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Computer modeling of light scattering
by atmospheric dust particles
with spheroids and ellipsoids
vii
Computer modeling of light scattering by atmospheric dust particles with spheroids and ellipsoids
viii
Preface
For protons, asteroids, stars
and croissants.
This thesis was prepared in the Finnish Meteorological Institute (FMI)
with the generous support from the Vaisala foundation, the Academy of
Finland and the Magnus Ehrnrooth foundation. The subject has been
shifting from solar power usage on the surface of Mars to plasma physics
measurements in the Earth’s orbit all the way up to the electric solar
wind sailing technologies before finally narrowing into the current theme
of light scattering. At one point the working title was ambitiously ’Photons, protons and asteroids - scattering events in the Solar system’. The
scattering is still present, but as the focus of this thesis I chose the smallest of the three: photons.
I express my gratitude for the pre-examiners, Dr. Hester Volten from
the RIVM and Professor Ping Yang from the Texas A & M, for carefully
commenting and approving this thesis. I deeply thank Dr. Gorden Videen
from the US Army Research Lab for agreeing to be the opponent of this
thesis: hope you will enjoy Finland! I feel very honoured and priviledged
to have such great scientists as examiners of my thesis.
I feel huge gratitude towards my supervisors Timo Nousiainen and AriMatti Harri from the Finnish Meteorological Institute. Timo has helped
me immensely in staying in focus; this work and the publications included
would not be the same without his countless constructive comments and
good anger management skills. Not that long time ago, in this galaxy far
far away from any faraway galaxies, Ari-Matti hired me into the Finnish
Meteorological Institute. For this, and for the support ever since, I am
eternally grateful. Professor Jukka Tulkki has graciously supported me
since times of Helsinki University of Technology (now going by a new wavy
Preface
name, Aalto University) and is sincerely thanked for this.
I am also grateful for my boss Gerrit de Leeuw for creating an invigorating working environment. Gerrit is also thanked for scientific insights
and being always the first to join sing-alongs in little Christmas parties!
I also thank Leif Backmann, whose group I had a privilege to be part of
for several great years. I also wish to thank the upper leadership, Unit
Head Ari Laaksonen and Research Director Yrjö Viisanen, for their part
in creating the dynamical scientific working environment of FMI.
I thank all my co-authors for their contributions and fruitful discussions along the way. In addition to previously mentioned, these include
Hanna-Kaisa Lindqvist, Michael Kahnert, Olga Muñoz, Anu-Maija Sundstrõm, Timo H. Virtanen, Matti Horttanainen and Osku Kemppinen in
the papers that are included in this thesis. Quite a few others have been
involved in work and publications on other topics of research - these accomplices are thanked for helping me in keeping perspectives wide; Pekka
Janhunen and other e-sailers deserve a special thanks for building the future of the space travel - it has been great to be part of Electric Solar Wind
Sail development since its early days and to see this groundbreaking technology moving from an idea into realization. I have been lucky for being
able to work in an environment such as FMI and want to thank all my
colleagues for creating this great big family. Especially I thank Markku
Mäkelä for friendly jests and ornithological insights, Johan Silen for his
philosophical take on life and Minna Palmroth for inspiring attitude.
Great many colleagues in the international light-scattering community
have taken part in shaping my understanding of the world. Especially I
thank David Crisp from NASA JPL for advises and encouragement, not
to forget tips on car tuning. Olga Muñoz and Hester Volten are thanked
for providing their publicly available measurements. Zhaokai Meng and
Oleg Dubovik are thanked for the use of their model particle databases.
Both measurements and databases were vital to this study.
For friends and family, especially the furry ones, I owe an apology and
will promise to shift my attention your way right now as this project is
done. Huge hug and thank you for being here!
Myrskylään paljon lämpimiä ajatuksia: kiitos Margit, Birgit ja UllBrit Högström varauksettomasta tuestanne ja aivojen hengähdysmahdollisuuksista pitkin lumisia metsiä suomenhevosten kyydissä matkaten.
Helsinki, January 28th, 2016
Sini Merikallio
x
Contents
Contents
Original publications
1. Review of papers and the author’s contribution
2. Introduction
xi
xiii
xv
1
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2.2 Mineral aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2.3 Scope and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
3. Theory
11
3.1 Properties of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
3.2 Microphysical properties . . . . . . . . . . . . . . . . . . . . . . . . .
15
3.3 Optical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
4. Laboratory measurements
19
4.1 Mineral dust samples . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
4.2 Size Distribution Measurements . . . . . . . . . . . . . . . . . . . .
20
4.3 Scattering Measurements . . . . . . . . . . . . . . . . . . . . . . . .
21
5. Modelling
25
5.1 Spheroids and ellipsoids . . . . . . . . . . . . . . . . . . . . . . . . .
27
5.2 Summing over shapes . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
5.3 Fitting and simulated annealing . . . . . . . . . . . . . . . . . . . .
32
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
6. Summary of results and discussion
35
References
47
Errata
73
xi
Contents
xii
Original publications
This thesis consists of an overview, followed by four internationally peerreviewed research articles. These papers are cited by roman numerals in
the introductory part as follows:
I Merikallio, S., Lindqvist, H., Nousiainen, T., and Kahnert, M. (2011).
Modeling light scattering by mineral dust using spheroids: assessment
of applicability,
Atmospheric Chemistry and Physics, 11:5347–5363.
http://dx.doi.org/10.5194/acp-11-5347-2011
II Merikallio, S., Nousiainen, T., Kahnert, M. and Harri, A.-M. (2013).
Light scattering by the Martian dust analog, palagonite, modeled with
ellipsoids,
Optics Express, 21, 15:17972–17985.
http://dx.doi.org/10.1364/OE.21.017972
III Merikallio, S., Muñoz, O., Sudström, A.-M., Virtanen, T. H., Horttanainen, M., de Leeuw, G., and Nousiainen, T. (2014). Optical modeling
of volcanic ash particles using ellipsoids,
Journal of Geophysical Research: Atmospheres, 11:5347–5363.
http://dx.doi.org/10.1002/2014JD022792
IV Kemppinen, O., Nousiainen, T., Merikallio, S. and Räisänen, P. (2015).
Retrieving microphysical properties of dust-like particles using ellipsoids: the case of refractive index,
Atmospheric Chemistry and Physics, 15:11117–11132.
http://dx.doi.org/10.5194/acp-15-11117-2015
xiii
Original publications
xiv
1. Review of papers and the author’s
contribution
Paper I assessed whether and how single-scattering properties of mineral
dust particles could be modeled using spheroidal model particles. Model
performance was evaluated by comparing simulated scattering matrix elements with measurements from five dust samples, namely feldspar, red
clay, green clay, Saharan dust and loess. The best performing ensemble of various spheroidal shapes was sought at two wavelengths, 632.8
and 441.6 nm. Spheroidal model particles were shown to work well for
the purpose, but no single best-fit shape distribution could be found that
would consistently perform well for all the samples at both wavelengths.
A previously suggested power-law shape distribution was also tested and
found to be suitable. Also a simple equiprobable distribution was found
to work well on most cases. My contributions to this paper included: (i)
accessing database for model particle scattering characteristics, (ii) developing the computer codes required, (iii) performing the modeling required,
(iv) analyzing the results, and (v) writing the majority of the paper.
Paper II studies the performance of ellipsoidal model particles in simulating light scattering from palagonite dust particles. Palagonite is an
often used Martian dust analog material and a good candidate for modeling light scattering from, as real Martian dust was unavailable at the
time this thesis was written. Ellipsoidal model particles were found to
be well suited for modeling light scattering characteristics of palagonite
and, with optimization, very good fits between the measurements and
the model were obtained. The simple equiprobable distribution of ellipsoids performed relatively well. Particle shape was found to be an important parameter affecting the asymmetry parameter and single scattering
albedo, as its variations could be used to deviate their values as much as
typical uncertainties associated with particle sizes and refractive indices.
Both single scattering albedo and asymmetry parameter are important
xv
Review of papers and the author’s contribution
parameters in radiative transfer models, indicating that scattering particle shape could thus be of high importance for them. My contributions to
this paper included: (i) accessing database for model particle scattering
characteristics, (ii) developing the computer codes required, (iii) performing the modeling required, (iv) analyzing the results, and (v) writing the
majority of the paper.
Paper III turns back to Earth and studies the modeling of light scattering by volcanic ash. Modelling volcanic ash single scattering characteristics using ellipsoidal model particles was performed and the modelling
results compared to the measurements from several real volcanic dusts.
The ash was collected and its light scattering characteristics measured
from vicinities of multiple volcanoes. Two of these volcanic ash samples,
Eyjafjallajökull and Puyehue, were previously unpublished. The results
were encouraging in that ellipsoidal model particles seem to work well
in modelling light scattering by volcanic ash. The work continues now
in building look-up tables to be used with algorithms to retrieve volcanic
ash properties from satellite remote sensing data. My contributions to
this paper included: (i) accessing database for model particle scattering
characteristics, (ii) developing the computer codes required, (iii) performing the modeling required, (iv) analyzing the results, and (v) writing the
majority of the paper.
Paper IV studies the usage of ellipsoidal model particles in refractive
index retrievals. This was done by first modeling synthetic random particles single scattering parameters with set refractive indices. The scattering matrices of these synthetic particles were then fitted by scattering
matrices of ellipsoidal model particles calculated with several different
refractive indices. The best-fitting refractive index were then compared
with the original set refractive indices of the synthetic random particles.
A striking discrepancy between set and retrieved refractive index was
found, leading to a conclusion that ellipsoidal model particles can not be
trusted in retrievals of refractive indices of the atmospheric dust. My contributions to this paper included preparing the optical characteristics of
the ellipsoidal model particles and writing a part of the paper.
xvi
2. Introduction
Beware lest you lose the
substance by grasping at the
shadow
Aesop, 620 - 560 BCE
2.1
Background
The Universe is a dust-ridden place with a dusty past. From the birth
of the stars to tiny particles traversing vast empty spaces, it is hard to
find any area or topic that does not share some connection with small
solid particles of matter that can be called dust. Small dust particles
exist in the vicinity of most solar system bodies — from our own atmosphere to cometary comas. Our own solar system is riddled with dust
particles, called the zodiacal cloud, best seen as a halo of scattered light
in the ecliptic plane right before and after the Sun makes its appearance in the sky (Gustafson, 1994; May, 2007). Interstellar dust particle clouds blur our view of parts of the Universe; the light absorbed and
scattered by them, as well as by the exo-zodiacal clouds around other
stars are major sources of noise in detection of exoplanets (Kaltenegger
et al., 2006). Even the design of space technology has been influenced by
threat of small dust particle impacts. For example, the Electric solar wind
sail, a novel technology envisioned to be able to move asteroids from their
tracks (Merikallio and Janhunen, 2010), has its tethers manufactured out
of multiple wires to make them more resistant to micrometeorite impacts
(Janhunen et al., 2010; Seppänen et al., 2013).
