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UNIVERSITY OF READING
Department of Meteorology
Measurements of the Microwave Emissivity of Sea Ice and Their Application to Operational Data Assimilation
David Pollard
A dissertation submitted in partial fulfilment of the requirement for the degree of MSc in Weather, Climate and Modelling.
2004
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David Pollard MSc Dissertation 2004
Abstract In order to assimilate satellite measurements of microwave radiances, particularly
from the more transparent channels, into numerical weather prediction (NWP) models
it is important to have an understanding of the surface emissivity and the error
statistics associated with it. While this is currently possible for the sea surface and to a
certain extent over land, it is not possible for sea ice due to the complexity of the
formation and evolution processes, which results in large spatial and temporal
inhomogeneities. The ability to assimilate data over regions of sea ice is of particular
importance to NWP models as these regions are traditionally poorly served by
conventional observations.
During March 2001 the Met Office conducted an airborne measurement campaign
over the Arctic using microwave radiometers with channels at 24, 50, 89, 157 and 183
GHz and other aircraft instrumentation to derive the surface emissivity of the various
types of sea ice encountered.
In order to classify the ice types over flown in a manner which can be implemented
operationally, the NASA TEAM and ARTIST sea ice products derived from the
Special Sensor Microwave Imager (SSM/I) measurements have been used to generate
emissivity spectra for first and multi year ice. The resulting emissivty spectra are in
good agreement with previous work where the ice types were classified by
observations made during flight.
There is also a definite relationship between the emissivities at 157 GHz and 183 GHz
irrespective of the ice type (R2 = 0.97), and while this is not the case for the window
channel at 89 GHz and the two higher frequencies (R2 = 0.55), it will be shown that by
sub setting the emissivities according to ice type results in a stronger relationship
between these frequencies for first year ice (R2 = 0.71 between 89 and 157 GHz)
while the relationships for multi year ice are weaker. It is hoped that these
relationships, in conjunction with the SSM/I derived sea ice products, may be
exploited in order to improve fast emissivity models for assimilation purposes.
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David Pollard MSc Dissertation 2004
Acknowledgements I would like to thank Nathalie Selbach and Tim Hewison for their valued guidance on
the nature and direction of this work as well as the benefit of their experience, not to
mention the organisation and implementation of the POLEX-SEPOR campaign in the
first place.
The support and advice of Jonathan Taylor and Alan O’Neil on the preparation of this
dissertation was also appreciated.
I would also like to acknowledge the dedication and experience of the scientists,
technicians, air and ground grew of the Meteorological Research Flight without whom
this work would not have been possible.
Most of all I would like to express my appreciation for the inspiration of Alec Pollard.
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David Pollard MSc Dissertation 2004
Table of Contents 1 Introduction............................................................................................................1
1.1 Motivation......................................................................................................1
1.2 Aims and Outline of Dissertation ..................................................................4
2 Physical Basis ........................................................................................................5
2.1 Electromagnetic Quantities............................................................................5
2.2 Radiative Transfer..........................................................................................6
2.2.1 Gaseous Emission and Absorption ........................................................6
2.2.2 Surface Emissivity .................................................................................8
2.2.3 Radiative Transfer Equations.................................................................9
2.3 The Inverse Problem....................................................................................12
2.4 The nature of sea ice ....................................................................................14
2.4.1 Electromagnetic properties of sea ice ..................................................15
3 Data ......................................................................................................................18
3.1 Sea Ice Emissivity Measurements ...............................................................18
3.1.1 Instrumentation ....................................................................................19
3.1.2 Methodology ........................................................................................20
3.1.3 Estimation of skin temperature ............................................................22
3.2 Operational Sea Ice Products .......................................................................26
4 Results and Analysis ............................................................................................32
4.1 Measured Sea Ice Emissivities.....................................................................32
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David Pollard MSc Dissertation 2004
4.2 Emissivity relationships ...............................................................................34
4.3 Uncertainty Analysis....................................................................................44
5 Conclusions..........................................................................................................47
5.1 Future Work .................................................................................................49
6 References............................................................................................................50
6.1 Journal Articles ............................................................................................50
6.2 Books ...........................................................................................................52
6.3 Articles in Books..........................................................................................52
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David Pollard MSc Dissertation 2004
1 Introduction The process of producing accurate weather forecasts using numerical weather
prediction (NWP) is highly dependent upon, among other things, the availability of
good quality observations of meteorological parameters such as temperature, pressure,
humidity and winds. It is important that these observations are also distributed
globally in order to represent the entire earth system.
