Tomographic views of the middle atmosphere from a satellite platform
Kristoffer Hultgren
AKADEMISK AVHANDLING for¨ filosofie doktorsexamen vid Stockholms Universitet att framlaggas¨ for¨ offentlig granskning den 3 oktober 2014
Department of Meteorology Stockholm University Stockholm 2014 Cover image: Polar Mesospheric Clouds above Vallentuna, Sweden Photographer: P-M Hed´en,www.clearskies.se
Tomographic views of the middle atmosphere from a satellite platform
Doctoral thesis Kristoffer Hultgren
ISBN 978-91-7447-974-4 © Kristoffer Hultgren, Stockholm, 2014 Stockholm University Department of Meteorology 106 91 Stockholm Sweden
Printed by US-AB Stockholm, 2014 Summary
The middle atmosphere is a very important part of the Earth system. Until recently, we did not realize the importance of the structure of this vaporous shell and of the fundamental role it plays in both creating and sustaining life on the planet. Thanks to the development and improvement of new sounding methods and techniques, our knowledge of the composition of the atmosphere has become more detailed than ever before. We have also learned how to reveal complex interactions between different species and how they react to the incoming solar radiation. The middle part of the Earth’s atmosphere serves as a host for the Polar Mesospheric Clouds. These clouds consist of a thin layer of water-ice particles, only existing during the summer months and only close to the poles. These clouds can be used as a proxy for middle atmospheric dynamics. In order to fully utilize Polar Mesospheric Clouds as tracers for atmospheric variability and dynamics, we need to better understand their local properties. The Optical Spectrograph and Infra-Red Imager System (OSIRIS) is one of two instruments installed on the Odin satellite. The optical spectrograph of this instrument observes sunlight scattered by the atmosphere and thus the Polar Mesospheric Clouds. This thesis deals with a tomographic technique that can reconstruct both horizontal and vertical structures of the clouds by using observations from various angles of the atmo- spheric region. From this information, microphysical proper- ties such as particle sizes and number densities are obtained. The tomographic technique presented in this thesis also pro- vides a basis for a new satellite concept - MATS. The idea behind the MATS satellite mission is to analyze wave activity in the atmosphere over a wide range of spatial and tempo- ral scales, based on the scientific heritage from Odin/OSIRIS and the tomographic algorithms presented in this thesis.
Contents
1 Introduction 7 1.1 The Earth’s atmosphere ...... 8 1.2 The Noctilucent Clouds ...... 11
2 Atmospheric Radiation 15 2.1 Electromagnetic spectrum ...... 15 2.2 Basic radiometric quantities ...... 16 2.2.1 Solid angle ...... 16 2.2.2 Radiant flux ...... 17 2.2.3 Irradiance ...... 18 2.2.4 Radiant intensity ...... 18 2.2.5 Radiance ...... 18 2.3 Concepts of scattering and absorption ...... 18 2.3.1 Scattering angle and phase function ...... 19 2.3.2 Scattering cross-section ...... 19 2.3.3 Index of refraction ...... 20 2.3.4 Size parameter ...... 20 2.3.5 Rayleigh and Mie scattering ...... 20
3 Remote Sensing 23 3.1 Overview ...... 23 3.2 The inverse problem ...... 24
4 Odin/OSIRIS 27 4.1 The satellite platform ...... 27 4.2 The optical spectrograph ...... 28 4.3 Original retrievals ...... 30 4.3.1 Measured radiance ...... 30 4.3.2 PMC brightness ...... 31 4.3.3 Particle sizes ...... 33
5 Tomographic Inversions 35 5.1 Background ...... 35 5.2 Inversion method ...... 36 5.3 A model of Odin/OSIRIS ...... 39 5.3.1 Atmospheric grid ...... 40 5.3.2 Coordinate systems ...... 40 5.3.3 Model description ...... 41
6 The MATS Satellite Concept 43
7 Summary of The Papers 45
Bibliography 49
Acknowledgements 53
Paper I: Hultgren, K., Kornich, H., Gumbel, J., Gerding, M., Hoffmann, P., Lossow, S., and Megner, L. (2010). What caused the exceptional mid- latitudinal Noctilucent Cloud event in July 2009? J. Atmos. Solar-Terr. Phys., 73, 2125-2131.
Paper II: Hultgren, K., Gumbel, J., Degenstein, D., Bourassa, A., Lloyd, N., and Stegman, J. (2013). First simultaneous retrievals of horizontal and vertical structures of Polar Mesospheric Clouds from Odin/OSIRIS tomog- raphy. J. Atmos. Solar-Terr. Phys., 104, 213-223.
Paper III: Hultgren, K. and Gumbel, J. (2014). Tomographic and spec- tral views on the life cycle of polar mesospheric clouds from Odin/OSIRIS. Submitted to J. Geophys. Res.
Paper IV: Gumbel, J., Hultgren, K., and the MATS Science Team (2014). Mesospheric Airglow/Aerosol Tomography and Spectroscopy (MATS) - a satellite mission on mesospheric waves. To be submitted to ESA’s Living Planet Symposium.
Chapter 1
Introduction
Why are we interested in the Earth’s atmosphere?
Earth - a big round planet, yet so small when viewed from space. The atmosphere - a thin gaseous layer, just like the crust of an apple. Just recently, it has been understood that the atmosphere is a very important part of the Earth system. We did not realize the importance of the structure of this vaporous shell and of the fundamental role it plays in both creating and sustaining life on the planet. Up until the mid 20th century, the mean state of the atmosphere was assumed stable and not likely to be noticeably affected by anthropogenic activity. Thanks to the development and improvement of new sounding methods and techniques, our knowledge of the composition of the atmosphere has become more detailed than ever before. We have also learned how to reveal complex interactions between different species and how they react to the incoming solar radiation. In the atmospheric mixture, a wealth of molecular species have been discovered and measured. Together, these gases control the balance between the incoming and outgoing radiation, which, in turn, contributes to the motion of the atmosphere. Some of these gases act as a shield against the harmful ultraviolet radiation from the Sun and as a thermal blanket that traps the heat and insulates the Earth from the cold space. In other
7 words, life on Earth, as we know it, is highly dependent on a sparse layer of molecules floating around above us. Another part of the mixture is present in the atmosphere only as a result of human activities. These gases have an effect that modifies the natural balance of the atmosphere. The long-term consequences of these alterations are yet to be fully evident.