Also lifeforms on the planet Earth are influenced by the dustiness of
their environment, be it through destructively invading their lungs, sticking to and abrading their mucous membranes (Nkhama et al., 2015; Zeleke
1
Introduction
et al., 2010), impairing the growth of their leaves (Farmer, 1993; Wu
and Wang, 2014; Zia-Khan et al., 2014), acting as fertilizer (Rodríguez
et al., 2011; Bristow et al., 2010; Yu et al., 2015) or indirectly by scattering the radiation in the atmosphere, thus affecting the climate (Quaas
et al., 2008; Prospero and Lamb, 2003). Climate then affects the whole
biosphere (Bahn et al., 2014; Peñuelas et al., 2013), but the biosphere also
influences the climate (Chapin III et al., 2014; Paasonen et al., 2013), so
the climate-biosphere system is complex and atmospheric dust one of its
components (Carslaw et al., 2010).
Aerosol is a mixture of gas and particles suspended in it, but the term
aerosol is commonly generalized also to refer to those aerosol particles
suspended in gas. The particles can be of a liquid or a solid composition, or a mixture of both. There are several types of aerosols in the atmospheres of Earth and other planets. In more humid environments of
Earth, aerosols are formed by sea spray and evaporation products from
vegetation. Dryer aerosol species include volcanic ash, black carbon pollution and wind-blown dust. The sources of these particles are various;
some are lifted from the eroding surface by wind (Pye and Tsoar, 2009),
while others are spewed high into the atmosphere by volcanoes or meteoric impacts. Yet others get hit by the particles dropping back to the
surface and get lifted by the impact in a process called saltation (Kok
et al., 2012; Beladjine et al., 2007). Saltation is an important mechanism
especially on dry bodies with weak gravity and plenty of dust on their
surface, such as the Moon, Mars and comets. Especially on Mars, the
process is more efficient than on Earth and is the dominating dust lifting mechanism (Greeley, 2002; Almeida et al., 2008; Ayoub et al., 2014).
On the Earth, several types of aerosol particles are emitted into the atmosphere by both natural and human activities, the latter including, e.g.
fossil fuel combustion associated with transportation and energy production, and biomass burning (Pikridas et al., 2013; Dordević et al., 2014;
Beecken et al., 2015; Jalkanen et al., 2015; Sakamoto et al., 2015). These
emissions are affecting the climate (Ramanathan et al., 2001; Mahowald,
2011; Spracklen and Rap, 2013; Charlson et al., 1992), but there is considerable uncertainty in estimating these effects (Boucher et al., 2013).
Mineral dust is a very abundant aerosol species in the Earth’s atmosphere, with a considerable and largely uncertain radiative impact (Stocker
et al., 2013). This impact is caused by scattering, absorption and reemission of radiation, resulting in a measurable change in the spectrum
2
Introduction
and angular dependence of solar and thermal radiation that can tell us
much about the properties of these culprit particles (Kaufman et al., 2002,
2005). Dust also has an indirect effect on the solar radiation field, by modifying reflectivity, formation and lifetime of clouds, which it does by acting
as condensation nuclei (Nenes et al., 2014; Garimella et al., 2014; Määttänen et al., 2005; Klüser and Holzer-Popp, 2010; Spiegel et al., 2014)
and ice-forming nuclei (DeMott et al., 2003; Atkinson et al., 2013). Again
here, the effect is not one sided. Clouds also affect the physical properties, namely composition, shape and size of the dust particles and particle
distributions in exchange (Matsuki et al., 2010). Understanding, and being able to accurately model, the interaction between solar radiation and
atmospheric particles is vital in order to produce reliable models and predictions of weather and climate, both of which are important when considering the future, both short term and long term, of our societies and the
biosphere around us (Revesz et al., 2014; Field et al., 2014; Barros et al.,
2014).
Modelling interaction of light with atmospheric particles is not a trivial
task, especially considering the heterogeneous populations of dust particles with hugely varying compositions, shapes and sizes. Exact analysis
of the scattering event lies often beyond our theoretical or computational
capabilities. Fortunately modeling provides tools and methods that have
proven useful in improving the understanding of this phenomenon. Previously, however, the models have been much too simplistic. As an example,
approximating real mineral dust particles as spherical, homogeneous and
isotropic, i.e. Mie scatterers, is a widely used approach in remote sensing
of trace gases and aerosols, utilized for example in analyzing data from
the Ozone Monitoring Instrument (OMI) (Veihelmann et al., 2007), in a
NASA GISS GCM ModelE (Li et al., 2010) and in lidar observations of
atmospheric desert dust (Pitari et al., 2015), but is also present in other
areas like modeling the scattering by the dust around the Moon (Glenar
et al., 2011). This approximation has long been known to produce inaccurate results (Mishchenko et al., 1995; Yi et al., 2011; Mishchenko et al.,
2003), which was also comfirmed by Papers I, II and III. Although it is
a working assumption for small liquid particles, using spheres to model
light scattering from atmospheric dust and ash particles has increased
the estimation errors and thus impaired forecast accuracies of the models, producing potentially misleading results (Wang et al., 2003; Kylling
et al., 2014), such as overestimation of ash cloud optical depth by 25%
3
Introduction
(Krotkov et al., 1999).
There is thus a profound need for more accurate models to describe light
scattering by real particles, development of which, nonetheless, is not a
simple task: on the one hand we would desire them to be as accurate as
possible, but then also be governed by only a few variables, so that their
optimization and analysis could be manageable and meaningful (Kahnert
et al., 2014). Moreover, the models should not be too straining computationally.
In the mid-90’s, models of light scattering by spheroidal particles were
introduced as a possible tool for improving the accuracy of the singlescattering modeling schemes of irregular particles (Voshchinnikov and
Farafonov, 1993; Voshchinnikov et al., 2000; Mishchenko et al., 1996b;
Schulz et al., 1998, 1999). With the development of more advanced measurement technologies, the whole scattering matrix data of real dust particles became available in the early 2000s (Volten et al., 2001; Muñoz
et al., 2001). A couple of years later, in 2003, it was first shown that
spheroids could be used to simulate laboratory measured data from light
scattering by micron-scale mineral dust particles (Nousiainen and Vermeulen, 2003). It was then logical to question whether spheroids would
provide adequate means for modeling all atmospheric dusts, or if something more complex was needed. This thesis presents further progress
along this path, seeking to add a layer of both depth and width on the
knowledge of the topic. This is done by computer modeling, taking use
of available measurements (see Chapter 4.) and precomputed databases
of optical characteristics of different model particles (Chapter 5). Before
that, however, the target particles are discussed below, and some central
theoretical aspects are introduced in Chapter 3.
2.2
Mineral aerosols
Mineral aerosols form a part of the solid-form aerosol particles, which exhibit various shapes, compositions and mixtures depending on their origins (Taylor et al., 2015). Mineral composition, type of lifting event and
forcing endured while suspended, i.e. by acids, radiation, oxidicing agents,
collisions and agglomeration with other particles, all influence the timevarying form of atmospheric mineral aerosol (Fitzgerald et al., 2015; Sullivan et al., 2007). Typically, these aerosols are very irregular in shape
and vary substantially in mineral composition between different locales
4
Introduction
and from particle to particle (Kandler et al., 2011; Formenti et al., 2011;
Linke et al., 2006). The atmospheric mineral dust content depends on
the relative humidity and wind speed (Csavina et al., 2014), as well as on
the surface characteristics, biggest sources being deserts, arid and semiarid lands (Tegen and Schepanski, 2009). Climate warming and changing
land use is foreseen to affect the amount of dust in the atmosphere in the
future by changing the vegetational cover and weather conditions (Muhs
et al., 2014).
Shape, surface roughness, mineralogical composition, size and internal
structure affect the way single dust particles scatter light. In nature,
these particles occur in various size-, shape-, compositional, structural
and spatial distributions. Ideally all of these particle properties would
have to be taken into account in assessing the influence dust has on the
thermal and solar radiation fields, but this is usually impractical. Remote
sensing observations used in efforts to retrieve these quantities often rely
heavily on assumptions on some of the particle characteristics and mainly
concentrate on retrievals of the total amount of particles present in the
atmosphere (Dubovik et al., 2011; Su et al., 2014; Mishchenko and Travis,
1997; Tanré et al., 1997; Kokhanovsky and de Leeuw, 2009).
Mineral dust and ash can also impare health of Earth’s inhabitants via
a process called silicosis (a condition that has been quite humorously referred to as pneumonoultramicroscopicsilicovolcanoconiosis (Oxford University Press, 2015; Occupational and Environmental Health Department
of Protection of the Human Environment, 1999). The causative link between silica and quartz dusts and lung cancer has been confirmed (Sogl
et al., 2012; Koskela et al., 1994; Yu and Tse, 2014). Moreover, other
symptoms, such as esophageal cancer, cardiovascular disease and chronic
obstructive pulmonary disease (COPD) have been linked with exposure to
dust (Yu et al., 2005; Pan et al., 1999; Chen et al., 2012; Wang et al., 2013)
and dusty atmospheres might even have shaped our genomics (Borzan
et al., 2014). Strenghtening air pollution measures could minimize these
adverse health effects, but on the downside might then lead to accelerated climate change, since airborne sulphate and dust particles increase
the albedo of the Earth, mitigating the impact of greenhouse gas warming by reflecting solar radiation back to space (Makkonen et al., 2012;
Mickley et al., 2012; Arneth et al., 2009). Black carbon particles, on the
other hand, always have a strong warming effect on the climate (Jacobson, 2000; Ramanathan and Carmichael, 2008); minimising their emis-
5
Introduction
sions is thus always worthwhile. Climate change is perceived to be one
of the biggest challenges for humanity to tackle and adapt to in the future and will affect, among other things, agriculture (World Bank Group,
2014; Nelson et al., 2014), food security (Wheeler and von Braun, 2013;
Schmidhuber and Tubiello, 2007), marine ecosystems (Doney et al., 2012;
O’Neil et al., 2012), spread of diseases (Altizer et al., 2013; Pautasso et al.,
2012), species diversity (Thuiller et al., 2011; Bellard et al., 2012; Moritz
and Agudo, 2013), economy (Tol, 2012; Stern, 2013-09-01T00:00:00), and
even sex determination in some species (Neuwald and Valenzuela, 2011;
Holleley et al., 2015). Presumably there also exists effects we are not yet
even aware of.
