Figure 3. The results of synthetic testing used to validate the presented tomographic 354 technique. a) A synthetic layer was used to produce synthetic projection data, which were 355 then reconstructed to produce a b) 2D image. The effect of imaging geometry on this 356 method was also analyzed using various other altitudes and spacing factors (distance 357 between imaging sites). c) The average pixel difference was calculated as a function of the 358 number of receivers used to collect projection data. 359 360 While edge effects are present in the reconstruction (as to be expected), the overall structure 361 and variability in thickness has been preserved. These results were produced using the same 362 Gaussian initialization and PCART algorithm applied to the CIPS data and provide confidence in 363 the presented technique. 364 We were also interested in determining the effect which imaging geometry had on 365 reconstruction accuracy. The AIM satellite transited over the PMC layer at an altitude of 600 km. 366 The average height of the layer above the surface was 83 km. As such, the altitude of the receiver 367 was assumed to be 517 km. The CIPS cameras acquired images every 43 seconds, resulting in a 368 physical separation of ~130 km (hereafter referred to as a spacing factor). This combination of 369 distances constituted the AIM imaging geometry in which CIPS observation angles ranged from 370 0o (directly overhead) to 41.1o at the far edges of the bowtie albedo images. In a previous study 371 involving OH airglow emissions (~83 km altitude), two ground-based cameras were included, 372 separated by a distance of 100 km [Hart et al., 2012]. As such, this study included a spacing 373 factor of 100 km and an altitude of 83 km. 374 Five additional geometries were evaluated, including spacing factors ranging from 100-400 375 km and altitudes ranging from 83-662 km. These combinations are shown in Figure 3 c), which 376 includes plots of the average pixel difference (APD) calculated between the synthetic layer and 377 the corresponding reconstruction. The CIPS data included five receivers and the AIM geometry 378 is represented by the blue line in the figure. This plot demonstrates the AIM geometry resulted in 379 lower errors than several others included in the study, notably the configuration from our 380 previous OH airglow study (black line). There is also an obvious downward trend as increasing 381 the number of imaging sites resulted in lower errors and more accurate image reconstructions. 382 383 2.4 Centroid Method

384 The CIPS albedo data were used as projections (푝푚) in the PCART algorithm. These projections 385 were reconstructed to produce 2D PMC images (an example of which is shown in Figure 4 b)). 386 By fanning away from the zenith, multiple 2D reconstructions could be produced inside of the 387 physical 3D space from which the albedo data were collected. The 2D reconstructions were 388 observed to converge to a thickness of 2-3 km, consistent with the physical PMC cloud layer. 389 They were then smoothed using an isotropic Gaussian filter with a kernel size of σ =10 pixels to 390 better identify the dominant spatial features. When these adjacent 2D reconstructions were 391 aligned (Figure 4 a)), they formed a 3D volume representing the physical PMC layer. This is 392 referred to hereafter as the 3D PMC volume. 393 As the CIPS data were collected with a nadir spatial resolution of 2 km, which is comparable 394 to the depth of the PMC layer, the resultant 3D reconstruction was physically too narrow to 395 investigate gravity wave variations within the layer using classical tomographic cross-sectional 396 views (e.g., as employed by Hultgren et al. [2014]). Instead, we utilized a novel intensity- 397 weighted centroid technique to enhance the visibility of the overall structure of the reconstructed 398 PMC layer and to hence determine the horizontal dimensions and vertical variations at various 399 locations. The vector position 푅̅ of this centroid is given by: 푁 1 푅̅ = ∑ 푎 푟̅ (7) 퐴 𝑖 푖 𝑖=1

400 where 푎𝑖 represents the albedo of the 푖푡ℎ pixel, 퐴 the total albedo along a vertical column of 푁