1.1 The Earth’s atmosphere
The vaporous atmosphere is mainly made up of molecular nitrogen (N2 ∼ 78%) and molecular oxygen (O2 ∼ 21%), but also of a small part of noble gases (Ar, He, Ne, Kr, Xe) and minor constituents (CO2, CO, CH4,N2O, O3,H2O) can be found. All of these gases possess very long lifetimes against chemical destruction and are therefore relatively well mixed. However, even if most of the gases are well mixed, the atmosphere itself is highly stratified with significant vertical variations in composition, temperature, pressure, and density. In addition to gases, the atmosphere also contains various solid and liquid particles, such as water droplets, ice crystals, and aerosols. These particles play an important role in the absorption and scattering of solar radiation, as well as the physics of clouds and precipitation. The ratio of molecular species is controlled by either chemistry, molecular diffusion, or mixing due to fluid motion. Molecular diffusion works together with gravity to try to order the atmosphere in such a way that the lightest molecules are present at the top and the heaviest ones at the bottom. The mixing due to fluid motion of the gases is on the other hand independent of molecular mass. At lower altitudes, the time between molecular collisions is so small that the time necessary for molecular diffusion is many orders of magnitude greater than the time required for turbulent motion. However, at higher altitudes, the collisions between molecules occur so seldom that molecular diffusion is the dominant mechanism. As a consequence, the atmosphere is well mixed at altitudes below 100km (the homosphere) and stratified and well ordered by mass above 100 km (the heterosphere). The magnitude of the atmospheric temperature varies greatly, both vertically and horizontally. However, the vertical structure is qualitatively
8 Figure 1.1: The temperature profile of Earth’s atmosphere.
similar everywhere. It is therefore meaningful to think of a typical temperature profile. Figure 1.1 shows a typical example of the vertical temperature profile of the atmosphere. As can be seen, the profile is divided into a set of layers based on the different vertical temperature gradients. These are the troposphere, stratosphere, mesosphere, and thermosphere, each characterized by substantially different chemical and physical processes. The boundaries between these layers are called the tropopause, stratopause, and mesopause. The altitudes at which these boundaries are located are not fixed but vary in time and location, depending on the amount of energy input. The regions are commonly also referred to as the lower atmosphere (troposphere), the middle atmosphere (stratosphere and mesosphere), and the upper atmosphere (thermosphere and above). The focus of this thesis will be on the middle atmosphere. The structure of the temperature profile can be explained by considering the dominant processes occurring at specific altitudes. From a bottom-up approach, a large part of the electromagnetic radiation coming from the
9 Sun at wavelengths in or near the visible part of the spectrum reaches the ground where it is absorbed. From this absorption, the Earth’s surface is heated and re-emits the energy as black-body radiation which, in turn, heats the lower atmosphere. This “blocking” of the outgoing radiation by the atmosphere is referred to as the greenhouse effect and keeps the surface of the Earth warmer than it would have been in the absence of an atmosphere. The phenomenon also causes active convection and, as the air rises, a decrease in temperature with increasing altitude. This gradient defines the troposphere, which ranges in thickness of about 18 km over the tropics, 12 km at mid-latitudes, and 6-8 km near the poles. Much of the variability observed in the atmosphere occurs within this layer, which accommodates approximately 90% of the atmospheric mass and is characterized by strong instability with significant vertical exchange of energy and mass. It is also in this layer most of the weather phenomena takes place. Above the troposphere, in the stratosphere, about 90% of the atmospheric ozone (O3) is held (commonly referred to as the ozone layer). Most of the solar ultraviolet radiation is absorbed by this “layer”, which thus acts to protect all living organisms on the planet from this harmful energy. Due to the absorption by ozone, the stratosphere is heated and, consequently, the vertical temperature gradient reverses. The increase of temperature with altitude suppresses vertical motion, leading to very stable conditions dominated by radiative processes. This leads to a stratified layer extending up to 50 km, which prevents vertical transport between the troposphere and the stratosphere. Since only very little water (∼3 ppm) can cross the cold tropopause, the stratosphere is very dry. An additional middle atmospheric source of water is the oxidation of methane (CH4), which contributes to another ∼3 ppm of H2O. Above the stratosphere, from about 50 km to 90 km, comes the mesosphere. Since the ozone concentration decreases with altitude, there is no heating occurring here. Like in the troposphere, the temperature in the mesosphere again declines with altitude, reaching a minimum at the mesopause. The temperature at the mesopause can reach as low values as −180◦C, which are the lowest temperatures in the whole Earth system. This allows for the very small amounts of water vapor existing in the mesopause region to form water-ice particles which gives us the beautiful Noctilucent Clouds, observable during twilight at the near-polar summer latitudes. These clouds are discussed further below. The mesosphere lies above the maximum altitude for aircraft and balloons and below the
10 minimum altitude for orbital spacecraft. It has therefore only been accessed through the use of sounding rockets. As a result, the mesosphere is the most poorly understood part of the whole atmosphere. From about 90 km, in the thermosphere, the temperature once again rises. This time this mainly happens due to the absorption of solar radiation (mainly EUV and X-ray radiation) by molecular oxygen (O2) and the stripping of electrons from NO, O2, O, and N2 (photoionization). This causes the refractive index to change (see section 2.3.3), which enables radio waves to be “reflected” and received beyond the horizon. The maximum temperature values are strongly dependent on the solar activity and can exceed 2000◦C. However, even though the temperature is so high, one would not feel warm in the thermosphere. This is because the pressure is so low that there is not enough contact with the few atoms of gas to transfer much heat. A normal thermometer would read significantly below 0◦C since the energy lost by thermal radiation would exceed the energy acquired from the atmospheric gas by direct contact. Above the thermosphere lies the exosphere. Here, the atmosphere gradually turns into space.
1.2 The Noctilucent Clouds
The atmospheric region mainly discussed in this thesis is the mesosphere. This region is characterized by a negative gradient of temperature. The exponential decrease of density with altitude leads to very low pressure, which causes large particles to rapidly sediment out of this region. The mesosphere can therefore only host very small particles. Despite this behavior, the particles that do exist in the mesosphere influence the physics of the region significantly; it has been shown that particles influence both the charge balance and the chemistry of the mesosphere. As we shall see, they also enable ice formation in this very dry region, giving rise to the Noctilucent Clouds (NLCs). We know today that NLCs are composed of water-ice particles, possibly with small nucleation cores. For the small amount of water vapor existing in the region to be able to condense, the saturation ratio needs to be sufficiently high and, hence, the temperature needs to be low enough. This exceptional state only occurs during summer, a counter-intuitive
11 phenomenon that can be explained by the general circulation of the atmosphere; gravity waves, generated in the troposphere by frontal systems or by airflow over mountains, propagate through the atmosphere and dissipate at higher altitudes. When the waves break, they transfer their momentum to the mean flow, being an east-west flow during summer. This deposition of energy induces a small (but important) north-south circulation which leads to an upwelling of air at the summer pole and a downwelling at the winter pole. Air that rises will expand and cool, giving rise to the extremely cold summer mesopause. Once the ice particles have formed, they grow by a direct surface deposition of the surrounding water vapor. Due to gravity, they then consume the available water vapor while falling through the mesosphere. Eventually, the particles can reach sizes exceeding 30 nm and they will be able to scatter light efficiently enough to be observed optically from space or by ground based instruments (see Paper III).
Figure 1.2: Noctilucent Clouds. Image courtesy of NASA.
The geometry for observing NLCs is illustrated in Figure 1.3. During daytime, the molecular scattering of sunlight in the lower atmosphere exceeds the signal scattered by the NLC. When the Sun has set, however, and the troposphere and stratosphere are in shadow, the mesospheric clouds still reflect light until the Sun has proceeded even further below the
12 horizon. These short time periods of twilight are the only occasions when NLCs can be seen by the naked eye.
Figure 1.3: The scattering geometry of Noctilucent Clouds.
When the clouds are observed by space borne instruments, the light scattered by them can be recorded at all times. When viewed from space, the clouds are often referred to as Polar Mesospheric Clouds (PMCs), which is the term used throughout the rest of this thesis.