The work that will be presented in this dissertation is concerned with investigating a
possible method by which the exploitation of observations from passive microwave
sounding instruments on board satellites might be improved in regions of sparse data
coverage, namely the Arctic region.
1.1 Motivation
High latitude regions have an important effect on global synoptic and mesoscale
weather systems (Bromwich, 1997) and so an accurate representation of these regions
is necessary for the initialisation of NWP models. However, the Arctic region is very
sparsely served by conventional meteorological observations, due to its sparse
population and inaccessibility.
The observations that are available are generally made from meteorological stations
on the coasts surrounding the Arctic Ocean. These stations conduct upper air
observations by releasing radiosondes. However, these provide only very limited
spatial and temporal coverage as typically stations will only release two sondes during
a day.
Therefore the observations available are insufficient to fully represent the important
processes that exist in this region.
The amount of atmospheric water vapour in these regions tends to be very low,
because of the low temperatures. However, the water vapour that is present has very
important effects on meteorological conditions. This can be due to variability in ice
cover, which affects heat and moisture exchange between the sea surface and the
atmosphere (Massom, 1991). Atmospheric water vapour is also the source of snow
cover in the arctic and hence is important for an understanding of the mass balances
within the region and hence sea levels (Przybylak, 2003). The radiation budget in
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David Pollard MSc Dissertation 2004
polar regions is also a significant feedback in studies of climate change and the
amount of water vapour and hence cloud cover constitutes a significant uncertainty in
this process (Key et. al., 1997).
The use of satellite remote sensing provides an obvious solution to the lack of
conventional observations. Satellites provide the opportunity to make observations
with excellent spatial and temporal resolution and provide an increasingly important
contribution to the observing system.
An important component of the satellite observing system is Advanced TIROS
(Television Infrared Operational Satellite) Operational Vertical Sounder (ATOVS)
(English et. al., 2000). ATOVS has been operated on the NOAA series of polar
orbiting satellites since the launch of NOAA-15 in 1998.
ATOVS consists of three instruments: the High-resolution Infrared Sounder (HIRS)
and the Advanced Microwave Sounding unit A and B (AMSU-A and AMSU-B).
HIRS is an infrared temperature sounder, AMSU-A is a microwave temperature
sounder and AMSU-B is a microwave humidity sounder.
In this work I will focus on the exploitation of data from the AMSU instruments,
particularly AMSU-B. The spectral distribution of the AMSU channels in relation to
atmospheric absorption due to oxygen and water vapour is shown in figure 1.1. For a
satellite instrument observing radiation at the top of the atmosphere it is apparent that
the layer of the atmosphere emitting that radiation will vary according to the
atmospheric opacity for that channel. Therefore, for channels with sufficiently low
opacities, there will be a contribution to the measured radiation from the surface.
It is for this reason that it is necessary to have a good understanding of the surface
emission, or to discard measurements from channels where the surface effect is
unknown (English, 1999).
Over ocean surfaces, the emissivity, which varies according to the salinity, roughness
of capillary waves and foam cover, can be modelled by fast emissivity models such as
FASTEM (Hewison and English, 1999)
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David Pollard MSc Dissertation 2004
Figure 1.1 AMSU channels in relation to atmospheric absorption features due to water vapour
and oxygen.
Over land, the emissivity is more complex, being affected by the surface type, its
moisture content and the type and coverage of vegetation. This problem can be
mitigated by using emissivity atlases, or assuming a fixed value of emissivity or by
discarding the affected measurements which normally doesn’t significantly degrade
forecast skill due to the availability of conventional observations.