Then, we go to Mars. I have sought to provide a modeling tool which
could be used to improve dust particle treatment in models designed to
study the radiative transfer in the Martian atmosphere (Paper II). Airborne dust is an especially prevalent feature in the otherwise optically
thin atmosphere of Mars. Dust can also have a substantial impact on the
thermal properties of the atmosphere, global circulation and climate on
Mars. Due to the low gas density of Mars, only about one hundredth of
that of the air close to the Earth’s surface, the force of wind is very feeble
and majority of dust particles are presumably lifted by dust devils (Basu
et al., 2004; Jackson and Lorenz, 2015). Dust devils in Mars are bigger
than those found on Earth, reaching typically heights of 2 - 6 kilometers
(on Earth 250 - 1500 m) and having a diameter of around a quarter of
a kilometer (only 5 - 30 m on Earth) (Cantor et al., 2006; Sinclair, 1964;
Metzger, 1999; Ryan and Carroll, 1970; Ryan and Lucich, 1983; Thomas
and Gierasch, 1985). This difference in size is thought to be due to input
of heat by the aerosol particles that are warmed by solar radiation. Solar
heating of the dust increases the upward drift within the dust devil (Fuerstenau, 2006). Studies of the absorption and scattering of solar radiation
by this dust provide the principle source of information on the processes
generating and maintaining the dust distribution, and its effect on the
climate. Interpretation of remote sensing observations can also be complicated by processes of scattering, absorption and emission by airborne
dust. Physical and optical properties of the atmospheric dust are still
inadequately understood despite ongoing efforts in the field.
Naturally, most of the measurements and data available from atmospheric mineral dust particles concern terrestrial dust. Retrievals of airborne dust properties in the atmospheres of other planets is even more
6
Introduction
challenging, starting from the fact that remote sensing options are far
fewer and then also the measurement technology available is heavily dictated by mass and environmental design constraints. Nevertheless, our
neighbouring planet, Mars, has had several instruments flown in its orbit
or delivered on its surface. Measurements performed by these instruments have given us some constraints on the properties of the Martian
aerosols, see e.g. (Dlugach et al., 2003; Korablev et al., 2005; Smith, 2008;
Wolff et al., 2006) and surface dust deposits, e.g. (Vaniman et al., 2014;
Bish et al., 2013; Morris et al., 2004; Christensen et al., 2004; Ruff and
Christensen, 2002). These have still only given us a sneak peek on the
full range of parameters still unknown to us.
There are currently also small research laboratories on Mars: NASA
has two rovers, named Opportunity and Curiosity (Arvidson et al., 2011;
Grotzinger et al., 2012), operational on the surface. There are also many
future missions, including Insight, which will be concentrating on seismology (Panning et al., 2012) and Exomars, which will focus on preparing
for manned flights (Bost et al., 2015). Opportunity and Curiosity have
been active on the surface of Mars since 2004 and 2012, respectively,
but are more focused on geology and not aimed at examining the atmospheric particles (Squyres et al., 2003; Mahaffy et al., 2012; Grotzinger
et al., 2012). A photo of Martian dust, taken by MSL Curiosity, is shown
in Figure 2.1. In the absence of samples returned to Earth, where more
thorough laboratory investigations could be run, the shapes and characteristics of the Martian dust particles are particularly loosely constrained.
Noteworthily, preparation for human exploration of Mars has been mentioned as one of the goals in a recent NASA report (Mars Exploration
Program Analysis Group (MEPAG), 2015) and novel technologies might
make it possible and economically feasible in the near future (Janhunen
et al., 2015). Challenges of this endeavor include health effects by dust
(Ahmadli et al., 2014), as well as trouble it may cause to machinery by
invading into small spaces and stucking on the surfaces. Accurate models
of Martian dust particles’ single scattering parameters help in retrieving
Martian atmospheric dust properties from remote sensing measurements.
Being able to analyze the amount and quality of atmospheric dust might
then be important considering the safety of operations on the Martian
surface.
7
Introduction
Figure 2.1. Martian surface dust particles that have passed through a 150 μm sieve.
Picture is about 6.5 mm wide and taken by NASA’s Mars rover Curiosity’s
Mars Hand Lens Imager (MAHLI) on Oct. 20, 2012. Image credit: NASA
2.3
Scope and Objectives
In this work, I take a closer look into scattering of light by small atmospheric dust particles with the underlying goal of improving the treatment of scattering by atmospheric dust particles in climate and radiative
transfer models. By comparing measured and modeled scattering matrix
elements, I have found that quite simple models incorporating an assembly of different spheroidal or ellipsoidal model particles perform quite well
in comparison. This provides a useful compromise between a low computational burden and a high modeling performance.
In Paper I we demonstrated the utility of spheroidal model particles
in modeling light scattering from mineral dust aerosols. Paper II then
studied how slightly more complex shapes, ellipsoids, perform in modeling
light scattering from palagonite dust, often used Martian dust analogue.
After this, we returned to Earth and studied the use of ellipsoids on modeling dust particles from volcano eruptions (Paper III). In all these applications, the chosen model particles improve tremendously on the still
often used spherical model particles, but also weaknesses for the tested
models were identified. For example, assessing the best possible shape
distribution proved to be a complex issue, with no clear one favoured distribution standing up for all cases. This indicated that neither spheroids
nor ellipsoids were performing perfectly or even consistently, and raised
8
Introduction
a concern about their usage in retrievals. This was the subject of the Paper IV, where the use of ellipsoidal model particles in retrievals of optical
parameters of dust was discussed. We found that, at least in the case of refractive index, the ellipsoidal model produces erroneous retrieval results.
One should thus be cautioned and not trust the results blindly when using such model particles in retrievals of particle refractive indices. While
models based on ellipsoids generally outperform those assuming spherical or spheroidal particles, further studies are called for, both to assess
the usefulness of ellipsoids in retrievals of other parameters and also in
search of even better performing modeling methods.
9
Introduction
10
3. Theory
Croyez ceux qui cherchent la
vérité, doutez de ceux qui la
trouvent
André Gide
A homogeneous particle’s microphysical properties include its size, shape
and composition. Out of these the optical properties, i.e. scattering and
absorption cross-sections, scattering matrix and quantities retrieved from
those such as single scattering albedo and asymmetry parameter, can
be calculated. Doing this is called solving the direct, or forward singlescattering problem. Going the other way, retrieving the microphysical
properties from the optical properties, is called an inverse problem. Being able to accurately relate the optical and microphysical properties enables solving these problems. Should the solution for the forward problem
have errors, we should expect even more trouble with solutions of the inverse problem. It is important to be able to model light single scattering
by atmospheric particles accurately as it has direct consequences on how
well we can retrieve the properties of these particles from remote sensing
measurements and on how accurately we can estimate their impacts on
forward problems.
In this section, first we look at what light is, after which relevant optical properties of matter are introduced, followed by the microphysical
material properties used, including effective size and effective refractive
index.
3.1
Properties of light
Electromagnetic (EM) radiation has a so-called dual wave - particle nature and can be modeled as either a propagating wavefront of transverse
11
Theory
electromagnetic fields or as a particle of light, a photon (Einstein, 1905).
EM radiation is characterized by its wavelength, λ, which determines the
energy of a photon as E = hc/λ, where h is the Planck constant, 6.6 ·
10−34 Js, and c the speed of light in vacuum, 3.00 · 108 m/s. When the
wavelength is roughly between 400 and 700 nm, the electromagnetic radiation can trigger photoreceptor cells in our eyes and is thus called visible
light. Radiation with wavelengths just below this range are called ultraviolet (UV) light. UV radiation is invisible to us, but can be seen by some
other animal species (Osorio and Vorobyev, 2005; Lind et al., 2013). More
energetic shorter wavelengths beyond this include X-ray and gamma radiation, important especially in medical and astronomical imaging. Light
with longer than visible wavelengths of up to 1 mm, is called infrared (IR)
light. Beyond IR, with decreasing photon energy, there exist microwaves
and radio waves, both used in various contemporary technologies.
On inner planets of the solar system, like Earth and Mars considered in
this study, the main source of light is our own star, the Sun. Our eyes, as
well as plants using light for photosynthesis, have evolved to have their
best sensitivity to the very wavelengths that are both emitted by the Sun
and transmitted through the atmosphere. When the black body radiation
emitted by the Sun propagates through the atmosphere, the atmospheric
molecules and aerosols adjust its intensity, polarization and spectrum.
They do this by absorbing, scattering and emitting electromagnetic radiation.
Light can be described as mutually perpendicular fluctuating magnetic
and electric fields, B and E, both of which are also perpendicular to the
direction of the light propagation. Magnetic and electric fields are related
with each other by four so called Maxwell’s equations, which all electromagnetic fields must satisfy. The first one, Gauss’s law, relates the electric
charge to the electric field it produces (Grant and Phillips, 1990):
= ρ,
∇·D
(3.1)
where ρ is the charge density and D the electric displacement. D is relating E with its environment by a constitutive relation:
+ p,
= r 0 E
D
(3.2)
where 0 (= 8.85 · 10−12 F/m) is the permittivity of free space, r is the
relative permittivity of the medium and p is the polarization, which is
non-zero for dielectric mediums in an electric field. In vacuum, D is equal
to 0 E.
12
Theory
The second law, Gauss’s law for magnetism is
= 0.
∇·B
(3.3)
It states in effect that magnetic monopoles do not exist. The third law
of Maxwell’s, Faraday’s law of induction, describes how time-varied magnetic field induces an electric field:
= − ∂ B,
∇×E
∂t
(3.4)
where t denotes time. Similarly Ampère’s law describes how an electric
current produces a magnetic field circling it:
= J + ∂ D,
∇×H
∂t
(3.5)
where J the current density and H the magnetic intensity. H can be
related to B by another constitutive relation, similarly as D is to E in Eq
(3.2), as
=
H
B
− M,
μr μ0
(3.6)
where μ0 = 4π · 10−7 N/A2 is the permeability of the free space, μr the
wavelength dependent relative permeability of the medium and M the
magnetization of the medium. Both r and μr are dependent on the wavelength of radiation.