13 14 Chapter 2
Atmospheric Radiation
Why do we see the things we see?
2.1 Electromagnetic spectrum
The most important physical quantity responsible for energy transfer in the atmosphere is electromagnetic radiation. Electromagnetic radiation travels in wave form at the speed of light. Visible light, ultraviolet light, infrared radiation, microwaves, gamma rays, x-rays, television signals, and radio waves are all electromagnetic waves and constitute the electromagnetic spectrum (shown in Figure 2.1). The human eye is sensitive to electromagnetic radiation with wavelengths from about 400 to 700 nm (or, equivalently, frequencies between 4.3 − 7.5 × 1014 Hz). This wavelength band is therefore called the visible region of the electromagnetic spectrum.
15 Figure 2.1: The electromagnetic spectrum.
2.2 Basic radiometric quantities
The whole area of optical techniques can roughly be divided into the two areas of photometry and radiometry. The central problem of photometry is the determination of optical quantities closely related to the sensitivity of the human eye, and radiometry deals with the measurement of energy per time (power) emitted by light sources or incident on a particular surface. Therefore, the units of all radiometric quantities are based on watts, [W].
2.2.1 Solid angle
When investigating phenomena connected to a radiation field, there is often need to consider the amount of radiant energy confined to an element of solid angle. A solid angle is defined as the ratio of the area η of a spherical surface intercepted at the core to the square of the radius r and has units of steradians, [sr]. It can be written as
η Ω = . r2
16 A differential area is, in polar coordinates, given by
dη = (rdθ)(r sin θdφ) , where θ and φ represents the zenith and azimuthal angles, respectively. Hence, the differential solid angle is
dη dΩ = = sin θdθdφ r2 and the solid angle of a sphere is
Z Z 2π Z π ΩSphere = dΩ = sin θdθdφ = 4π. Sphere 0 0
Figure 2.2: Definition of the solid angle.
2.2.2 Radiant flux
Radiant flux is defined as the radiant energy, W , per unit time and given in units of watts: dW Φ = [W]. dt
17 2.2.3 Irradiance
Irradiance is defined as the power incident on a surface, also called radiant flux density, and is given in units of watts per square meter: dW E = [W · m−2]. dt · dA
2.2.4 Radiant intensity
Radiant intensity is defined as the power per unit solid angle and given in units of watts per steradian: dW I = [W · sr−1]. dΩ · dt
2.2.5 Radiance
Radiance is defined as the power per unit solid angle per unit projected source area and is given in units of watts per steradian per square meter: dW L = [W · sr−1· m−2]. dΩ · dt · dA
2.3 Concepts of scattering and absorption
Most of the light that reaches our eyes is not coming directly from the source but indirectly through the process of scattering. When we look at the sky, the clouds, land, water, or objects surrounding us, we see the light that they scatter. In the atmosphere, we see a lot of colorful examples created by sunlight scattered by molecules, aerosols, and clouds containing water droplets and ice crystals, such as the blue sky, white clouds, magnificent rainbows, and halos. Scattering is a fundamental physical process associated with light and its interaction with matter which occurs at all wavelengths of the electromagnetic spectrum. The process is evident when a particle in the path of an electromagnetic wave absorbs energy from the incident wave and re-emits that energy in (more or less) all directions.
18 2.3.1 Scattering angle and phase function
The scattering angle, θ, is defined as the angle between the incident direction n and the observed direction n0, such that cos θ = n · n0. If θ < π/2, the incident light is scattered in the forward direction. If, on the other hand, θ > π/2, the incident light is scattered in the backward direction. When discussing scattering patterns, a commonly used concept is the scattering phase function, which is represented by a probability function Φ(Θ) of scattering in the direction Θ = cos θ. The scattering phase function is normalized to the total solid angle by
1 Z 2π Φ(Θ)dΘ = 1, 4π 0 such that Φ(Θ)dΘ is the probability that a scattered photon is deflected by an angle θ for which Θ = cos θ is between Θ and Θ + dΘ. Note that the azimuthal dependence (φ) is removed, which is possible under the assumption of a spherical particle. For scattering by arbitrarily shaped particles, Φ(Θ) can become very complex.
2.3.2 Scattering cross-section
In the field of light scattering and radiative transfer, it is customary to use a term called cross-section, σ [m2], to denote the amount of energy removed from the original beam by the particle (the scattering center). The scattering cross-section is a hypothetical area which describes the likelihood of light (or other radiation) being scattered by a particle. In general, the scattering cross-section is different from the geometrical cross-section of the particle.
2 −1 The differential scattering cross-section, σdiff [m sr ], is defined as the amount of radiation scattered into an element of solid angle dΩ in the direction (θ,φ), or, in terms of the phase function Φ(Θ),
dσ σ = = σ · Φ(Θ). diff dΩ The concept thus provides a measure of the strength of the interaction between an individual scatterer and the radiation field. Multiplication with
19 the scatterers’ column density reveals the total scattering along a given path.
2.3.3 Index of refraction
The properties of the medium that the light is traveling through are fully given by the complex index of refraction,
m(λ) = n(λ) − ik(λ), where n(λ) and k(λ) are the real and the imaginary parts, respectively, given as functions of the wavelength λ. Roughly, n and k can be interpreted as the scattering and absorption part of the refractive index. A particle with k = 0 will not absorb light, but scatter light. Typically n has values larger than 1 but not much bigger than a few.
2.3.4 Size parameter
In the atmosphere, the particles that are responsible for the scattering range in size from gas molecules (∼ 0.1 nm) to aerosols (∼ 103 nm), water droplets (∼ 104 nm), ice crystals (∼ 105 nm), and large raindrops and hail particles (∼ 1 cm). The size parameter, x, is a physical term describing the relation between particle size and scattering. For a spherical particle, it is defined as 2πa x = , λ where a is the particle radius.
2.3.5 Rayleigh and Mie scattering
Figure 2.3 illustrates the scattering patterns of spherical aerosols of sizes 0.1 − 1000 nm illuminated by visible light with a wavelength of 500 nm. If x 1, the scattering is known as Rayleigh scattering. A small particle in the Rayleigh regime tends to scatter light equally in the forward and backward directions. When the particle becomes larger, x & 1, the scattering is commonly referred to as Mie scattering and the scattered energy becomes increasingly concentrated in the forward direction with increasing particle size.
20 Figure 2.3: Angular patterns of scattered intensity from spherical aerosols of three sizes illuminated by visible light with a wavelength of 500 nm: (a) 0.1 nm, (b) 100 nm, and (c) 1000 nm. The forward scattering pat- tern for the 1000 nm aerosol is extremely large and is scaled for illustrative purposes. Image source: Liou (2002).