401 pixels, and 푟𝑖 the altitude of the 푖푡ℎ pixel. During processing of the CIPS data, a constant particle 402 size of 60 nm was assumed. This prevents the use of this equation for studying altitude 403 variability as a function of particle size. 404 Figure 4 b) shows an end-on view of the 3D PMC layer in which horizontal structuring in the 405 layer is identified by colored contours. The calculation of this centroid along all columns in a 2D 406 image slice through the 3D layer is represented by the black dots shown in the figure. These data 407 result in a 1D horizontal perturbation height vs. distance profile, as shown in Figure 4 c). 408 Calculation of the centroid for multiple slices constituting the entire 3D volume results in a 2D 409 surface plot, as shown in Figure 4 d), which is our working data product. These 2D centroid 410 surface plots (hereafter referred to as “surface maps”) are rich in structure and exhibit strong 411 periodicities identifying the dominant gravity wave structures evident in the original albedo data. 412 413 414 Figure 4. Development of the PMC surface plot from the 3D tomographic reconstructed PMC 415 layer after smoothing. a) Depicts the computed 3D PMC volume, b) shows an end-on 2D slice 416 through the 3D volume identifying internal structure, c) displays the 1D intensity-weighted 417 centroid analysis plot (also depicted by the black dots in ‘b’), and d) shows the derived 2D 418 horizontal surface map. Note the three dashed vertical arrows identify the relation between 419 structure in the 2D slice and the 1D plot. The colorbar corresponds to vertical displacement in d) 420 and c), whereas the interior color in b) and a) represents relative albedo. 421 422 In order to assess the viability of this proposed centroid technique, a synthetic wave perturbation 423 was induced in an artificial PMC layer. In a process similar to the synthetic testing described in 424 Section 2.3, this artificial layer (containing the synthetic wave) was used to generate projection 425 data which were then input to the PCART algorithm. The proposed centroid technique was then 426 applied to this reconstructed layer and the resulting centroid was compared to the induced 427 (ground truth) wave structure. An example of this testing is shown in Figure 5. As is evident in 428 the figure, the induced wave (top) and reconstructed wave (bottom) exhibit a high degree of 429 similarity, with an APD of 0.0821. This result supports the use of the proposed centroid 430 technique as a viable imaging tool for quantifying small-scale vertical structures in sparse 431 tomography images. In the following results section, we compare and contrast the gravity wave 432 surface maps (reconstructed from CIPS data) with the original PMC albedo imagery from AIM 433 and use these new results to further investigate the vertical as well as horizontal structure of 434 waves perturbing the PMC layer. 435

436 437 Figure 5. The results of synthetic centroid testing. A wave pattern (top) was induced in 438 an artificial PMC layer, which was used to generate synthetic projection data. The 439 PCART algorithm was then used to reconstruct a layer from these data. Finally, the 440 centroid technique was applied to measure vertical structures in the resulting image. This 441 centroid (bottom) exhibits a high degree of similarity to the induced wave (top), a result 442 which supports the viability of the proposed method. 443 444 3 Results 445 3.1 Gravity Wave Structures 446 CIPS albedo data from five different AIM orbital tracks were selected from the first Northern 447 Hemisphere season in 2007, when the original flat-fielded bowtie scenes were available as an 448 initial data product [e.g., Rusch et al., 2009]. Our criteria were to select orbits and scenes with a 449 variety of well-defined gravity waves visible in the PMC albedo imagery. The five orbits used in 450 this study were Orbits 01242_199, 01243_199, 01244_199, 01245_199, and 01299_202, of 451 which four were consecutive. In the case of Orbits 01244_199 and 01245_199, two different sets 452 of scenes were acquired on the same orbital path. In total, seven sets of PMC scenes were 453 acquired and processed for this pilot study. These data were then reconstructed and the results 454 combined to form 3D PMC volumes, as depicted in Figure 4 a). The intensity weighted centroid 455 method was then applied to each of the seven volumes resulting in series of 2D PMC surface 456 maps as shown in Figure 6. 457 458 459 460 Figure 6. Example results of the intensity-weighted centroid analysis applied to the seven 461 reconstructed PMC volumes. Each 2D surface map shows strong evidence of short-period 462 gravity wave perturbations. The corresponding AIM orbital numbers are included on the 463 left of each profile. For visibility, the surface plots are canted to reveal their constituent 464 wave structure, coherence, and amplitude/altitude variations. 