Speed of light can be calculated from:
c = (μr μ0 r 0 )−1/2 .
(3.7)
For vacuum both μr and r equal unity. The rate of energy trasported by
light is described by a so called Poynting vector N [W/m2 ] as
=E
× H,
N
(3.8)
and if the light faces a surface, it exerts a radiation pressure amounting
to N/c on it (Grant and Phillips, 1990).
In vacuum, absence of charges and currents leads to both ρ and J to
equal zero, respectively. We can then reach the so called wave equations
by applying a curl (∇×) to both Faraday’s and Ampère’s laws, and using
both Gauss’s laws:
2
− ∇2 E
= 0,
μ0 0 ∂∂2 t E
∂2 2
= 0.
μ0 0 ∂ 2 t B − ∇ B
(3.9)
Solutions to these equations describe time harmonic fields in vacuum. A
plane wave solution can be expressed as
E = E0 ei(ωt−kz) ,
(3.10)
13
Theory
where E0 is the amplitude of the wave, ω = 2πc/λ is the angular velocity
of the radiation, k = ω/c is the wave number of the radiation, t describes
time and z is the distance propagated into direction perpendicular to both
and B.
E
Alas, we are not living in a vacuum, nor is our environment homogeneous, and the previously shown Maxwell’s equations that include source
terms can be very hard to solve around real scattering particles. In Section 3.3 a look is taken into how optical properties of matter, i.e. how it
interacts with the electromagnetic radiation, can be calculated from the
microphysical properties (3.2) - as we will see, often via some approximation.
two important properties of light can be calFrom the field vector E
culated: intensity from the magnitude and polarization state from the
however, is
direction and the movement of the electric field vector. E,
changing its direction at such a fast rate that direct measurements of
its values are unfeasible and some measurable derived quantities are
called for. Sir George Gabriel Stokes, an Irish mathematician working
in Cambridge, introduced in 1852 four parameters that could be used to
describe light (Stokes, 1852). These parameters have been widely used
consists of four components:
ever since. The so called Stokes vector, S,
= [I, Q, U, V ], the first one of which describes the total intensity (polarS
ized and unpolarized) while others describe polarization state; Q and U
linear polarizations at 45◦ angles with respect to each other, and V the
circular polarization. It is common for the light to have non-zero components of all of these so called Stokes parameters simultaneously. However,
for atmospheric scatterers, V is usually vanishingly small. In a cartesian
(x, y, z) coordinate system, for a light ray propagating in the z direction,
the Stokes parameters can be expressed with electric field strength components, Ex and Ey , as:
I=
Q=
U=
k
2
2
2μ0 ωf (|Ex | + |Ey | ),
k
2
2
2μ0 ωf (|Ex | − |Ey | ),
k
∗
μ0 ωf Re(Ex Ey ),
(3.11)
V = − μ0kωf Im(Ex Ey∗ ),
where ωf denotes the angular frequency, asterisk ∗ the complex conjugate operation, Re() the real part, and Im() the imaginary part of the
complex-valued object, respectively. For a fully polarized monochromatic
radiation the Stokes parameters fulfill Q2 + U 2 + V 2 = I 2 . In nature, light
is rarely fully polarized and the degree of light polarization can then be
14
Theory
calculated as Ip /I =
Q2 + U 2 + V 2 /I. The parameter for intensity, I, is
thus always positive, while polarization elements can have either sign.
For natural, unpolarized light, I is the only element differing from zero.
Light is said to be coherent, if it is monochromatic and has a constant
phase difference between all sources. Laser (Light Amplification by Stimulated Emission of Radiation) emits coherent radiation and is often used
in various measurements, including scattering measurements described
later in Chapter 4.
3.2
Microphysical properties
In this section quantities used to describe microphysical properties of dust
particles in this thesis are introduced. An important parameter describing the material properties of the scatterer is its refractive index m. The
refractive index is a complex number; the real part describes the ratio of
the speed of light in vacuum, c, to the phase velocity of the light, v, as it
traverses the material: Re{m} = c/v. The imaginary part of the refractive
index quantifies the relative rate of light that is absorbed into the matter. Thus, for vacuum, the refractive index equals unity, as light moves at
c and no absorption takes place. Refractive index can also be calculated
from the permeability μ and permittivity of the material, as:
m=
μ
,
μ0 0
(3.12)
where μ0 and 0 are the permeability and permittivity of free space, respectively.
For an ensemble of particles, often also the refractive index should be
considered as a distribution of different values as it can change quite significantly in-between individual particles. Also the porosity and inhomogeneity of the particles leads to various refractive index regions within
the particles and can be taken into account by calculating the weighted
average of constituent material refractive indices. Still we didn’t find this
approach to work very well and thus did not use it any further in our
studies. For simplicity a homogenous material, and thus also a singular
m, is almost always assumed.
Absolute sizes of the particles are not needed to calculate the scattering
matrix elements. In the databases used the optical parameters are conveniently tabulated as a function of the so called size parameter X, quantity
15
Theory
relating a particle radius r to the wavelength λ as:
X=
2πr
.
λ
(3.13)
In natural dusts, particle sizes vary a lot and are described by a size distribution. Conveniently, as shown by Hansen and Travis (1974), different
size distributions of similar particles with the same effective radii, reff ,
and effective variances, νeff , have comparable ensemble-averaged optical
characteristics such as single-scattering albedo and asymmetry parameter. This makes the use of reff and νeff very suitable for characterizing size
distributions. The geometric cross-section-weighted mean radius, or the
effective radius, is defined as
rπr2 n(r)
,
reff = r
2
r πr n(r)
(3.14)
where r is the particle radius and n(r) is the number of particles with radius r. Dimensionless geometric cross-section-weighted effective variance
νeff is defined as:
νeff =
r )2 πr2 n(r)
r (r −
eff 2
.
2
reff r πr n(r)
(3.15)
The effective standard deviation of the radius of a distribution of particle
√
sizes is then defined as σeff = νeff (Hansen and Travis, 1974).
3.3
Optical properties
Optical properties of scattering particles describe the way particles interact with incoming light. Quantities discussed in this section are scattering and absorption cross-sections, single scattering albedo, scattering
matrix, and asymmetry parameter, but we first take a brief look into how
these can be calculated.
There is no general analytical solution for calculating optical properties
from the microphysical properties of the particles. Exact analytical solutions for Maxwell’s equations only exist for certain specific geometries,
such as a sphere (described by Mie theory, Mie (1908)), infinite cylinders
(Stratton, 1941) and spheroids (S.Asano and Yamamoto, 1975). Thus, assumptions often have to be made either about the target particle properties, physics involved, or computational accuracy has to be relaxed.
One of the most used computational methods for calculating the optical properties is the T-Matrix method, where boundary conditions for
Maxwell’s equations are used for obtaining the solution (Mishchenko et al.,
1996b). Also the finite-difference time-domain (FDTD) method (Taflove
16
Theory
et al., 2013; Kunz, 1993), where the electric and magnetic fields are iterated by solving them in a discretized grid alternatingly from each other,
i.e. in a leap-frog manner, is popular. Approximations in particle characteristics lead for example to Rayleigh approximation, which is derived
by assuming scattering particles to be much smaller than wavelength (i.e.
X 1). Similarly, for very large particles ray-tracing with geometric optics provides a solution. A Discrete Dipole Approximation (DDA), where
the scattering particle is described by finite number of individual electric
dipoles, is used to model light scattering from small particles of general
shape, but its accuracy is constrained by computational capacity available
(Purcell, 1973; Draine and Flatau, 1994).
Only part of the light is affected by the scatterers. The relative rate of
energy scattered by a particle is indicated by the scattering cross section,
Csca . The scattering cross section also depends on the incident wavelength
and often differs greatly from the geometrical cross section of the particles
(van de Hulst, 1981). Similarly, Cabs indicates the absorption cross-section
and summed together Csca and Cabs form the extinction cross section Cext .
The single-scattering albedo ω then indicates scattering efficiency relative
to the total extinction:
ω=
Csca
.
Csca + Cabs
(3.16)
The single-scattering albedo equals unity when scattering particles are
non-absorbing. In contrast, highly absorbing particles are described by
very small values of ω.
A scattering event can be described by a four-by-four scattering phase
matrix P, which transforms the Stokes vector describing the state of the
sca :
in into one describing the scattered radiation, S
incoming radiation, S
in ,
sca = Csca PS
S
4πr2
(3.17)
where r is the distance from the scatterer. The scattering matrix depends
on the wavelength of the radiation, particle size, composition and shape,
and can be written open as:
⎛
P11 (θ) P12 (θ) P13 (θ) P14 (θ)
⎞
⎟
⎜
⎜ P (θ) P (θ) P (θ) P (θ) ⎟
22
23
24
⎟
⎜ 21
P(θ) = ⎜
⎟,
⎜ P31 (θ) P32 (θ) P33 (θ) P34 (θ) ⎟
⎠
⎝
P41 (θ) P42 (θ) P43 (θ) P44 (θ)
(3.18)
where θ denotes the scattering angle, i.e. the angle between directions of
the incident and the scattered electromagnetic radiation. The scattering
17
Theory
matrix can be reduced to only six independent non-zero matrix elements
when an ensemble of randomly oriented particles with their mirror particles in equal numbers is considered (van de Hulst, 1981; Bohren and
Huffman, 1983):
⎛
P11 (θ) P12 (θ)
0
0
⎜
⎜ P (θ) P (θ)
0
0
22
⎜ 12
P(θ) = ⎜
⎜
0
0
P33 (θ) P34 (θ)
⎝
0
0
−P34 (θ) P44 (θ)
⎞
⎟
⎟
⎟
⎟.
⎟
⎠
(3.19)
Here we have used the so-called phase matrix, P, as a scattering matrix,
which is normalized such that the integral of the first element, P11 , over
the scattering angle θ is
1
2
π
P11 (θ) sin(θ)dθ = 1.
0
(3.20)
P11 is called the phase function and for unpolarized incident light, it describes the angular distribution of intensity for scattered radiation. The
other non-zero elements of the matrix, namely P12 , P22 , P33 , P34 and P44 ,
relate the different polarization components between the incident and
scattered rays.