A well known everyday example of Rayleigh scattering is the scattering of visible light by atmospheric molecules, a process leading to the blue color of the sky. This phenomena can be explained by the heavy wavelength dependence of the scattering cross-section in the Rayleigh regime, given by
6 2 2 2 5 (2a) m − 1 σRayleigh = π . 3 λ4 m2 + 2 The scattering opacity of small particles in the Rayleigh regime therefore goes roughly as 1/λ4, making the blue (shorter) part of the spectrum scatter more strongly than the red (longer) part. This results in the indirect blue light coming from all regions of the sky. Mie scattering, on the other hand, is roughly independent of wavelength (although dependent on particle size) and produces the almost white glare around the Sun when a lot of particulate material is present in the air. It also gives us the the white light from mist and fog. Mie theory only works for spherical particles. The T-matrix method, where matrix elements are obtained by matching boundary conditions for solutions of Maxwell’s
21 equations, is an extension to non-spherical particles (Mishchenko et al., 1996). Though this method still works best for relatively simple shapes such as ellipsoids. Understanding Mie theory is not an easy task, and the derivation of the equations is somewhat elaborate. For complex-shaped particles, a fully numerical method has to be employed to solve the Maxwell equations.
22 Chapter 3
Remote Sensing
What if we look at things from a different angle?
3.1 Overview
Remote sensing satellites can roughly be divided in operational satellites and scientific satellites. Generally speaking, operational satellites have a long lifetime and often several near-identical copies, whereas scientific satellites are unique and have a more limited lifetime, but produce more advanced data. An example of a scientific satellite is the Odin satellite, a Swedish led mission being part of an international project involving the space agencies of Sweden (SNSB), Finland (funded by TEKES), Canada (CSA) and France (CNES). Space borne remote sensing instruments have provided the Earth sciences with a wealth of information in recent decades. The first Earth observation satellite was the Television Infra-Red Observation Satellite-1 (TIROS-1), a weather satellite launched April 1960 by the National Aeronautics and Space Administration (NASA), part of the TIROS
23 program and eventually replaced by the satellite series operated by the National Oceanic and Atmospheric Administration (NOAA) (Rees, 2001). Scientific and operational Earth observation satellites carry a variety of passive and active instruments operating in wavelength regions ranging from microwaves to UV. Data acquired from such instruments is used by the scientific community, meteorological agencies, and other organizations. Combining data from different satellites allows for powerful and innovative applications. As defined by Rees (2001), remote sensing is the measuring of physical properties of a system without being in physical contact with it. It can be divided in active remote sensing, where the instrument transmits a signal and measures the signal coming back, or passive remote sensing, where the system simply measures radiation coming from the source. Examples of common technologies for active remote sensing are RADAR and LIDAR. Passive remote sensing is commonly done with radiometers or imagers. For measuring the atmosphere, space borne sensors can either point towards the limb of the atmosphere, or in the nadir (downward) direction.
3.2 The inverse problem
There is an important difference between in situ and remote sensing observations. The former can normally be interpreted as true point measurements, while retrieved satellite quantities always represent a weighted average over all parts of the atmosphere that contribute to the signal observed by the satellite instrument. Following Rodgers (2000), we call the variables that we wish to estimate the state variables, and assemble them into a state vector,
x1 x2 x = . . . xn
24 We similarly assemble the measurements into a measurement vector, y1 y2 y = , . . ym where m is not necessarily equal to n. Our understanding of the relationship between x and y is described by a physical model F, called the forward model, y = F(x, b) + , (3.1) where b is a parameter vector including all model variables that we do not seek to optimize (we call them model parameters) and is the measurement error, including contributions from the observations, the forward model, and the model parameters. The function F thus relates the natural state x to the measurement y and by inverting equation 3.1, we can thus obtain x given y. In the presence of error ( 6= 0), the best we can get is an estimate. We therefore need to weigh the resulting information against our prior (a priori) knowledge xa of the state vector before the observations were made. The optimal solution of x reflecting this ensemble of constraints is called the a posteriori, the optimal estimate, or the retrieval. A simple case of the inverse problem can be formulated for a linear model around the a priori estimate xa and noise-free measurements. The measurements and the state vector are then simply related:
∂F(x, b) y = (x − x ) + F(x , b). (3.2) ∂x a a
The partial derivative of the model with respect to the state vector is called the Jacobian matrix of F(x, b) and in the context of an inversion is often referred to as the kernel matrix, K. In general K is an m × n matrix, where each column vector represents the derivative of F(x, b) with respect to a single element of the state vector,
∂F1 ... ∂F1 ∂x1 ∂xn . .. . K = . . . . ∂Fm ... ∂Fm ∂x1 ∂xn
25 If m = n, K is a square matrix and equation 3.2 can be solved directly to yield the retrieved state,
−1 xˆ = xa + K (y − F(xa, b)) . (3.3)
If F is non-linear, the solution 3.3 must be iterated with recalculations of the Jacobian around successive guesses for x until the result converges.
26 Chapter 4
Odin/OSIRIS
What if we would have an eye in the sky?
4.1 The satellite platform
The Odin satellite was launched on February 20 in 2001 from Svobodny in Eastern Siberia. The satellite was placed into an almost circular Sun-synchronous orbit1 near 600 km with the ascending node2 at 18:00 local time and with a period of approximately 96 min (Murtagh et al., 2002; Llewellyn et al., 2004). Aboard Odin, two instruments are installed: the Sub-Millimeter Radiometer (SMR) and the Optical Spectrograph and Infra-Red Imager System (OSIRIS). The former one, SMR, was designed to (among other things) provide information about the amount of water vapor present in both the atmosphere and in space (Nordh et al., 2003).
1In a Sun-synchronous orbit, the satellite passes over the same section of the Earth at roughly the same local time each day, thus making it synchronized with the Sun. 2The ascending node is the point, or longitude, where the satellite passes over the equator going northward. Similarly, the descending node is the point where the satellite passes over the equator going southward.
27 Figure 4.1: Odin. Image courtesy of Swedish Space Corporation, SSC.
The latter one, OSIRIS, consists of a spectrograph and three IR imagers; this instrument is discussed further below. The Odin mission was designed as a shared mission for both astronomers and atmospheric scientists by looking out into deep space when performing astronomy measurements and to Earth for atmospheric observations. The astronomy part of the mission was, however, completed during 2007. Odin is now operated as an ESA Third Party Mission and runs in pure aeronomy mode. For this latter purpose, the satellite is pointed towards the limb of the Earth, usually in the direction of the satellite track. When performing limb measurements, the entire satellite is nodded so that the co-aligned optical axes of SMR and OSIRIS sweep over selected altitude ranges. Both instruments are designed to retrieve altitude profiles of atmospheric minor species by observing limb radiance profiles.
4.2 The optical spectrograph
The OS part of OSIRIS is an optical spectrograph which measures sunlight scattered by the atmosphere at wavelengths between about 275 - 800 nm and with a resolution of approximately 1 nm (Llewellyn et al., 2004). The
28 geometry of the setup is shown in Figure 4.2. As can be seen in this picture, the line of sight of Odin crosses a range of altitudes over which the scattered signal is integrated. The largest contribution to the observed sunlight do, however, originate at altitudes closest to the tangent point, indicated with a darker gray shade. Figure 4.2 also shows the three main types of scattering that have to be dealt with by atmospheric remote sensing. These are (from left to right in the figure) multiple scattering, which means that the sunlight is scattered multiple times before arriving at the instrument, surface reflection, which means that the sunlight is reflected at the surface of the Earth before returning into the atmosphere and contributing to the signal, and single scattering, which means that the sunlight is scattered once before OSIRIS captures it.