Snow and ice present a more complex problem in terms of estimating the emissivity,
which in this case is dependent upon factors such as ice density, the presence of an
overlying layer of snow and inclusions of brine and air. This means that the emissivity
is highly variable both spatially and temporally. This is compounded in high latitude
regions where the cold, dry atmospheric conditions lead to more channels being
influenced by the surface. Physical models for the emissivty of sea ice do exist
(Fuhrop et. al., 1998), but are generally limited to lower frequencies, less than 100
GHz, and require knowledge of a large number of physical parameters that are not
available on the spatial and temporal scales required by NWP assimilation schemes.
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David Pollard MSc Dissertation 2004
Attempts have also been made to use fast models such as FASTEM to determine the
emissivity of sea ice, but the accuracy of these methods is very limited.
It is therefore desirable to develop a method for determining the emissivity of sea ice
from measurements that are available to the assimilation system with the same degree
of coverage as the observations that are to be assimilated.
1.2 Aims and Outline of Dissertation
The objective of this work is to use in-situ observations of sea ice emissivity to derive
simple, empirical relationships between the emissivities in the AMSU-B channels at
89, 157 and 183 GHz and information about the sea ice available from operational sea
ice products..
In chapter 2, a brief overview of the underlying physics will be given in order to
provide a contextual setting for the following work.
Chapter 3 will describe the data that will be utilised. The chapter will concentrate on
the measurement of surface emissivity from airborne radiometers including the
assumptions and corrections that need to be applied as well as a consideration of the
resulting measurement uncertainty. This chapter will go on to describe the supporting
information that is used in the analysis, such as observations of surface ice type and
concentration both from aircraft scientists and satellite remote sensing products.
The fourth chapter will present the data described in chapter 3 and provide an analysis
of it, including a proposed algorithm for using sea ice product information and the
emissivities at 89 and 157 GHz as predictors for the 183 GHz emissivity.
Conclusions will be drawn in chapter 5.
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David Pollard MSc Dissertation 2004
2 Physical Basis This chapter will provide a basic background on the physical treatment of
electromagnetic radiation and in particular microwave radiation.
It will begin by introducing the physical quantities associated with electromagnetic
radiation and their relationships.
The principal atmospheric influences on radiation relevant to this work will then be
described, leading to a simplified form of the equation for radiative transfer to the top
of the atmosphere.
There will follow a discussion of the inverse problem, concentrating on the one
dimensional variational retrieval method.
A description will also be given of the evolution and types of sea ice and the
electromagnetic properties associated with them.
2.1 Electromagnetic Quantities
The frequency (ν ) and wavelength (λ ) of electromagnetic radiation in free space are
related by:
λν c= 2.1
where c is the speed of light.
The microwave part of the electromagnetic spectrum is the part which lies between
infrared and radio frequencies and is broadly accepted as ranging from 0.3 GHz to
300 GHz, although definitions vary among the literature.
All matter will emit electromagnetic radiation if its temperature is above absolute
zero. The intensity of the emitted radiation, in the case of a black body, is given by
Planck’s radiation law:
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David Pollard MSc Dissertation 2004
⎟⎠⎞
⎜⎝⎛ −
=1exp
22
3
kThc
hBν
νν 2.2
where is the black body spectral radiance which has units of [WmνB-2sr-1Hz-1], is
the temperature of the emitting body in Kelvin, is Planck’s constant and k is
Boltzmann’s constant.
T
h
In the case of microwave frequencies where 1
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David Pollard MSc Dissertation 2004
gas these transitions are simply the transitions between allowed electronic energy
levels. For molecular gases, rotational and vibrational energy states also exist.
The differences between rotational energy levels are generally much smaller than for
vibrational states and hence rotational lines can be considered as ‘fine structure’ about
the vibrational lines.
The spectral frequency of an absorption/emission line for a change in energy E∆ is
given by the Plank’s law:
hE∆
=ν 2.4
Emission occurs during collisions within the gas, and hence the amount of radiation
emitted is related to the density of the gas and the kinetic energy of the particles, and
hence the temperature of the gas.