Even in the simplest of atmospheric radiative transfer models, three key
parameters are needed to describe the single scattering characteristics of
the scattering particles. The rate of light scattered and absorbed can be
calculated from single scattering albedo, ω, and scattering cross section
Csca , related by Equation 3.16. Also a measure for the direction of light
scattering is needed. This is often provided by the asymmetry parameter,
g, which is a cosine-weighted integral of the phase function P11 over the
scattering angle θ:
g=
1
2
π
0
P11 cos(θ) sin(θ)dθ.
(3.21)
It describes the relative amount of forward scattering occurring in the
media. If the light is scattered isotropically, g = 0. If it is scattered mostly
in the forward direction, g approaches unity. If it is strongly scattered
back toward the source, g approaches −1. Due to their central role in
radiative flux computations, we have in Paper II used g and ω as key
quantities in comparing the performance of different models.
18
4. Laboratory measurements
A man with one watch knows
what time it is; a man with two
watches is never quite sure.
Lee Segall
First necessary condition for validating the usage of spheroidal and ellipsoidal model particles for modelling light scattering is their ability to
accurately reproduce the measured optical parameters of sample particles. This however, is not sufficient by itself, but also the microphysical
particle properties that are input in the models, should correspond with
the measured material properties. To assess these qualifications, measurements of both real particle microphysical and optical parameters are
needed. In this chapter, an overview is presented about the apparatus
and principles of these measurements.
The measurements have been performed in Amsterdam and Granada
by suspending sample dust in air and measuring the scattering of a laser
beam in various scattering angles (Muñoz et al., 2012). Both intensity and
polarization parameters, i.e. all scattering matrix elements as described
in Chapter 3, have been measured. The measurements for Puyehue and
Eyjafjallajökull are originally published in Paper III and a palagonite
dust sample was used as a proxy for the real Martian dust (Laan et al.,
2009). Other measurements of mineral and volcanic dusts used in this
study have been published by Volten et al. (2001); Muñoz et al. (2002,
2004, 2011) and Laan et al. (2009).
4.1
Mineral dust samples
The samples have either been collected from the surface or they have been
ground from blocks of solid material. In Figure 4.1, Scanning electron mi-
19
Laboratory measurements
Figure 4.1. SEM-pictures of different sample types discussed in this thesis; mineral dust,
volcanic ash, and Martian analog dust are shown. Each of the red bars is
100 μm in length.
croscope (SEM) images of three types of samples discussed in this thesis
are shown: mineral dust typical for Earth’s astmosphere (Sahara, Paper I), volcanic ash (from Puyehue, Paper III), and palagonite (proxy
for Martian dust, Paper II). The reader should note the characteristic
shapes of volcanic ash particles with sharp edged crystals and vesicular
structures (Maria and Carey, 2002; Riley et al., 2003) as opposed to more
homogenous and rounded shapes of studied mineral dusts.
4.2
Size Distribution Measurements
Light scattering characteristics of particles are strongly influenced by
their sizes (van de Hulst, 1981). This is why before being able to model
light scattering from an ensemble of particles, it is vital to have estimates
of their sizes. Laser sizing is done by measuring the intensity distribution
pattern from the particles and comparing that with scattering patterns
for various sizes provided by the instrument software. A spherical particle shape is assumed and either exact Mie theory or more approximate
Fraunhofer theory are used for calculating the lookup-tables. The Fraunhofer diffraction theory assumes large distance from the scatterer and
a large particle size in addition to spherical shape, which is also the assumption made by the Mie theory. Two instruments were used to measure
the sizes of particles in the samples: a Fritsch laser particle sizer (Konert
and Vandenberghe, 1997) was used for samples measured in Amsterdam
and a Mastersizer2000 (Malvern instruments) was used for samples that
were measured later in Granada, Spain.
The samples considered in this thesis presented various particle sizes:
the effective radiuses are tabulated in Table (4.1) according to the theo-
20
Laboratory measurements
Table 4.1. Effective radiuses of sample particle grouped in volcanic (first) and mineral
dust (later) groups.
Sample
Eyjafjallajökull
Mie
Fraunhofer
reff [μm]
reff [μm]
7.8
4.0
7.0
Lokon
Pinatubo
8.0
2.9
Puyehue
8.6
5.0
4.1
Redoubt A
Spurr Ashton
5.2
2.6
St. Helens
8.9
4.1
feldspar
1.0
green clay
1.55
loess
3.9
palagonite
11.1
4.5
red clay
1.5
Saharan dust
8.2
ries used in their calculation. To grasp the scale of these dust particles,
one can compare them with e.g. human hair, radius of which varies between individuals typically around 8 - 60 μm (Robbins, 1988), whereas
particularly soft furred vicuña (Vicugna vicugna) has an average hair radius of only 7 μm (Bergen and Krauss, 1942) equaling that of a volcanic
particle from Lokon. Normalized projected-surface-area, number and volume size distribution tables for all the samples are freely available in the
Amsterdam-Granada Light Scattering Database, www.iaa.es/scattering/
(Muñoz et al., 2010).
4.3
Scattering Measurements
Light is said to be singly scattered, when it has undergone only one scattering event by independently scattering particles. Multiple scattering,
on the contrary, involves light getting scattered sequentially by multiple
targets, e.g. when passing through an optically thick atmophere. For the
light to be singly scattered requires an optically thin sample. Neverthless,
understanding, and being able to quantify, single scattering behaviour of
the atmospheric particles is essential also when using multiple scattering
21
Laboratory measurements
Figure 4.2. Dust is levitated by brushing it gently from the reservoir into an air stream
so that it can be measured when falling in the air.
radiative transfer applications, which require parameters describing single scattering, such as scattering cross sections, single scattering albedo
and phase functions or asymmetry parameter, as an input (Merikallio,
2003).
Here light scattering measurements from the dust particle samples seek
to determine the scattering parameters for that particular sample so that
those can be compared with or used in the light scattering, radiative
transfer or climate models. Here we briefly outline the principles of these
measurements. In order to acquire Stokes parameters of the sample in
the single scattering regime, target dust must first be suspended in air
in a sufficiently sparse amounts. This is done in the way pictured in Figure 4.2 by brushing the sample little by little into an air stream, which
transports it in front of the measuring laser beams path.
A photomultiplier tube, which multiplies the signal produced by a photon, is used as a detector. In this experimental setup used in Amsterdam
and Granada, the photomultiplier moves along a ring around the target
measuring scattering angles from at most 3◦ to 177◦ (Figure 4.3). The
signal fluctuates slightly due to changes in measured particle flow size
and amount. These fluctuations are detected and corrected for by using
a reference signal from another fixed-location photomultiplier tube. By
using various optical filters and electro-optic modulators, both between
the transmitter and the sample, and between the sample and the detector, different scattering matrix parameters can then be deduced from the
measured intensities (Berry et al., 1977).
22
Laboratory measurements
Figure 4.3. Measurent apparatus showing the sample in the middle and detector able to
rotate around it.
Special tests, as described by Muñoz et al. (2011), are used to ensure
that the experiment stays within the single scattering regime. Checks are
also performed to assure that the measurements fulfill at all measured
scattering angles the so called Cloude coherency matrix test (Hovenier
et al., 1986, 2004) within the experimental errors, assuring that the measured matrix is a sum of scattering matrices of single particles. A detailed
description of the data acquisition, calibration process and experimental
apparatus is available in Muñoz et al. (2010).
The phase matrix, P, is related to the measured scattering matrix, F, by
some unknown normalization factor, a, as F = aP. Because the normalization factor is unknown, values of F11 (θ) in the Amsterdam - Granada
database are normalized simply by setting F11 to equal unity for scattering angle θ=30◦ . This makes database samples comparable with each
other, but it should be noted that in the modelling part of my studies I
renormalized these measurements by extrapolating them with modelling
results so that Eq.(3.20) could be applied. Similarly, in the database,
synthetic scattering matrices are now provided for newer samples measured in Granada. These are produced in the way described in Muñoz
et al. (2007) by extending the measurements to the whole scattering angle
range and including conditions at exact forward and backward directions
as proposed in Hovenier and Guirado (2014). The Amsterdam-Granada
23
Laboratory measurements
light scattering database, http://www.iaa.es/scattering/, provides experimental data and the corresponding extrapolated matrices for all samples
discussed in this work (Muñoz et al., 2012).
24
5. Modelling
Alea iacta est
Julius Cesar, Jan 10th, 49 BCE
Being able to model our environment grants us the ability to compare
the evolution of different environmental states, thus giving us tools for
decision making on future actions. Regarding climate change, this aspect
is crucial, as without good models there is no way to make trustworthy
assessments of our actions into the future of Earths’ climate. Modelling
light scattering by suspended dust particles is only one part of the whole
picture, but there is a very large uncertainty in the amount, and even in
direction, of aerosols’ impact in radiative forcing of our atmosphere. These
uncertainties are larger than with other factors such as trace gas concentrations or solar activity especially when considering cloud albedo changes
that can be considerably affected by atmospheric dust particles (Stocker
et al., 2013). A model can, however, all too easily end up being an oversimplification, in which case the details of real events get either blurred
under the assumptions, or perhaps more gravely, downright wrong conclusions are reached.
I have investigated whether the optical properties of mineral dust and
volcanic ash particles could be simulated by using spheroidal and ellipsoidal model particles. By using these model particles, I am not suggesting that dust particles really have ellipsoidal or spheroidal forms,
but rather that the single-scattering properties of dust particle ensembles
might be simulated numerically by using suitable ensembles of ellipsoidal
or spheroidal model particles.
Scattering matrix measurements of real sample particles were compared
with simulations based on ellipsoids and spheroids. In Paper I we performed a study of spheroids, whereas in Papers II, III and IV we have
progressed toward using ellipsoids as model particles. In this chapter,
25
Modelling
the model particles are introduced and the modelling procedures clarified. As pointed out by Nousiainen (2009), spheroids perform quite well
in modelling light single scattering from mineral dust. They have also
been shown to work pretty well in simulating optical properties of terrestrial clays [Paper I]. Moreover, spheroidal particles optical properties
can be computed within acceptable computational time and pre-calculated
databases exist (Dubovik et al., 2006), making them easy to apply. Although good, spheroids are not perfect, so the logical ’next step’ upgrade
from them was to add one more degree of freedom, most naturally achieved
by using ellipsoids instead of spheroids. The optical properties of terrestrial feldspar particles have been shown to be fairly well reproducable by
models employing ellipsoidal particles (Bi et al., 2009).