Figure 4.2: The three main types of scattering significant for a limb viewing instrument. Image source: Bourassa et al. (2008).
The instrumental design of OSIRIS is illustrated in Figure 4.3. When the measurements are performed, sunlight scattered by the atmosphere enters the telescope through the exit vane, reflects primarily against the objective mirror, secondly against the field mirror, and then enters the spectrograph through the slit. Inside the spectrograph, the sunlight is collimated3 by a convex mirror before it is splitted by a grating into its different wavelengths. The diffracted light is then redirected further by another mirror and a prism to finally hit the CCD detector. The CCD consists of 1353×32 pixels, where the latter number refers to the 32 columns containing spatial information about the horizontal field of view, which is approximately 40 km at the tangent point. However, due to the limited on-board data storage capacity, the image is compressed to 1353 × 1 pixels, thereby eliminating the horizontal resolution.
3Collimated light is light whose rays are parallel and therefore will spread minimally as it propagates.
29 Figure 4.3: A schematic view of OSIRIS. Image source: Llewellyn et al. (2004).
The pixels of the CCD are exposed to the diffracted sunlight during a time between 10 ms and 10 s, depending on the observed altitude; at the mesopause region, the typical exposure time is 1 s. During nominal aeronomy observations, the vertical field of view is 1 km at the tangent point and the scan speed is 0,75 km/s. The resulting height resolution is approximately 1,5 km in this region.
4.3 Original retrievals
4.3.1 Measured radiance
When sunlight entering the optical spectrograph hits the CCD detector, the information is stored in an on-board data storage. Since the wavelengths of the light are separated by the optical setup of the instrument, it is possible to look further into the relationship between the radiance and the different wavelengths. Figure 4.4 shows an example of a typical spectrum recorded by OSIRIS. By looking at images of this type, the fact that different molecules (species) absorb light of different wavelengths (see section 2.3
30 Figure 4.4: An early mission limb image sequence obtained with the optical spectrograph when Odin was near 80◦N. The altitude range of the tangent line of sight of the scan is between approximately 10 and 60 km. Image source: Llewellyn et al. (2004). above) provides information about what kind of species the light has been traveling through (which wavelengths have been absorbed). For example, the low amount of radiance to the left in Figure 4.4 is due to the presence of ozone (O3) and the small dip centered around 7620 A˚ is due to absorption of O2.
4.3.2 PMC brightness
Figure 4.5 shows the radiance measured at wavelengths 275-310 nm. This specific wavelength interval has been chosen in order to minimize the amount of radiation scattered back from the lower atmosphere and the Earth’s surface. This is possible since light at these wavelengths is absorbed by the stratospheric ozone layer. As Figure 4.5 shows, the radiance is increasing substantially at tangent altitudes around 65-85 km. This is due to the presence of PMCs (see section 1.2) that efficiently scatter light, making more radiation reach the satellite. The line in Figure 4.5 indicated as “Rayleigh background” is the level of radiance originating from
31 Figure 4.5: A typical radiance measurement by OSIRIS at wavelengths 275 − 310 nm.
the background (in other words: without any PMCs). When analyzing properties of PMCs, the background therefore has to be subtracted from the data. The Rayleigh background is calculated using modeled atmospheric density profiles and is a function of latitude, date, and time of day. PMC brightness is then retrieved as the difference between the measured limb radiance and the Rayleigh background for each measurement point between 80 and 88 km at seven different wavelengths: 277, 283, 288, 291, 294, 300 and 304 nm. Figure 4.5 also shows an excellent example of the need for tomographic methods; as can be seen, the PMC brightness has a gradually decreasing appearance below about 80 km. This appearance is simply an artifact of the observation geometry (depicted in Figure 4.2), since an observation along a line of sight at any given tangent altitude also includes contributions to the signal from the fore- and background. This problem is neatly solved by the
32 tomographic techniques discussed in Chapter 5 and Papers II-III.
4.3.3 Particle sizes
To be able to draw further conclusions from the PMC data, for example, about the particle sizes of the observed cloud, the data must be compared to theoretical scattering spectra. In order to do this, the retrieved PMC brightness is converted into a scattering efficiency by relating it to the incident solar spectrum by the ratio between the radiance scattered towards the instrument and the solar irradiance at each wavelength (Karlsson and Gumbel, 2005). The resulting quantity is referred to as a directional albedo, which can be compared to theoretical scattering spectra calculated for various particle sizes and scattering angles.
Figure 4.6: Mie scattering simulations for spherical ice particles (solid lines) together with the directional albedo for various wavelengths (crosses). The circles show the corresponding results without corrections for light scattered back from the ground and the lower atmosphere. Image source: Karlsson and Gumbel (2005).
Figure 4.6 shows theoretical scattering spectra as Mie scattering simulations for spherical ice particles (solid lines) together with the directional albedo for various wavelengths (crosses). This shows a basis
33 for fitting a particle size to the measured PMC data. In this example, the resulting particle radius is 53 nm. The above method is an example of fitting a single size parameter to the spectral data. A similar 1-parameter approach has been shown by von Savigny et al. (2005) who, by assuming that only single scattering occurs, proposed that the radiation scattered by the PMC particles only depends on the solar spectrum S(λ) and on the differential scattering coefficient σdiff (λ, θ) as IPMC (λ, θ) ∝ σdiff (λ, θ) × S(λ), where λ is the wavelength and θ is the scattering angle. The differential scattering coefficient can, in the narrow spectral window used here, be −α approximated by a power law: σdiff (λ, θ) ∝ λ , where α is the so-called Angstrom˚ exponent. By using Mie calculations, the derived Angstrom˚ exponents can be related to the PMC particle sizes and, in turn, the particle sizes to the measured light.
34 Chapter 5
Tomographic Inversions
What if we look at things from every possible angle?
5.1 Background
Tomography refers to imaging by sections, or sectioning, and is usually the representation of a three dimensional object by means of its two dimensional cross sections. The technique has been used for many years in the field of medical imaging, although their application to the atmosphere is still in its infancy. The mathematical basis for tomographic imaging was laid down during the early 20thcentury by Johann Radon (Radon, 1917). The resulting two dimensional Radon transform is used to transform a two-dimensional field f(r, φ) into a formulation that is based on line integrals through the field. If it is possible to determine line integrals at every point within such a field and the angles between successive lines are infinitesimal, then the inverse transform can be used to obtain a solution of the field (Herman, 2009). The Radon transform provides a retrieval of a two dimensional field from knowledge of line integrals through that field. The atmospheric
35 tomography discussed in this thesis also uses a knowledge of line integrals, although made by an optical instrument aboard a satellite platform, to recover the two dimensional volume emission rate profile of the atmosphere. The application of tomographic techniques for satellite measurements of the atmosphere induces some particular limitations not experienced by conventional applications. The solid Earth limits the atmospheric look directions so that only a very limited interval of viewing angles can provide line integrals through a given point. Figure 5.1 shows this scenario. The paths shown are tangent to the solid Earth and therefore represent limiting paths. For an observational point at 85 km, these limiting paths are separated by an angle θ ≈ 20◦. The possible lines of sight intersecting the given point are then all paths between these boundaries. In a geocentric system the same angle θ is also determining the movement of the satellite between positions 1 and 2 and thereby defines the angle along the orbit (AAO) used throughout this thesis, where 1◦ corresponds to approximately 110 km. For a satellite speed of 7 km/s, this implies that the time interval between a set of boundary paths for sampling a given point in the mesopause region is about 5 min. This time interval is consequently also the temporal scale for sampling a specific volume in space at 85 km.