Similarly, absorption occurs when radiation at a frequency which satisfies equation
2.4 interacts with a molecule. The amount of absorption is also proportional to the
density of the gas.
Equation 2.4 implies emission and absorption only occur at discrete frequencies. This
however is not the case as there are a number of processes at work which have the
effect of broadening the line spectra.
Natural broadening occurs due to the inherent quantum-mechanical uncertainty in the
magnitude of the allowed energy transitions.
Doppler broadening is caused by a shift in frequency due to the relative motion of the
emitting molecule with respect to the observer.
Finally pressure broadening is caused by collisions between molecules that are in the
process of emitting or absorbing. It is this process that dominates the characteristic
broadening of atmospheric absorption lines within the microwave region.
Within the microwave region (figure 1.1) there are oxygen absorption bands at 60 and
118 GHz and water vapour bands at 22 and 183 GHz. The water vapour absorption
also exhibits a continuum that absorbs more strongly at higher frequencies.
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David Pollard MSc Dissertation 2004
2.2.2 Surface Emissivity
We have already seen that the radiance emitted by a perfect black body is given by
expression 2.2, and that in the case of microwave frequencies and terrestrial
temperatures this simplifies to the Rayleigh-Jeans approximation given by 2.3.
However not all surfaces are as perfect emitters as black bodies are. Kirchoff’s law
states that for a body in thermodynamic equilibrium the energy absorbed from any
direction is the same as that emitted in the same direction at the same frequency:
( ) 1, =ϒ+Γ+θνe 2.5
where is the emissivity at frequency ( θν ,e ) ν and incidence angle θ , is the
reflectivity and is the transmittance of a layer of the medium.
Γ
ϒ
In the case of a layer that can be considered infinite, ϒ tends to zero, and so the
emissivity can be defined as the ratio of the emitted radiance to that of a black body at
the same temperature:
( )bbB
Be
ν
νθν =, 2.6
The reflectivity, ( )θpΓ , at polarisation and incidence angle p θ for a specular
surface is given by the Fresnel relations:
( ) ( )( )
2
2
2
sincos
sincos
θµεθµ
θµεθµθ
−+
−−=Γh 2.7
( ) ( )( )
2
2
2
sincos
sincos
θµεθε
θµεθεθ
−+
−−=Γv 2.8
where µ is the relative permeability and ε the relative permittivity of the medium,
both of which vary as a function of frequency. In the microwave region 1=µ for
most terrestrial matierials and so matierials can be described in terms of ε , which is a
complex number:
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David Pollard MSc Dissertation 2004
εεε ′′−′= i 2.9
2.2.3 Radiative Transfer Equations
If we consider the propagation of a beam of radiation along a finite path within a
medium, then its intensity may be decreased due to scattering out of the beam or
absorption. It may also be increased by scattering into the direction of propagation or
emission.
Let us first consider the decrease in intensity of a beam with intensity
travelling through a finite path, , of a gas with density
νdI νI
s ρ which, having defined an
absorption coefficient, , is given by: νk
dsIkdI ννν ρ−= 2.10
Integrating this expression along s gives Beer’s law:
⎟⎠⎞⎜
⎝⎛−= ∫
sdskII
00exp ρννν 2.11
It is possible to consider an increment in the radiance by defining a quantity, , in a
similar manner to the absorption coefficient. However it is more convenient to
consider a source term which satisfies
νj
νJ
ννν Jkj = 2.12
Now, the net change in the radiance due to propagation along can be given by s
dsJkdsIkdI ννννν ρρ +−= 2.13
or
ννν
ν
ρJI
dskdI
+−= 2.14
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David Pollard MSc Dissertation 2004
This expression can be generalized for radiation propagating vertically in a plane
parallel medium where I and are functions of the vertical coordinate , and the
direction of propagation defined by the zenith and azimuth angles
J z
θ and φ
respectively.
We can also define the optical depth
∫∞
=z
dzk ρτ ν 2.15
Thus equation 2.14 becomes
),,(),,(),,(
φθφθµτ
φθνν
ν zJzIdzdI
+−= 2.16
where θµ cos= .