We have adopted spheroidal and ellipsoidal model particles for their
simple parametrization (see Section 5.1) and due to the availability of
databases where their optical properties are tabulated (Dubovik et al.,
2006; Meng et al., 2010), but also for the promise they have shown in
previous studies (Bi et al., 2009; Nousiainen and Vermeulen, 2003; Nousiainen et al., 2006; Veihelmann et al., 2006). Moreover, the databases
provided for both spheroids and ellipsoids cover such a wide parameter
space of particle sizes and refractive indices, that they can be readily applied to modelling of atmospheric dust. Other models for particle shapes
have also been considered, be they cylinders (Mishchenko et al., 1996a),
Chebyshev particles (Mishchenko and Travis, 1994; Ding and Xu, 1999;
Petrov et al., 2007), polyhedral prisms (Nousiainen et al., 2006), nonsymmetric hexahedra (Bi et al., 2010), convex polyhedra and deformed
spheroids (Gasteiger et al., 2011), Gaussian random spheres (Muinonen
et al., 1996; Nousiainen et al., 2003; Muinonen et al., 2007, 2009), random
blocks (Kalashnikova et al., 2005), irregular rhombohedra (Dabrowska
et al., 2013), concave fractal polyhedra (Liu et al., 2013), spatial PoissonVoronoi tessellation (Ishimoto et al., 2010; Zubko et al., 2013), or stereogrammetric shapes (Lindqvist et al., 2014) to name a few. However,
databases of sufficiently wide parameter space are not available for these
more refined model shapes. The choice of model particle shape depends on
the problem, target particles and resources at hand, as different shapes
and sizes of particles require different means to calculate their light scattering behaviour.
26
Modelling
5.1
Spheroids and ellipsoids
When spheres are elongated or squashed (one of their dimension varied),
we reach spheroidal shapes. These shapes are called oblate, when one
axis is shorter than the other two, or prolate, when the varied axis is
lengthened. Examples of both an oblate and a prolate spheroid are shown
in Figure 5.1. An assembly of different spheroidal particles can be used to
create different ensemble-averaged optical properties by varying the relative amounts of differently shaped spheroids, i.e. by varying the spheroid
axial ratio distribution. The three dimensional analogue of ellipse, with
three differing main axes, is called an ellipsoid; spheroids are a subset of
ellipsoids with two equal semi-principal axes. An example of an ellipsoid
is shown in Figure 5.2, although it has to be remembered that both oblate
and prolate spheroids (Figure 5.1), and spheres are all ellipsoids as well.
Any ellipsoids surface can be described in Cartesian coordinates, [x, y, z],
by three perpendicular semi-principal axes of length ax , ay and az , as
y2
z2
x2
+ 2 + 2 = 1.
2
ax ay
az
(5.1)
When ay is set equal to ax = axy , a spheroid is reached:
x2 + y 2 z 2
+ 2 = 1.
a2xy
az
(5.2)
All ellipsoids are mirror-symmetric and spheroids are also rotation symmetric; a sphere is an ellipsoid with three equal semi-principal axes. Volume of an ellipsoid can be calculated as
4
V = πax ay az ,
3
(5.3)
which for a sphere becomes the familiar 4/3 πr2 .
The aspect ratio is used in describing the form of a spheroid. Following
conventions used by Nousiainen et al. (2006), the one main-axis length
that differs from the others is placed in the denominator when calculating
the , so that = axy /az . The shape of a spheroid can thus be described
also by a so called shape parameter ξ
⎧
⎪
⎪
⎨ −1
ξ=
1 − 1/
⎪
⎪
⎩
0
as:
> 1 (oblate)
< 1 (prolate)
(5.4)
= 1 (sphere).
Unlike with , the response of shape parameter ξ to the adjustment of
the longest axes’ lengths for both prolates and oblates is similar and linear. This symmetrical behaviour leads to ξ suiting for shape distribution
parametrisation more easily than .
27
Modelling
Figure 5.1. An oblate spheroid (left) is an ellipsoid with two of its largest semimajor axis
being of the same length, whereas a prolate spheroid (right) is an ellipsoid
with two of its shortest semimajor axis being of the same length. Also shown
as shadows are the projections of the spheroids on the x = 0, y = 0 and z = 0
planes.
Figure 5.2. All of the three main axis lengths of an ellipsoid are independent from each
other. Here an ellipsoid is shown with semimajor axis of length 0.5, 1 and 2.
Also projections are shown similarly to Figure 5.1.
28
Modelling
5.2
Summing over shapes
The scattering properties for individual spheroid shapes and sizes were
acquired from the dust optical database of Dubovik et al. (2006), while the
properties for ellipsoids were acquired from the database of Meng et al.
(2010). When considering an ensemble of particles, quantities such as the
cross sections (Cxx , where ’xx’ stands for ’abs’, ’sca’ or ’ext’) can simply be
summed over all participating individual particles shapes and sizes as
Cxx =
ηi
nr Cxx (r, i),
(5.5)
r
i
where nr and ηi are the relative weights for the size, r, and shape, i, bins in
the distribution, respectively, and are naturally normalized to unity. Additional weighting with the corresponding Csca of each particle is needed
in order to calculate the ensemble averages of asymmetry parameter and
the scattering matrix elements. For example,
ηi
nr Csca (r, i)g(r, i)
.
g = i r
η
i
i
r nr Csca (r, i)
(5.6)
The model ensemble scattering matrix P (θ) is similarly obtained by integrating over the measured size distribution and assumed shape distribution as
P(θ) =
i
i η
r
i ηi
nr Csca (r, i)P(θ, r, i)
,
r nr Csca (r, i),
(5.7)
where i is the index of shape, r the particle size, and Csca (r, i) the scatter
ing cross-section. Sum of shape-distribution weights, i ηi , is normalized
to unity.
In the case of spheroids, we have mainly used the power law distribution
suggested by Nousiainen et al. (2006) for shape distribution, f (ξ), which
is defined as:
f (ξ) = |ξ n | ,
(5.8)
where n is a free parameter defining the shape distribution’s form. For
ellipsoids, no equally simple best-guess shape distribution could be identified, so we have been using either the retrieved best-fit shape distribution
or an equiprobable distribution.
Figure 5.3, which has the same content as Figure 1 of Paper I, demonstrates spheroidal model particles scattering matrices for one sample with
a particular wavelength, refractive index and size distribution. It can be
seen that whilst scattering matrices for different spheroidal forms differ
quite a lot between each other, at many instances they do not overlap
with measurements. This is most notable on scattering matrix elements
29
Modelling
P
1
-P /P
11
12
10
P /P
11
22
0.5
11
1
0.8
0.6
0
10
0
0.4
0.2
-1
10
0
45
90
P /P
33
135
180
-0.5
0
45
90
-P /P
11
34
1
135
0
45
90
P /P
11
44
0.5
135
180
135
180
11
1
0.5
0.5
0
0
0
-0.5
-1
0
180
-0.5
0
45
90
T
135
180
-0.5
0
45
90
T
135
180
-1
0
45
90
T
Figure 5.3. Simulated and measured scattering-matrix elements at wavelength λ = 632.8
nm for the sample of loess. Small black dots represent the measurements,
whilst the black line represents the Mie simulation for a sphere. Results
for different spheroidal model particles, all with refractive indices of m =
1.55 + 0.001i are shown in colors and range from prolate (red) to oblate (blue)
aspect ratios. This Figure is reproduction of the Figure 1 from Paper I.
P22 and P44 , but other elements also have such regions especially on small
scattering angles. For these, no ensemble of spheroidal model particles
will be able to exactly reproduce the measurements. Nonetheless, the results for a sphere (black line) often fall even further away from the truth,
demonstrating how often any combination of spheroids will improve the
model when compared with using plain spheres.
The performance of some other generalized shape distributions besides
the previously discussed equiprobable and power law distributions were
also investigated. Simply leaving the most spherical particle shapes out
altogether was found to improve the results slightly. With spheroids, shifting the distribution towards prolates or oblates would also be an easily
applied small adjustment that was tested, as well as different cosineweighted distributions, where the sphere had the heaviest weight of all
the particles. Nevertheless, the results were quite inconsistent and if
for some scattering matrix elements the fits were better, they usually deteoriated for the others so that any significant overall improvement was
30
Modelling
rarely reached. Moreover, the cosine-weighted distribution often underperformed the equiprobable distribution. It thus became quite clear that
spherical particles are far from the optimal choice in modelling real mineral dust particles.
Among themselves, the oblates (bluish lines in the Figure 5.3) have
lightly more variations in their scattering matrix elements than do the
prolates (reddish lines in the Figure 5.3). This might be the reason why
purely oblate shape distributions outperform by a small margin those consisting of purely prolate particles. A distribution consisting of both prolates and oblates usually performs best overall when good fits are pursued
for the whole scattering matrix and for the whole scattering angle range
(0 to 180 degrees). Adding more weight to either the oblate or prolate end
of the distribution occasionally yielded better fits. To do this, however, an
additional modelling parameter would need to be introduced to quantify
the bias between oblates and prolates. As this did not consistently, or even
notably, improve the results the focus with spheroids was kept with the
original ξ n distribution.
As the database for ellipsoids contains tabulations for over 40 different
shapes, and also the measurements are available at more than 40 scattering angles for each of the six independent scattering matrix elements,
the task of optimization is not a trivial one. So for computational reasons
the number of shapes used in fitting was constrained to a manageable
amount. Thus, from both databases, we then carefully selected a subset
of shapes that was used for fitting. We excluded from the analysis shapes
closely resembling the sphere (values of ax /az and ay /az close to unity),
but included the sphere itself (ax = ay = az ). This selection was based on
the work done for Paper I, where it was determined that best-fit shape
distributions for mineral dusts consist mostly of the shapes that have the
largest axial ratios. We finally adopted 34 shapes for the ellipsoids, including six oblate and six prolate spheroids as well as the sphere.
When summing over sizes, we followed the measured size distributions
of the corresponding samples, but acknowledge that making the measurements over particle ensembles is not a simple task and the measurements
might have error in them (Reid et al., 2003). Real refractive indices of the
samples are also not known, which is why we have analyzed many different values for m, but the question still remains if we might be completely
missing the right values. We also considered whether the dependence on
refractive index, m, over small intervals was sufficiently linear so that
31
Modelling
our computed values were not missing anything unexpected. To put it the
other way, when the m-value is bracketed, are the single-scattering characteristics, that would be obtained with the same model, also bracketed?