5.2 Inversion method
This part is a bit more abstract than the previous chapters due to the mathematical nature of the inversions. The derivations of the equations given below have therefore been omitted to provide the reader with a somewhat simplified view. A full description of the technique can be found in Degenstein (1999). The inversion method used for the work presented in this thesis has its roots in an approach to de-blurring ring pattern images collected by a Fabry-Perot interferometer. The problem was presented by Lloyd and Llewellyn (1989) as a system of linear equations,
B = AT, (5.1) where B, indexed by i, is the measured image of the object T, indexed by j and distorted by A. The technique, called the Maximum Probability (MP) method, associated Pij, the most probable contribution of the elements j
36 Figure 5.1: The viewing interval for tangent lines through a point at 85 km over which line integrals can be calculated. The points 1 and 2 represent the limiting satellite positions from where this point can be seen (to scale).
to the measurements Bi through the following two equations:
(Bi + ni)AijTj Pij = P − 1, (5.2) j AijTj P i Pij Tj = P , (5.3) i Aij where ni is the number of elements that contribute to measurement i and the use of an initial estimate in equation 5.2 gives a set of values Pij to be used in equation 5.3. This gives a new set of object elements and the process can be iterated until the result converges. McDade and Llewellyn (1993) modified the equations 5.2 and 5.3 to be used for simulations of measurements made with a simple imaging instrument on a satellite platform:
(Oi + ni)LijVj Pij = P − 1, (5.4) j LijVj
37 P i Pij Vj = P . (5.5) i Lij
Here, Oi is a single measurement, ni is the number of grid cells used, th th Lij is the path length of the i measurement through the j cell, Vj is the retrieved volume emission at grid cell j, and Pij is the expected contribution of the volume emission Vj to the measurement Oi. Following Degenstein (1999), modifications to the equations can be made further by substituting equation 5.4 into 5.5 to obtain
(O +n )L V (n−1) P i i ij j i P (n−1) − 1 (n) j Lij Vj Vj = P , (5.6) i Lij where the superscripts (n) and (n − 1) represents the current and previous iterations, respectively. By assuming that
Oi ni and that (n−1) (Oi + ni)LijV j 1, P (n−1) j LijVj equation 5.6 can be approximated as P OiLij i P (n−1) (n) (n−1) j Lij Vj Vj = Vj P . (5.7) i Lij
th As described above, Lij is the path length of the i measurement through the jth cell. Thus, the denominator in equation 5.7 represents the sum of the geometric path lengths of the measurements i through the cell j. Since this sum has no direct dependence on the individual measurements, we can set X Wj = Lij i so that ! (n) (n−1) X Oi Lij V = V . j j (n−1) P Wj i j LijVj
38 Using the fact that X Lij = 1, W i j we can assign Lij βij = . Wj This is then simply a geometry dependent, normalized weighting factor that is unique for each cell and shows the importance of the individual measurements of the iterative solution of each cell. This observation weighting filter determines the influence of each observation on the retrieval in any given cell. To interpret the relative importance of cells in the neighborhood, an averaging kernel can be determined from the weighting filter function value for each observation that intersects the cell. The observation weighting filter function is fundamental to the accuracy and speed of convergence of the final solution. Now, writing equation 5.1 as O = LV, it is possible to construct a forward model based on a previous estimate of the volume emission elements as (n−1) X (n−1) Oi,est = LijVj . j Together, this gives the final simplified iterative expression ! (n) (n−1) X Oi V = V β (5.8) j j (n−1) ij i Oi,est that tells us that the next estimate of the volume emission is given by the previous value multiplied by a weighted average of all measurements of that cell, divided by their estimates from the previous solution. The expression 5.8 is the one used as a basis for all tomographic retrievals made for OSIRIS, used in papers II, III, and IV.
5.3 A model of Odin/OSIRIS
To be able to apply the tomographic technique to measurements made from a satellite platform, it is necessary to create a model of the platform to be able to simulate measurements and to provide a basis for the line integrals Lij. A complete model is described in Degenstein (1999) and Degenstein et al. (2003) and summarized below.
39 5.3.1 Atmospheric grid
As can be seen in Figure 5.2, the atmosphere can be divided into a discrete grid. The grid cells are defined by the AAO (angle along the orbit) and the radial distance from the center of the Earth, creating angular divisions and radial shells. They are labeled with an index j, the same j as in the tomographic equations above, increasing with atmospheric layer and angular division. Associated with the atmospheric grid are the parameters ∆angle and ∆shell, describing the angular width and the radial height of the grid cells. The number of angles and shells are then given by specifying intervals in the two dimensions and, subsequently, dividing by ∆angle and ∆shell, respectively.
Figure 5.2: An illustration of a discrete grid used to model the atmosphere (not to scale).
5.3.2 Coordinate systems
To model the complete scenario where the optical spectrometer of OSIRIS is observing the atmosphere of the Earth from the Odin satellite, three different coordinate systems are used. These are the ascending node system, an Earth centered three dimensional Cartesian space (ˆxasc, yˆasc, zˆasc) with the x-axis pointing towards the ascending node of the satellite orbit, the satellite system, an Earth centered three dimensional Cartesian space (ˆxsat, yˆsat, zˆsat) rotating with the satellite motion and having the x-axis pointing through the local zenith, and the instrument system (ˆxinst, yˆinst, zˆinst) with the x-axis corresponding to a preferred direction within the focal plane and the z-axis pointing in the direction of the optical axis.
40 The satellite position is at any time given by
Sasc = Rsat (cos α · xˆasc + sin α · zˆasc) , where Rsat is the radial distance of the satellite from the center of the Earth and α is the angle along the orbit from the ascending node, and
Ssat = Rsat · xˆsat in the ascending node and satellite systems, respectively. For the instrument coordinate system, a unit vector for the field of view in the orbit plane can be defined as
Pinst = sin Ω · xˆinst + cos Ω · zˆinst, where Ω is the deviation of the look direction from the optical axis.