As we will only be considering cases in which scattering is not present, the source
term simplifies to the black body radiance at the temperature of the emitting layer.
As we are only considering nadir viewing instruments at present, we can also neglect
the angular dependence of the terms.
Integrating 2.16 from the surface (denoted by a subscript s) to the top of the
atmosphere gives:
( ) ( )( ) ( )∫ −+−=∞S dTBII SS
τττττ
0expexp 2.17
This formulation also neglects the reflection of atmospheric radiation by the surface,
which is a good approximation in most cases where the surface can be considered a
black body. If this contribution were included, then there would be a third term
describing the radiation emitted towards the surface by the atmosphere and reflected
towards the satellite.
At this point it is convenient to define the atmospheric transmittance ( )ττ −= expˆ and a vertical coordinate which allow us to rewrite 2.17, with the inclusion of a
weighting function,
py ln−=
( )dydyW τ̂= , to give:
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David Pollard MSc Dissertation 2004
( ) ( )∫+=∞ dyyWTBII SSτ̂ 2.18
The weighting function is a very important concept for satellite sounding as it
describes the sensitivity of the observation to various levels of the atmosphere. Ideally
the weighting function should be a square function or a delta function, in order to give
layer averaged or specific height measurements respectively. In reality however, the
weighting functions tend to be smoothly varying and cover a significant range of
altitude. The weighting functions of the AMSU-B channels for a standard atmosphere
are shown in figure 2.1. These show the range of altitudes which contribute to the
signal in each channel. It can also be seen that the peak in the weighting function for
the strongest absorbing of the 183 GHz channels is the highest while the most
transparent window at 85 GHz peaks the lowest with a significant contribution from
the surface.
As mentioned above, for the microwave spectrum and at terrestrial temperatures, it is
reasonable to use the Rayleigh Jeans approximation described in 2.3. In this case we
can re-write 2.18:
( ) ( )∫+=∞ dyyWyTTeT asss τ̂ 2.19
where is the brightness temperature measured at the top of the atmosphere, is
the surface emissivity, the surface temperature and is the atmospheric
temperature profile.
∞T se
sT )(yTa
Equation 2.19 represents a simplified version of the forward problem, i.e. the
calculation of the top of atmosphere brightness temperature given the state of the
atmospheric column.
The problem of taking a set of brightness temperature measurements and converting
them to the state of the atmospheric column, or the inverse problem, is much more
complicated.
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David Pollard MSc Dissertation 2004
Figure 2.1 Weighting functions for AMSU-B channels for a standard, mid-latitude atmosphere
2.3 The Inverse Problem
The object of microwave sounding is to use satellite measurements of the brightness
temperature in several channels to retrieve a profile of either temperature or some
constituent of the atmosphere. This leads to a problem that is formally ill-posed, i.e.
there exist an infinite number of solutions for a given set of measurements. Therefore,
it is impossible to find an exact solution.
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David Pollard MSc Dissertation 2004
In order to be able to solve the inverse problem, it is first necessary to discretise the
atmospheric profile information in order to produce a column of layer averaged
parameters. This has the effect of reducing the number of unknowns from infinity to a
more manageable number. However, in order to be able to solve the inverse problem
it is necessary to have a number of levels that is comparable to the number of
frequency channels for which information is available. This number would tend to be
less than the desired number of levels within the forecast model (up to 60). Also, any
solution found in this way is likely to be unstable, i.e. a small change in the magnitude
of the measured radiances, due to measurement uncertainty for example, is likely to
lead to large changes in the resulting atmospheric column. This is because the
measurements at the individual channels can not be thought of as independent pieces
of information because the inherent width of the weighting functions means that they
overlap and so the brightness temperature measurements are vertically correlated.
The system used to retrieve information from satellite soundings in operational NWP
assimilation schemes is one dimensional variational assimilation (1D-VAR) which is
a simplified form of the three or four dimensional variational assimilation schemes
that are used in model initialisation.