465 466 Each of these surface maps shows clear evidence of well-developed wave patterns perturbing 467 the PMC layer. For example, several surface maps exhibit strong wave features comprising large 468 amplitude (>1-1.5 km) wave crests and adjacent troughs (e.g., Orbits 01243_199 and 01245_199, 469 #6), which extend laterally across the surface maps indicating extended (>150 km) coherent 470 wave crests. Some of the surface maps also suggest a systematic change in altitude (1.5-2 km) 471 along the spacecraft track (e.g., Orbits 01242_199, 01244_199 (#3), and 01299_202). These 472 changes in height are due to a change in altitude of the intensity-weighted mean albedo at various 473 locations along the reconstructed 3D profiles. As such, they are similar to what would be 474 observed, for example, by ground-based observers measuring the height of the often continuous 475 NLC layer (and its perturbing wave structures) using two-station line-of-sight triangulation or 476 stereographic methods (compared further in discussion section) [Witt, 1962; Taylor et al., 2011]. 477 The sharp reduction in structure near the left end of Orbit 01245_199 (#5) also suggests the edge 478 of a wave packet or a “mesospheric front”. Such features are characteristic of short-period (<1 479 hour) gravity waves as frequently observed in the mesospheric airglow emissions [Ejiri et al., 480 2003; Snively et al., 2005] and in NLCs [Chandran et al., 2009; 2010; Pautet et al., 2011; 481 Thayer et al., 2003]. 482 483 3.2 Spectral Analysis of Surface Maps 484 To investigate the spatial properties of wave patterns evident in the PMC layer, the data were 485 analyzed quantitatively using a fast Fourier transform (FFT) applied to 1-D plots of altitude vs. 486 distance along the center of each surface map. Figure 7 a) shows two examples of centroid 487 albedo vs. altitude profiles for Orbits 01242_199 and 01245_199, spanning the length of the 488 PMC layer, while Figure 7 b) shows their computed FFT power spectra. These two events were 489 dominated by gravity waves with horizontal wavelengths of ~63 km and ~87 km, respectively. 490 The primary contributing waves for the other five cases were determined to vary between ~43 491 and ~98 km. These individual results are fully consistent with the reported horizontal spectra of 492 gravity waves by Chandran et al. [2009] and Taylor et al. [2011], using the same CIPS Northern 493 Hemisphere 2007 data set. 494 495 Figure 7. Example data and FFT power spectra for two of the seven PMC surface profiles. a) 496 The midplane altitude profile for orbit maps 01242_199 and 01245_199, and b) the 497 corresponding FFT power spectra identifying strong wave events with horizontal wavelengths of 498 63 and 87 km, respectively. 499 500 501 4 Discussion 502 Figure 8 presents a pictorial summary of our research method comparing the initial data input 503 and the tomographic results. The CIPS bowtie scene in Figure 8 a) was one of five sequential 504 scenes used to generate surface map #1 (Orbit 01242_199) in Figure 6. In Figure 8 b), the area of 505 the original scene used for the reconstruction (yellow rectangle) is outlined. For this investigative 506 study, we chose to apply the fanning technique to only one-half of the available area for the 507 tomographic analysis. The resultant surface map was 760 km by 148 km as depicted in Figure 8 508 c), which presents a false-color map where blue indicates lower altitudes and red higher altitudes, 509 with a scale ranging over ±1.2 km. The 3D format of this plot provides a new viewing 510 perspective helping to interpret the “planar” CIPS albedo imagery and its constituent data. In 511 particular, the tomographic results reveal new information on the relative amplitudes of the 512 differing wave crests and troughs and their extended spatial coherence. 513