A transformation of a look direction vector Pinst into an instantaneous field of view vector Psat in the satellite system can be performed by using the three rotation angles ω, θ, and φ, related to the yaw, pitch, and roll of the optical axis, as
1 0 0 cos θ 0 − sin θ cos ω − sin ω 0 Psat = 0 cos φ − sin φ 0 1 0 sin ω cos ω 0 Pinst. 0 sin φ cos φ sin θ 0 cos θ 0 0 1
To further transform the unit vector into the ascending node system, a rotation of the satellite angle α around they ˆsat axis completes the process:
cos α 0 − sin α Pasc = 0 1 0 Psat. sin α 0 cos α
5.3.3 Model description
A radial shell can be represented by the basic formula
r2 = x2 + y2 + z2. (5.9)
41 The position of a point at a distance d along a look direction Pasc is, in the ascending node frame, described as
xasc = Sx + Pxd, (5.10)
yasc = Pyd, (5.11)
zasc = Sz + Pzd, (5.12) where Sx and Sz are the satellite coordinates. By putting equations 5.10-5.12 into equation 5.9 a second degree equation is obtained and it is possible to solve for the distances from the instrument to the shell intersections by q 2 2 2 ds = − (Sasc · Pasc) ± (Sasc · Pasc) − Rsat + r , where the sign of the square root term indicates if the line of sight intersects the shell twice or not at all. To determine the distance of lines of sight to the angular divisions, the introduction of a plane z = x tan γasc is convenient. Here, γasc represents the angle of the plane along the orbit track in the ascending node coordinate system. The distance from the instrument to the plane is then given by
Sx tan γasc − Sz da = . Pz − Px tan γasc
The two sets of distances ds and da can then be combined to calculate all distances needed for the tomographic algorithm, including the parameter Lij, and hence all the constituents needed to run the retrieval are in place.
42 Chapter 6
The MATS Satellite Concept
What if we use our knowledge to create something entirely new?
The Swedish effort in space activities has during a long time been characterized by innovation and cost effectiveness, both by industry and academia. In the last decades, this has led to several successful scientific and technical satellite missions (e.g. Viking, Freja, Astrid 1, Astrid 2, Odin, and Prisma). Through this, the Swedish space program has shown the ability of being both extremely cost effective and able to deliver good results in terms of technology demonstrations and new scientific data. In October 2011, the Swedish National Space Board (SNSB) distributed a call for ideas to investigate innovative low-cost research missions using small satellites. The ideas should build on new technology to achieve cost effective designs and operations. The objective of the call was to “survey for feasible options for high-quality research missions and assess their potential for being accomplished to break-through low-cost budgets through the use of emerging technologies and innovative ways of working”. In order to be selected, the mission concept thus needed to fulfill requirements on both scientific quality and technical innovation.
43 In January 2012, twelve proposals of mission concepts had been laid forward by Swedish research groups within the fields of atmospheric science, solar-terrestrial interaction, planetary science and astronomy. Based on the tomographic ideas developed in this thesis, one of these concepts was MATS - Mesospheric Airglow/Aerosol Tomography and Spectroscopy. During the spring of 2012, the concepts went through a scientific evaluation. This was followed by a technical evaluation together with five leading organizations from the national space industry (OHB Sweden, AAC˚ Microtec, Omnisys Instruments, NanoSpace and RUAG Space). During 2013, OHB Sweden and AAC˚ Microtec continued to collaborate with the scientific groups and defined a new satellite platform, InnoSat (Larsson et al., 2014). InnoSat is a universal platform designed to be “low-cost” and compatible with several of the proposed missions. With regards to the new InnoSat concept, three of the original ideas were, in early 2014, invited by SNSB to submit updated proposals based on the technical evaluation. During spring 2014, SNSB chose the MATS project to go through a Mission Definition Phase during summer 2014.
The general ideas behind the MATS satellite mission are described in Paper IV. MATS is to investigate structures and wave activity in the MLT region over a wide range of spatial and temporal scales. The measurements are therefore based on optical emissions from the altitude range 80-100 km. Wave patterns will be analyzed in terms of emitter densities, temperatures and cloud structures derived from measured radiance from solar scattering and emissions by both molecules and PMCs. Based on the resulting global MLT wave climatology, a number of scientific questions will be addressed. The tomographic analysis techniques described in this thesis have become a central part of the MATS project. In addition to the tomography of Polar Mesospheric Clouds in the ultraviolet, described in papers II and III, this also includes tomography on airglow emissions (dayglow and nightglow) from excited O2 in the near-infrared. MATS is today based on an instrument consortium led by the Department of Meteorology at Stockholm University (MISU), involving MISU, Chalmers, the Royal Institute of Technology (KTH), and Omnisys Instruments.
44 Chapter 7
Summary of The Papers
What if we would tell the world what we have seen?
Paper I
Hultgren, K., Kornich, H., Gumbel, J., Gerding, M., Hoffmann, P., Lossow, S., and Megner, L. (2010). What caused the exceptional mid-latitudinal Noctilucent Cloud event in July 2009? J. Atmos. Solar-Terr. Phys., 73, 2125-2131.
The existence of PMCs requires, as discussed earlier in this thesis, a combination of very low temperatures, sufficient water vapor, and nuclei on which ice can grow. These conditions are occasionally met at latitudes pole-ward of 50◦ latitude. However, in July 2009, PMCs were observed from both Paris (48◦N, 3◦E) and Nebraska (41◦N, 100◦W). Paper I analyzes the atmospheric conditions on this day using temperature data from the Microwave Limb Sounder (MLS) aboard the Aura satellite, PMC radiance data from OSIRIS, winds and tidal data from the Global-Scale Wave
45 Model (GSWM), and microphysical simulations performed by using the Community Aerosol and Radiation Model (CARMA). The results suggest that the reason for the formation is a combination of local temperature variations by diurnal tides, favorably located large-scale planetary waves, and general mesospheric temperature conditions below the average compared to previous years. As Paper I introduces a number of important questions of current mesospheric research, it serves as a motivation for the new analysis methods that are the focus of Papers II-IV.
Paper II
Hultgren, K., Gumbel, J., Degenstein, D., Bourassa, A., Lloyd, N., and Stegman, J. (2013). First simultaneous retrievals of horizontal and vertical structures of Polar Mesospheric Clouds from Odin/OSIRIS tomography. J. Atmos. Solar-Terr. Phys., 104, 213-223.
This paper is the main paper of this thesis and focuses on tomographic retrievals of PMCs. The paper presents the algorithm outlined in chapter 5 and applies it on PMC observations made by OSIRIS. This is done by introducing local scattering from a cloud element in terms of the volume scattering coefficient βλ that includes the dependence on the scattering angle. The results include the first simultaneously retrieved vertical and horizontal PMC structures and shows that the tomographic algorithm is able to locate detailed structures such as tilts, stratifications, or holes that cannot be analyzed by other limb, nadir, or ground-based measurements.
Paper III
Hultgren, K. and Gumbel, J. (2014). Tomographic and spectral views on the life cycle of polar mesospheric clouds from Odin/OSIRIS. Submitted to J. Geophys. Res. on 2014/08/14
Paper III applies the tomographic algorithm developed in Paper II to retrieve microphysical parameters from PMCs, such as particle sizes,
46 particle number densities, and ice mass densities. The results show that the general structure is consistent with a well established growth-sedimentation scenario, where large numbers of small particles exist near the top of the observed cloud layer with a trend towards increasing particle sizes and decreasing particle number densities with lower altitudes. However, we find substantial horizontal variation of the clouds’ vertical structure and properties. A surprising finding is the presence of small numbers of rather large particles well below the brightest part of the cloud. This has important implications for PMC microphysics. It also has implications for the analysis of conventional (non-tomographic) PMC remote sensing techniques.
Paper IV
Gumbel, J., Hultgren, K., and the MATS Science Team (2014). Mesospheric Airglow/Aerosol Tomography and Spectroscopy (MATS) - a satellite mis- sion on mesospheric waves. To be submitted to a future ESA Living Planet Symposium or similar conference.