Nousiainen (2007) studied this problem and found that the dependence
between these quantities is monotonic when calculated over shape distribution, so it seems m-bracketing, even with relatively large intervals, is
sufficient.
5.3
Fitting and simulated annealing
To test the performance of our models, we assessed how well scattering
matrices measured in a laboratory can be reproduced with simulated distributions of spheroids and ellipsoids. In the case of the Martian dust analogue, palagonite, this turns out to be a demanding test, due to the fact
that the analogue particles have larger sizes than those that are typically
found in the Martian atmosphere. This is because we can expect simple
model particles to perform better in mimicking scattering behaviour of
samples with smaller reff (Eq. 3.14), as was shown in Paper I. To quantify the suitability of model particles in reproducing the observations, we
needed to find relative shape distribution proportions of different model
particles such that the measurements could be optimally matched by the
ensemble-averaged scattering properties. As negative weights would have
no physical meaning and thus could not be allowed, simple linear regression algorithms were not suitable for fitting. On the other hand, nonlinear fitting algorithms do not perform well or are not adequately fast in
problems with a large number of degrees of freedom.
We applied a classic Monte Carlo simulated annealing algorithm to find
the shape distribution providing the best fit (Robert and Casella, 2004;
Zelinka et al., 2012). This method starts with a randomized distribution
of shapes and proceeds by varying it stepwise with random deviations,
evaluating the cost function after each step. Should the varied shape
distribution provide a better fit, it is accepted with some probability as
the new starting distribution for the next round of variations. Thus we
slowly move into the direction of better performing shape distributions.
To avoid getting stuck in local minima, the algorithm sporadically accepts
also variations of the shape distribution which increase the cost function
and thus take the fit further away. The probability at which it accepts or
declines the next varied distribution depends on the simulation time in
32
Modelling
an inverse fashion so that this likelihood of acceptance is high at the beginning (i.e. the system is ’hot’) whereas with time the system is ’cooled’
and stray steps are fewer. As the use of the Monte Carlo optimization
method here requires merely summing up precomputed values with different weights, it can be easily performed by computers in a reasonable
time. More over, this method provided very consistent and acceptable results in all the cases where it was applied.
5.4
Discussion
Optical properties of dust depend on composition, homogeneity, surface
roughness, sizes and shapes of the particles. They are also varying with
the wavelength of the incoming light. As always in modelling real world
phenomena, not all characteristics can fully be accounted for. We have
here restricted ourselves into using homogeneous, isotropic, smooth surfaced and highly symmetrical model particles. However, real mineral particles are more often than not inhomogenous and most of them are also
anisotropic and birefringent. Moreover, we have assumed the same characteristics all through the size and shape distributions. In real particles,
the refractive index changes with particle size as do other scattering characteristics, not to mention the shape distribution. To fully account for
these features the model particle characteristics would have needed to
vary individually for each size-bin, but this would have vastly expanded
degrees of freedom in our model and its implementation was beyond our
resources (for the time being). In the future the models will get better,
measurement data sets more numerous, computational power greater and
coding skills ampler, which will all contribute in making possible the ever
more precise modelling of particle characteristics. This will increase our
understanding on our surroundings, perhaps most pressingly on the effects atmospheric dust particles are having on climate.
The models discussed in this thesis are increasing the modelling prowess
for forward applications (Papers I, II and III). There is, however, also a
question raised in Paper IV, whether the ellipsoidal model is so flexible
that it can too easily be bent around any problem to produce misleading
results. There it was found that retrieving the refractive index by using
ellipsoidal model particles produces erroneous results. Specifically, ellipsoids reproduce the target optical properties best with erroneous material
parameters: the refractive index used in calculating ellipsoidal model par-
33
Modelling
ticles optical parameters bears no resemblance to the real world counterparts refractive index [Paper IV]. These model particles might thus not
be suitable for use in retrievals, but they are, nonetheless, the best model
particles that at the moment have extensive databases available for the
required parameter space.
34
6. Summary of results and discussion
Kilteinkin Volta vihaa pölyä.
(Even the nicest Volta hates dust.)
A Finnish vacuum cleaner ad
In modelling light scattering by various atmospheric mineral dust particles, there often is a need for something simple, fast, and yet more accurate than the often used approximation of spherical isotropic particles,
the so called Mie spheres. In this work, the usefulness of spheroidal and
ellipsoidal model particles for this purpose has been assessed. It has to be
emphasized that these model particles are only used as a tool to assess, estimate or forecast the scattering behaviour of the particles and thus their
shape does not, and is not intended to, correlate with the real shapes of
the particles. Ellipsoids, as well as their spheroidal subset, were indeed
found to be superior to the Mie spheres in almost any combinations and
applications. Nevertheless, there were still various issues identified with
the models as well, such as their unreliability in retrievals, which calls for
even better methods to be developed in the future.
The usage of spheroidal model particles was investigated and partially
validated for atmospheric mineral dust (Paper I). It was also studied
whether best-fit shape distributions bear any similarities between different samples. Also, consistency of the best-fitting solution with varying
wavelength was tested for. Positive results from these tests, i.e. that
the best working shape distributions for different wavelengths would be
similar, would allow us to propose a generic, first-guess shape distribution to be used for any suspended dust of similar type as the samples
studied. Unfortunately, but not unexpectedly, although spheroids produce
good results for separate samples, it seems that there is much variation
between best-fit shape distributions of different samples, optimized parameters as well as between different wavelengths. This makes sugges-
35
Summary of results and discussion
tions for a shape distribution difficult to make even when considering a
specific type of particles, such as volcanic ash. Nonetheless, both ensembles of different spheroids and ellipsoids are found to fit all of the studied
measurements significantly better than Mie spheres. This might be because the light scattering characteristics of the individual spheroids and
ellipsoids differ from each other sufficiently so as to provide a good base
ensemble for replicating real measurements of various real particle populations, while spheres do not, due to their perfectly symmetric shapes. A
good starting point for any modelling application using either spheroids
or ellipsoids was found to be the use of an equiprobable shape distribution. In an equiprobable distribution all different model particle shapes
included in the study are present in equal proportions. With spheroids,
even a better solution is available though: a power-law shape distribution
with an exponent around three, as previously suggested by Nousiainen
et al. (2006). This kind of power-law distribution favours the particles
with the largest axial ratio differences.
There is a clear trend indicating that spheroids work best for modelling
particles of the smallest sizes, whereas scattering by ensembles with bigger grain sizes seemed to be more challenging and often impossible to
mimic well. Interestingly, the size dependent performance is strong with
all the other scattering matrix elements except for the polarization elements P12 and P34 ; spheroids perform quite well on reproducing both of
them regardless of the size range. When a generic shape distribution
(Nousiainen n = 3) is used to model the scattering behaviour of any of the
clay types studied, there were huge improvements found when compared
with the Mie particles (Paper I). This is demonstrated by Figure 6.1, identical in content to the Figure 6 of Paper I, where errors are compared
for different samples, wavelengths, quantities and models. The quantity
used for assessing the goodness of models in Paper I was called ψ - in
essence it describes the area in the plot between the measurement and
model curves. As a main message of Figure 6.1 it can be seen that already
an equiprobable distribution (n = 0) of spheroids almost universally reduces the fitting errors when compared with spheres. However, further
improvements can be achieved by using larger values of shape distribution exponent. Performance of spheroids can also be linked with sample
particle size, as results are clearly better for smallest particles. Impressively, when best-fit distributions of spheroids are used instead of the exponential ones in Figure 6.1 (not shown), the error of Mie models could be
36
Summary of results and discussion
reduced by 60 − 100% with the exception of large grained Saharan sand.
We then moved our attention further out into the solar system, to our
neighbouring planet Mars (Paper II). As we do not have the full scattering-matrix measurements of the real Martian dust particles, we had to
rely on an analogue material from Earth, namely palagonite dust. We also
relaxed all axis of our model particles, i.e. moved from spheroidal particles
to generic ellipsoids. We then investigated whether these model shapes
could reproduce the light-scattering measurents performed on palagonite.
Indeed, the fits were found to be very good, as can also be seen in Figure
6.2, which is similar to that of Figure 4 of Paper II. There results are
shown for when the whole scattering matrix of ellipsoidal shape distribution is fitted simultaneously into measurements of palagonite. When the
matrix elements are fitted individually (Figure 2 of Paper II) the fitting
results are close to perfect, but here we can see that trying to find a single
shape distribution of ellipsoids to describe the whole matrix leads into fitting errors. Not surprisingly, using only spheroids, a subset of ellipsoids,
leads to overall worse performance.
Ellipsoidal model particles were shown to be able to effectively reproduce features of the measured scattering matrix elements of the palagonite Mars analog dust. However, each scattering matrix element demanded the use of a unique best-fit shape distribution and these differed
considerably and apparently arbitrarily from each other as well as from
the best-fit shape distribution for when the whole scattering matrix was
optimized simultaneously. This can be seen in Figure 6.3, which is similar
to that of Figure 3 of Paper II, where best-fitting shape distributions for
Palagonite dust are shown both for individual scattering matrix elements
(black circles) as well as for the whole matrix (red crosses). These results
suggest, similarly to the results of Paper I for mineral dust, that using a
standard shape distribution for modelling light single scattering from various dust particles is not an optimal solution. Delightfully however, using
equiprobable shape distribution was found to produce scattering parameter values very close to those produced by using the best-fit shape distribution. This suggests that, if the palagonite can be thought of as being a
representive proxy for Martian dust, an equiprobable shape distribution
of ellipsoids might indeed be a reasonable starting point in modelling the
scattering behaviour of real Martian atmospheric dust particles. Compared with using the best-fit distribution for Palagonite this would provide a more general approach; best-fit shape distribution for palagonite is
37
Summary of results and discussion
Figure 6.1. Almost anything works better than a sphere in modelling light scattering
from mineral dust particles: deviation of asymmetry parameter and ψ values of modeled scattering matrix elements compared for five samples, two
wavelengths, and four models. Each row corresponds to a different sample
ranging from smallest (feldspar in the first row) to the largest (Saharan dust
in the last row). There are seven bar groups in each row, the leftmost (with
light blue background) of which describes the deviation in asymmetry parameter and the others are for each independent scattering matrix element. As
models compared, the three first bars represent different exponential shape
distributions, with exponents n having values of 0, 3 and 10, and the rightmost dark bar describes the error when using a sphere. Moreover, results for
two different wavelengths are presented, the 632.8 nm shown in wider and
colored bars, while 441.6 nm results are represented by thinner dark bars on
top of the others. This figure is identical in content with the Figure 6 from
Paper I.