514 515 516 Figure 8. Illustrates the enhanced visibility of the wave structure using the new 517 tomographic analysis technique. a) shows the original CIPS overhead scene with the 518 common imaging volume highlighted by the yellow box, b) an enlarged view of the 519 common volume showing wave structure in the PMC layer albedo, and c) an angled view 520 of the resultant surface map. Note the additional altitudinal information on the wave 521 pattern provided by the tomographic analysis centroid method. 522 523 524 4.1 Spatial Correlations 525 These comparative results depict a high spatial correlation between the horizontal wave 526 structures in the tomographic reconstructions and the original albedo data establishing their 527 potential for more in-depth studies of the selected gravity wave data. In particular, the new 528 tomographic surface perspective that these data provide and the clarity of the resolved waves 529 open the door to a range of possible studies involving the relative altitude distribution of the 530 structures. For example, a visual inspection of the enlarged CIPS albedo scene shown in Figure 8 531 b) and the computed surface PMC map suggests that dark (low-altitude/blue) regions in the 532 centroid profile directly coincide with the bright (high-intensity/red) regions in the albedo data of 533 Figure 8 a). This apparent relationship is demonstrated more clearly in Figure 9, which visually 534 compares four examples of our albedo-centroid image pairs where the CIPS albedo and the 535 derived tomographic surface maps are both presented as nadir views to facilitate the comparison. 536 Results from a broad (whole field) view and also from selected one-to-one PMC structure 537 comparisons clearly suggest that the lower altitude (blue) regions generally align well with the 538 higher PMC albedo (white) regions. Conversely, the lower albedo regions tend to be associated 539 with comparatively higher altitude regions and wave structures. The black arrows point to 540 examples to illustrate this finding. 541 542 543 Figure 9. Four examples comparing PMC albedo and centroid image pairs. A strong correlation 544 is visually evident in all of these data suggesting that low-altitude (blue) regions in the centroid 545 correspond well with high-intensity (white) regions in the PMC albedo. 546 547 To provide a more quantitative assessment of this visual correlation, we have employed the 548 Pearson Correlation Coefficient (PCC), a similarity metric commonly used to measure spatial 549 overlap in medical tomography. Each of the seven example CIPS albedo images (e.g., Figure 8 550 b)) was normalized and the data then squared to provide sufficient separation between high and 551 median albedos (a form of histogram equalization). The derived centroid profile was also 552 normalized in the same way but not squared as its histogram distribution was comparable to that 553 of the CIPS imagery. This procedure was done to test our hypothesis that low altitude centroid 554 data generally correlates with high PMC albedo. The normalized centroid images were then 555 inverted to compare bright regions with bright regions and dark with dark. The PCC ranges from 556 0 (no overlap) to 1 (identical images) and is calculated as: 푛 ̅ ̅ ∑𝑖=1(푋𝑖 − 푋) (푌𝑖 − 푌) 푃퐶퐶 = (8) 푛 ̅ 2 푛 ̅ 2 √∑𝑖=1(푋𝑖 − 푋) √∑𝑖=1(푌𝑖 − 푌)

557 where 푋𝑖 represents each pixel in the first image and 푌𝑖 represents the corresponding pixels in the 558 second image. The average pixel value of the first and second image is given by 푋̅ and 푌̅, 559 respectively. 560 Uncertainty in these values was quantified using the results of synthetic testing described 561 earlier. Each pixel in the centroid image was assigned a random error ranging from 0 to 0.1642, 562 resulting in an average of 0.0821, as calculated in the synthetic centroid simulation. We also 563 included errors resulting from typical wind speeds (30-60 m/s) occurring at mesospheric 564 altitudes. Although these values are lower in the summer than in the winter, over the 43 second 565 CIPS image intervals, they can result in motion ranging from 1-2 km. The results are shown in 566 Table 1, where a consistent high correlation was found in each case. Though it varies between 567 different applications, values exceeding 0.8 are typically considered to indicate good agreement 568 and strongly support the hypothesis relating high PMC albedo with lower PMC altitude. 569 570 571 Table 1. Results of the PCC analysis for each of the seven PMC scenes used in this study. The 572 high degree of similarity indicated by each of the PCC values (max =1) strongly support an 573 inverse relationship between centroid altitude and PMC albedo. 