This paper presents a future application of the tomographic inversions in terms of a new satellite concept - MATS. The idea behind the MATS satellite mission is to analyze wave activity in the MLT over a wide range of spatial and temporal scales, based on optical emissions from altitudes 80-100 km. Based on the resulting global MLT wave climatology, a number of scientific questions on wave properties and atmospheric coupling processes can be addressed. The paper describes both scientific ideas and the instrumental/analysis concepts behind the project.
47 48 Bibliography
Bourassa, A. E., Degenstein, D. A., and Llewellyn, E. J. (2008). SASK- TRAN: A spherical geometry radiative transfer code for efficient estima- tion of limb scattered sunlight. Journal of Quantitative Spectroscopy and Radiative Transfer, 109:52–73.
Degenstein, D. A. (1999). Atmospheric volume emission tomography from a satellite platform. PhD thesis, University of Saskatchewan, Saska- toon. http://ecommons.usask.ca/bitstream/handle/10388/etd-10212004- 001601.
Degenstein, D. A., Llewellyn, E. J., and Lloyd, N. D. (2003). Volume emis- sion rate tomography from a satellite platform. Appl. Opt., 42:1441 – 1450.
Herman, G. T. (2009). Fundamentals of Computerized Tomography: Image Recon- struction from Projections, 2nd ed. Academic Press.
Karlsson, B. and Gumbel, J. (2005). Challenges in the limb retrieval of noctilucent cloud properties from Odin/OSIRIS. Adv. Space Res., 36:935– 942.
Larsson, N., Lilja, R., Orth,¨ M., Viketoft, J., B¨ackstr¨om,J., K¨ohler,J., and Lindberg, R. (2014). An ingenious spacecraft architecture for innovative low-cost research missions. In Proceeding of the 4S Symposium, Porto Petro, Majorca, Spain.
Liou, K.-N. (2002). An Introduction to Atmospheric Radiation. Academic Press.
49 Llewellyn, E. J., Lloyd, N. D., Degenstein, D. A., Gattinger, R. L., Petelina, S. V., Bourassa, A. E., Wiensz, J. T., Ivanov, E. V., McDade, I. C., Sol- heim, B. H., McConnell, J. C., Haley, C. S., von Savigny, C., Sioris, C. E., McLinden, C. A., Griffioen, E., Kaminski, J., Evans, W. F., Puckrin, E., Strong, K., Wehrle, V., Hum, R. H., Kendall, D. J., Matsushita, J., Murtagh, D. P., Brohede, S., Stegman, J., Witt, G., Barnes, G., Payne, W. F., Pich´e,L., Smith, K., Warshaw, G., Deslauniers, D. L., Marchand, P., Richardson, E. H., King, R. A., Wevers, I., McCreath, W., Kyr¨ol¨a,E., Oikarinen, L., Leppelmeier, G. W., Auvinen, H., M´egie,G., Hauchecorne, A., Lef`evre,F., de La N¨oe,J., Ricaud, P., Frisk, U., Sj¨oberg, F., von Sch´eele,F., and Nordh, L. (2004). The osiris instrument on the odin spacecraft. Canadian Journal of Physics, 82(6):411–422. Lloyd, N. D. and Llewellyn, E. J. (1989). Deconvolution of blurred images using photon counting statistics and maximum probability. Can. J. Phys., 67:89–94. McDade, I. C. and Llewellyn, E. J. (1993). Satellite airglow limb tomogra- phy: methods for recovering structured emission rates in the mesospheric airglow layer. Canadian Journal of Physics, 71(11-12):552–563. Mishchenko, M. I., Travis, L. D., and Mackowskib, D. W. (1996). T-matrix computations of light scattering by nonspherical particles: A review. Jour- nal of Quantitative Spectroscopy and Radiative Transfer, 55(5):535–575. Murtagh, D., Frisk, U., Merino, F., Ridal, M., Jonsson, A., Stegman, J., Witt, G., Eriksson, P., Jim´enez,C., Megie, G., de La No¨e,J., Ricaud, P., Baron, P., Pardo, J. R., Hauchcorne, A., Llewellyn, E. J., Degenstein, D. A., Gattinger, R. L., Lloyd, N. D., Evans, W. F. J., McDade, I. C., Haley, C. S., Sioris, C., von Savigny, C., Solheim, B. H., McConnell, J. C., Strong, K., Richardson, E. H., Leppelmeier, G. W., Kyr¨ol¨a,E., Auvinen, H., and Oikarinen, L. (2002). Review: An overview of the odin atmospheric mission. Canadian Journal of Physics, 80:309. Nordh, H. L., von Sch´eele,F., Frisk, U., Ahola, K., Booth, R. S., Encrenaz, P. J., Hjalmarson, A.,˚ Kendall, D., Kyr¨ol¨a,E., Kwok, S., Lecacheux, A., Leppelmeier, G., Llewellyn, E. J., Mattila, K., M´egie,G., Murtagh, D., Rougeron, M., and Witt, G. (2003). The Odin orbital observatory. Astronomy and Astrophysics, 402(3):L21–L25. Radon, J. (1917). Uber¨ die bestimmung von funktionen durch ihre integral- werte l¨angsgewisser mannigfaltigkeiten. Berichte ¨uber die Verhandlun- gen der K¨oniglich-S¨achsischenAkademie der Wissenschaften zu Leipzig,
50 Mathematisch-Physische Klasse [Reports on the proceedings of the Royal Saxonian Academy of Sciences at Leipzig, mathematical and physical sec- tion] (Leipzig: Teubner), 69:262–277. Translation: Radon, J. and Parks, P.C. (translator) (1986). On the determination of functions from their integral values along certain manifolds. IEEE Transactions on Medical Imaging, 5(4):170-176. Rees, W. G. (2001). Physical Principles of Remote Sensing. Cambridge University Press. Rodgers, C. D. (2000). Inverse Methods for Atmospheric Sounding: Theory and Practice (Series on Atmospheric Oceanic and Planetary Physics). World Scientific Publishing. von Savigny, C., Petelina, S. V., Karlsson, B., Llewellyn, E. J., Degenstein, D. A., Lloyd, N. D., and Burrows, J. P. (2005). Vertical variation of NLC particle sizes retrieved from Odin/OSIRIS limb scattering observations. Geophys. Res. Lett., 32(7):L07806.
51 52 Acknowledgements
I would like to express my special appreciation and thanks to my supervisor Professor J¨orgGumbel - you have been a tremendous mentor for me. Also, huge thanks to Heiner for always being a bank of knowledge, to Jonas for keeping peace in the room, Peggy for acting as a mentor, and to the whole AP-group for always sharing so much cookies! A big thanks to all PhD students for making my time at MISU memorable and something I always will look back to as a special part of my life. I would like to send out a large amount of gratitude to Doug, Adam, and Nick for all your help with the algorithms and for the hospitality during my stay in Saskatoon. Adam, I won’t forget the day when we chased a balloon over the whole Canadian prairie and actually captured it. A special thanks to my family. Words cannot express how grateful I am to my mother and father for all of the sacrifices that you’ve made on my behalf. At the end I would like to express appreciation to my beloved wife Sara who always supports me and guides me in the right direction - I love you!
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