38
Summary of results and discussion
Figure 6.2. Comparison of measured (red error bars) and modeled scattering matrix elements of palagonite dust - black line shows the result when whole of the scattering matrix has been fitted simultaneously. Individual ellipsoidal shapes
produce the scattering matrix elements drawn in light pink color and sphere
creates the blue line. For comparison, also shown in dashed green line is the
solution for when only spheroidal shapes are used. This figure is similar to
that of Figure 4 from Paper II.
39
Summary of results and discussion
in any case bound to differ somewhat from the best-fit distribution for the
real Mars dust.
When considering volcanic dust, we also assessed the best working shape
distribution on the view points of satellite instrument data analysis. This
we did by considering only scattering matrix elements P11 and P12 on a
limited angle span visible to the instrument. Encouragingly these results
showed only modest variation in-between different wavelengths studied,
as can be seen in Figure 6.4, adapted from Figure 9 of Paper III. Interestingly, pure prolate shapes were missing from the best-fit shape distributions and majority of the favoured shapes had relatively modest aspect
ratios.
It has become very clear, that it is almost impossible to pick a specific
shape distribution for either ellipsoids or spheroids which would be the
best choice for modelling scattering behaviour for all samples and circumstances, even when quite similar samples are compared, as was done in
Paper I (mineral dust) and III (volcanic ash). Instead, the best shape distribution and the performance of the model depend on the sample that is
modeled, on the wavelength the modelling is performed and on the quantity of interest, e.g. which scattering matrix elements or angle spans are
emphasized. For climate modelling applications, the success in modelling
the asymmetry parameter is used to test the particle shape model. In
such situations, a power-law shape distribution, Eq. (5.8), with an exponent n = 3 is, on average, the best choice when using spheroids [Paper
I]. Here as well this generic shape distribution produces significant improvements when compared to Mie models. On the other hand, when the
whole phase function is of concern, a very low value of n (n < 1), or even
an equiprobable distribution (n = 0) seems to work best. Higher values of
n work best when all the elements of the scattering matrix are optimized
simultaneously; in half of the cases the upper limit of n available in our
models, 18, was reached. This aptly demonstrates the high variability
between optimal shape distributions for different uses.
Overall, a simple equiprobable distribution in all studied cases for both
the spheroids and ellipsoids produced good fits to the scattering parameters, which makes an equiprobable distribution a sensible initial approximation for a generic problem. This might be a symptom indicating that
these kinds of model particles provide a sufficiently multiform basis for
reproducing almost any real measurements, e.g. the scattering characteristics by individual shapes differ sufficiently from each other and their
40
Summary of results and discussion
Figure 6.3. Optimally working shape distribution weights when the whole scattering matrix is fitted with the same shape distribution (red crosses) and for when each
scattering matrix is fitted individually (black circles) as a function of largest
axis, be and ce , with respect to the shortest axis, ae . Thus, symbols on diagonal represent oblate spheroids whilst those on x-axis prolate spheroids. The
size of the marker is directly proportional to the weight of the corresponding
shape. This Figure is similar to the Figure 3 of Paper II.
41
Summary of results and discussion
E$YHUDJHEHVWILWRQO QPVDPSOHV F$YHUDJHEHVWILWRQO DQGQPVDPSOHV
E D
EHDH
H H
FHDH
FHDH
Figure 6.4. Best-fit shape distributions for volcanic ash averaged over different wavelengths: blue for the shorter and red for the longer wavelengths considered.
Shaded area in the background corresponds to the region spanned by the
model ellipsoids used and otherwise symbols are similar to those in Figure
6.3. This Figure is adapted from Figure 9 of Paper III.
ensemble smoothes any characteristics, finally providing an adequate,
generic matrix that never falls too far away from reality. As an example, spheroids can be used to describe light scattering from very different
shapes, such as cubes (Nousiainen et al., 2011). As we have seen, both
spheroidal and ellipsoidal model particles work well in forward modelling
applications.
For retrieval purposes, however, an ability to produce close to real optical parameters is not a sufficient demand for model particles. There also
needs to be a correlation between the microphysical characteristics of the
best performing model particles and those of the retrievals target particles. Alas, it was found that often ellipsoid distributions with incorrect
refractive indices were producing significantly better fits than those with
real set parameter values. Moreover, the retrieval of the refractive index failed also when a fixed shape distribution was used. Ellipsoids are
thus not necessarily well suited for retrieving real particle refractive index from remote sensing data and this most likely extends to other aerosol
properties as well.
Calculated optical properties are influenced by assumptions about the
size distribution, particle shapes, and imaginary part of the refractive index. In Paper II, the effects of different assumptions on size, shape and
m on scattering by palagonite particles were also assessed. Shape was
found to impact ω and g by amounts comparable to that caused by size
distribution and imaginary index variations when applied within reason-
42
Summary of results and discussion
λ QP
J
λ QP
λ QP
6SKHUH
%HVWíILW
(TXLSUREDEOH
.H\
.H\
ΔU MP
HII
Δ,PP ΔU
ΔU íMP
íMP
HII
HII
Δ,PP í
í
Q
QVSKHURLGV
Figure 6.5. The asymmetry parameters that are obtained with various size and shape
distributions, wavelengths, and refractive indices. Different shape distribution models are shown in x-axis; a sphere, three ellipsoid distributions and
an exponential spheroid distribution. n3 refers for the exponent of the shape
distribution weights being 3. Different colors indicate different wavelengths
and each group of boxes show results for different varying size distributions
(left) and imaginary parts of the refractive index (right) so that the top of the
box corresponds to the highest, and the bottom to the lowest value used. The
midline represents the values for the default case. This Figure is a reproduction from Figure 6 of Paper II.
able bounds. This is shown for g in Figure 6.5 that is a reproduction from
Figure 6 of Paper II. It even seems to be possible in various situations
to reach in the modelling the same values for ω and g by altering the
shape of the scattering particles rather than adjusting refractive indices
or sizes. An exception to this was found at infrared wavelengths, where
ω is quite insensitive to the shape of the scattering particles. The effect
of particle shape on scattering behaviour has previously been mostly neglected in retrieval algorithms used to analyze remote sensing data of the
Martian atmosphere. Such an omission might well have led to added uncertainties and misinterpretations in the retrieved characteristics of the
Martian atmospheric dust particles. Refractive indices and sizes of the
Martian particles might thus not be even as constrained as we currently
assume and reanalyzing existing data might prove productive.
In this work, I have sought to assess and validate the applicability of
simple particle shape models in replicating the measurements of various dust and ash samples. Atmospheric mineral dust was successfully
43
Summary of results and discussion
modeled with spheroidal model particles and ellipsoidal model particles
were applied for volcanic ash and Mars analog dust. It was found that
both spheroidal and ellipsoidal model particles could greatly improve on
spherical Mie-models as expected. Finding a generalized shape distribution proved to be difficult and a conclusion was reached that using an
equiprobable distribution is a good first trial option for most usages where
no prior optical parameter measurements of the modeled particles exist.
When such measurements exist, the adopted shape distribution should be
optimized to suit the purpose - in such a case, very good agreement of the
model with the measurements can almost always be reached. Finally, ellipsoidal particle shape model performance was tested in the retrieval of
preset synthetic particle refractive index. This test failed miserably, indicating that we can not assume that these model particles can consistently
and unambiguously be used to link the scattering dust particles optical
properties with their microphysical properties.
Model particles studied in this work, ellipsoids and their subset of spheroids with lesser deviations from the sphere, provide dramatic improvements in reproducing measured scattering matrices, when compared with
Mie-particles. There are databases available of precomputed values for
the optical parameter of both ellipsoids and spheroids, making their usages in modelling feasible. Nevertheless, there are shortcomings in these
models’ capability when used in solving the inverse problem, i.e. in retrievals. Clinging into some hope however, it is not far fetched to assume
that some other particle model might work better. Such a model should
nevertheless be sought, as humanity is depending heavily on truthful remote sensing measurements of the atmosphere (Yang et al., 2013), or as
we say in Finland: ”Lohi on niin hieno kala, että sitä kannattaa pyytää,
vaikkei kiinni saisikaan” (Big fish are worth fishing even if you don’t catch
one).
This work has increased our ability to understand the light scattering by atmospheric mineral aerosol and volcanic ash particles. Results
of this thesis can be utilized in both terrestrial and space sciences to
better understand and anticipate the effects of small dust particles on
climate and weather systems. Here on Earth, the results have already
been adopted in the ECHAM 5 climate model’s (Stier et al., 2005; Roeckner et al., 2003) lookup tables for atmospheric aerosols (Räisänen et al.,
2013). Work is also in progress to incorporate the ellipsoidal model in
Advanced Along-Track Scanning Radiometer, AATSR (European Space
44
Summary of results and discussion
Agency, 2002), satellite instrument data analysing algorithm look-up tables for atmospheric volcanic ash. Ellipsoidal and spheroidal model particles can also be used for increasing the reliability of remote sensing analysis of the atmospheres of Earth and other planets. Further away in space,
the results might be usable in other planets, moons and objects having
an atmosphere or coma with suspended non-spherical dust particles in it.
Being able to model light scattering in the environments of these objects is
important for deciphering accurately any optical remote sensing measurements to obtain information on their atmospheres or surface properties.
Accurate remote sensing data increases the scientific knowledge but then
also guides future mission planning and technology development as well
as political decision making, as is the case with climate change monitoring. It is thus imperative that this data represents reality as truthfully as
possible.
With improving measurement technologies and more measurements,
the future will bring us better knowledge of the real world atmospheric
dust particles and their scattering behaviour. Especially evident this
progress will be with other planetary bodies as each new spacecraft orbiter, probe or lander with suitable instrumentation will increase our
knowledge considerably. With the development of computational capacities and modelling tools these measurements can be more reliably interpreted. There is a need for all this, as understanding our dusty environment has direct consequences for us on various fronts, such as in combatting climate change, increasing public health and planning of manned
Mars flights.
45
Summary of results and discussion
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72
Errata
In Paper II, Eq.(15) should read:
ξe =
(1 − ce /be )2 + (1 − be /ae )2 .
(6.1)
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