574 575 This analysis can be taken a step further by correlating our tomographic results with other 576 available CIPS data products (http://lasp.colorado.edu/aim/index.html). For example, the CIPS 577 data and other satellite measurements [e.g., Hultgren et al., 2014] have previously established 578 that ice-water content (IWC) is directly related to cloud albedo. This is illustrated in Figure 10 579 which compares level 2 IWC data from the AIM database (available on the mission websites). 580 The figure comprises multiple images showing a) the overhead CIPS albedo scene for orbit 581 01245_199 (#6), identifying the tomographic region, b) an enlarged view of this region showing 582 high cloud albedo to the left side, c) the tomographic reconstruction surface map for this region, 583 d) part of a larger field CIPS level 2 orbital swath comprising data from multiple scenes along 584 the orbital track, and e) the CIPS level 2 derived ice-water content map. 585 The common area is identified in these latter two images which clearly show a high visual 586 correlation between the PMC albedo and the IWC. In comparison, our tomographic analyses 587 derived independently from the original bowtie scene albedo data suggest that high albedo (and 588 hence high IWC) regions occur mainly where the PMC layer has a lower centroid altitude. This 589 finding is qualitatively consistent with current theories of PMC nucleation, growth, and 590 sedimentation processes in the mesopause region [e.g., Rapp and Thomas, 2006], which result in 591 the development of high IWC and high albedo levels in the lower levels of the PMC cloud layer, 592 where the largest ice particle are also found to occur. Indeed, a key observation of the recent 593 tomographic study by Hultgren et al., [2014] was the detection of large ice particles (> 70 nm) 594 apparently falling through the base of the PMC layer. (Note isolated “raining out” events have 595 also been reported in ground-based NLC observations [e.g. Witt, 1962]). This said, a very recent 596 study by Rusch et al., [2016] using other CIPS data has occasionally detected an anti-correlation 597 between mean particle size and cloud albedo in isolated cloud regions (typically < 100 km) 598 usually associated with strong GW activity. While they found that very large particles (> 60-100 599 nm) occurred mainly in the troughs of the GW they also determined that these regions 600 unexpectedly exhibited reduced IWC. An accompanying modeling study suggested that sporadic 601 downward winds heating the upper PMC levels may have enhanced the detection of the lower 602 lying larger particles, but at the same time also reduced the total IWC. Specific conditions are 603 required for such warming to occur and the absence of PMC voids in our data would suggest 604 they were not present at the time of image acquisition. The occurrence rates for these large 605 particle events need to be studied in more detail. 606 These pilot tomographic results establish a general relationship between height and 607 brightness for PMCs, apparently consistent with current knowledge, supporting the validity of 608 the proposed centroid technique as a tool for investigating small-scale gravity waves in sparse 609 tomography images. They also provide compelling new views of structures perturbing the layer 610 and a new ability to quantify induced altitude variations, enabling future in-depth wave 611 investigations. 612 613 614 Figure 10. A composite image demonstrating the relationship between the overhead CIPS scene, 615 the centroid profile, and the ice-water content map for AIM Orbit 01245_199 (#6). It is evident 616 from the common analysis areas (rectangles) in each image that lower altitudes correspond well 617 with high albedo and high IWC. 618 619 620 4.2 Gravity wave structures and amplitudes 621 Another notable result is the differences which exist between each of the seven example surface 622 maps. Coherent variations can be seen in the occurrence and amount of wave activity and in their 623 maximum and minimum amplitudes. Adopting a median altitude of 83 km, the average altitude 624 for each map was calculated by summing over the entire region to determine their variability. 625 Figure 11 shows the calculated values for each map. The plot displays the mean value (central 626 line), upper and lower quartile (box edges), and total span (border lines) of the data. Average 627 changes in PMC layer height across the >750 km fields of view were small (<0.2 km), while 628 average wave amplitudes within the PMC layer were relatively large, varying from 0.6-1.2 km. 629 This suggests that the smaller-scale (<100 km) gravity waves tend to dominate the PMC layer 630 structuring at any given location. In contrast, much larger horizontal scale gravity waves and 631 tidal perturbations could also be investigated using continuous PMC tomographic measurements 632 along full orbital tracks (typically >2000-6000 km) to determine their amplitudes and variability. 633

634 635 Figure 11. A box-and-whisker plot showing the altitude distribution for each of the seven 636 centroid profiles included in this study. The data reveal differences in the range of altitudes as 637 well as in the mean altitude for each profile. 638 639 Finally, Figure 12 shows two examples of wave measurements of the vertical displacements 640 of the PMC layer caused by gravity waves. The upper plot a) reproduces a famous NLC 641 measurement by Witt [1962] who made two-station photogrammetric measurements of a 642 magnificent NLC display observed from Torsta (63o N) in central Sweden on 10-11 August, 643 1958 during the International Geophysical Year. The vertical coordinates are computed heights 644 (above sea level), while horizontal coordinates are distances to mapped NLC structures at cloud 645 level. The figure shows a time sequence of 3 consecutive 1D vertical cross sections through the 646 NLC layer separated by five min. The clouds were observed at low elevations of 10-15o and the 647 bottom of each (black) plot delineates the measured wave-induced undulations in the underside 648 of the cloud layer, while the top of the layer indicates the estimated thickness of the layer also as 649 determined from the stereo photogrammetry. The horizontal wavelength of the dominant NLC 650 bands was 50 km, while their measured wave amplitudes varied from 0.5-4 km. Figure 12 b) 651 shows a canted side view of one of our tomographic surface maps, 01245 (#5), calculated using 652 the new intensity-weighted centroid technique. This surface map also displays altitude vs. 653 distance across the PMC layer but, in addition, provides a 2D measure of the gravity wave 654 perturbations with alternating crests and troughs separated by ~90 km intervals. The similarity in 655 these two figures is striking, both of which identify significant and variable undulations in the 656 PMC layer induced by similar horizontal scale gravity waves. In comparison, lidar measurements 657 of PMCs show that these amplitude variations are typical [Chu et al., 2003; Collins et al., 2009] 658 but are limited to a single measurement in the zenith vs. time. 659

660 661 Figure 12. a) Height vs. distance plotted for an NLC layer observed from the ground, modified 662 from Figure 9 in Witt [1962]. The data show NLCs of varying heights across the field of view 663 characterized by their constituent wave structures [Gadsden and Schroder, 1989]. b) An elevated 664 side view of surface map 01245 (#5) showing a well-defined wave event. Troughs and crests are 665 easily identified which are separated by ~90 km intervals. Note the strong similarity in wave 666 structures between these two figures. 667 668 Limited-angle tomography with our chosen reconstruction algorithms has proven effective 669 for gleaning new information from albedo measurements and furthering our understanding of the 670 effect of gravity waves seen in PMCs. Notably, our new ability to quantify and compare centroid 671 heights provides additional opportunities for future in-depth seasonal and hemispheric 672 investigations. The assumption of a constant particle size (60 nm), used in the procurement of the 673 flat-fielded bowtie data precludes further quantitative comparisons at this time. 674 We were, however, interested in the effect this assumption may have on the proposed 675 tomography algorithm. As such, a Mie scattering simulation was conducted using parameters 676 from the CIPS data, including a particle size of 60 nm, an index of refraction of 1.3 (ice), and a 677 wavelength of 256 nm. The total scattered intensity (normalized to unity over 4π steradians) for 678 particle diameters ranging from 30 nm to 90 nm is shown in Figure 13. 679

680 681 Figure 13. The result of a Mie scattering simulation for varying particles sizes, ranging from 30 682 nm to 90 nm. Other parameters were assumed to agree with CIPS conditions, including a 683 wavelength of 256 nm and an index of refraction equal to 1.3. The data have been normalized to 684 unity over a complete solid angle. 685 686 The angle of observation for the CIPS cameras varied from 0o (overhead) to ~41.1o at the edge of 687 the bowtie scenes. AIM acquired images in the summer hemisphere between the terminator and a 688 dayside latitude of about 40 degrees [http://lasp.colorado.edu/aim/]. At higher latitudes, the angle 689 between incident and scattered light can reside in the region of the graph where the curves 690 intersect and the difference between scattered intensities is small for varying particle sizes. As 691 such, the effect of particle size on scattered intensity depends largely on the latitude at which the 692 images were acquired. 693 694 5 Conclusion 695 A key result of the early CIPS data was the sheer abundance of gravity waves evident throughout 696 the summer polar mesosphere [e.g., Rusch et al., 2009]. Satellite data are inherently sparse due to 697 the limited number of available viewing angles. We examined the imaging configuration of the 698 CIPS data and the favorable use of limited-angle PCART tomography for application to a 699 geometrically thin (1-3 km) PMC layer. Algorithm validation was conducted using synthetic data 700 based on an earlier study of mesospheric OH airglow emissions. As part of our analyses, we 701 utilized a previously-developed ‘fanning’ technique to generate the 3D PMC volume retrievals 702 [Hart et al., 2012]. A novel imaging technique was also introduced for measuring wave-induced 703 structures in the tomographic reconstructions of the PMC layer. An intensity-weighted centroid 704 was then calculated along vertical columns of the derived 3D layer to generate novel 2D surface 705 maps containing prominent gravity wave perturbations. These patterns were found to comprise 706 waves with horizontal wavelengths ranging from 43-98 km, confirming previous studies by 707 Chandran et al. [2009] and Taylor et al. [2011], using the same CIPS 2007 data set, and paving 708 the way forward for further detailed wave studies. 709 In particular, the new tomographic surface perspective that these data provide have revealed 710 a marked spatial correlation between CIPS albedo imagery and the derived tomographic surface 711 map altitudes. Observations across a broad field of view suggest that lower altitude regions 712 generally aligned well with the higher PMC albedo regions, while selected one-to-one PMC 713 wave comparisons clearly showed deep wave troughs coinciding with strong albedo wave 714 structures. This hypothesis was tested with a correlation metric and image pairs were found to be 715 in high agreement with an average PCC value near 0.8 calculated across seven profiles from five 716 AIM/CIPS orbits. This new finding appears to agree with current theories of PMC growth and 717 ice particle sedimentation in the mesopause region. However, our study, and that of Rusch et al., 718 [2016], were both based on limited samples of the CIPS data set and require further 719 investigation. 720 As of 2017, the AIM mission has far exceeded its originally planned two-year operational 721 period, which began in 2007, and has acquired 10 years of extensive CIPS instrument imagery 722 available for mapping the geographical extent, structure, and seasonal variability of PMCs over 723 the summer polar regions. This pilot tomographic study demonstrates a valuable new capability 724 for investigating a broad range of mesospheric gravity waves (and other dynamical features) in 725 both the northern and southern summer polar regions, important for investigating their 726 longitudinal, inter-hemispheric, and inter-annual characteristics and variability. 727

728 Acknowledgments 729 This pilot tomographic study was supported by Grant No. ATM 0536876 from the National 730 Science Foundation (NSF) and utilized data collected as part of NASA's Aeronomy of Ice in the 731 Mesosphere (AIM) satellite. This mission was developed as part of the NASA Small Explorer 732 Program under contract NAS5-03132. The gravity wave research presented herein was supported 733 as part of this program through a subcontract from Hampton University to Utah State University 734 # 05-17. We would also like to thank the CIPS imaging team, in particular C. Jeppesen at the 735 Laboratory of Atmospheric and Space Sciences, for their considerable help in acquiring and 736 processing the initial AIM bowtie imagery. 737 738 Data 739 CIPS level 2 PMC data products are available on the AIM website 740 (http://lasp.colorado.edu/aim/index.html). 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