1D-VAR can be thought of as the process of finding the most likely solution for a set
of brightness temperature measurements given a first guess or a priori information
about the state of the atmosphere and an understanding of the uncertainty in the
background and the measurements. This is achieved by minimising a cost function
: ( )xJ
( ) ( ) ( ) ( )( ) ( )( )xHyRxHyxxBxxxJ TbTb −−+−−= −− 11 2.20
where B and R are the error covariances of the background and the measurements
respectively, the observation operator H is an operator that translates between the
geophysical variables that are being retrieved, , and the observations, , and can be
thought of as the forward model. The subscript b in 2.20 denotes the background
state (also referred to as the first guess or a prioi).
x y
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David Pollard MSc Dissertation 2004
The background state can be from climatology, although it is more usually taken from
a short range forecast from the previous run of the NWP model as the uncertainties
associated with this will be much smaller.
2.4 The nature of sea ice
Sea ice cannot be considered the same as freshwater ice because it is formed from
saline water. This has the effect of reducing the freezing point to approximately -
1.8ºC for typical salinities (Selbach, 2003).
Once the freezing point has been reached, ice begins to form as platelets and needles
on the sea surface, known as Frazil (the naming convention used here will follow
WMO, 1989). As more freezing occurs, this evolves into what is known as grease ice
which consists of an unconsolidated mixture of ice crystals and sea water. The next
stage in the growth of the ice is nilas (figure 2.2) which is an elastic layer of ice less
that 10 cm thick. The action of wind and waves will tend to break the nilas up into
pancakes which are so called because of their circular shape between 0.3 and 3 m in
diameter (figure 2.3). Pancakes will tend to have ridges of a few cm in height at the
edges due to collisions between them. Young ice is formed from the consolidation of
nilas and pancakes and typically has a thickness of between 10 and 30 cm. Once the
ice has become consolidated, the underlying ocean becomes insulated from the cold
atmosphere. At this point, the principle mechanism for the growth of the sea ice is
direct freezing of sea water onto the bottom of the ice sheet. First year ice is defined
as ice that has had no more than one winters growth and has a typical thickness of
between 30 cm and 2m (figure 2.4). Older ice falls into two categories, second year
ice which has formed over two winters and multiyear ice which has survived at least
two melt seasons (figure 2.5) and reaches a typical thickness of 3m.
A sheet of consolidated sea ice does not consist merely of ice but also includes
pockets of brine and gas. The amount of brine in the ice is highly dependent on the
conditions during the formation of the ice and the age of the ice. The rate of growth of
the ice affects the size of the ice crystals themselves and hence the amount of brine
trapped within the ice. If the ice has formed quickly, then the crystals are larger and
the ice contains more brine (Tucker et. al., 1992). Brine inclusions can also occur at
the boundaries between ice plates and as pockets in consolidated ice.
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David Pollard MSc Dissertation 2004
As the ice ages, the salinity will be reduced by a number of processes. The dominant
process is gravity drainage where the higher density of the brine near the colder
surface allows the brine to drain through the ice. This process is accelerated at lower
layers in the ice where it is more permeable. For ice that has been through a melt cyle,
melt water from the melting of surface ice and snow will also act to reduce the
salinity.
The temperature within the ice ranges from the freezing point of the sea water (at
approximately -1.8ºC) at the water-ice interface and decreases to the air temperature
at the ice-air interface or even warmer at the ice-snow interface.
2.4.1 Electromagnetic properties of sea ice
In the microwave region, pure freshwater ice can be considered a lossless medium
with a penetration depth of approximately 10 wavelengths (Hallikainen and
Winebrenner, 1992; Haggerty and Curry, 2001). Therefore, for the frequencies of
interest in this work, the ice will generally be thicker than the depth of penetration.
When considering the interaction of microwave radiation with sea ice, it is necessary
to consider the effects of both surface and volume scattering. For multiyear ice, air
pockets within the ice act as efficient scatterers while first year ice can be considered
electromagnetically lossy (Selbach, 2003).
Measurements of pure, freshwater ice show that the real part of the relative
permittivity is relatively constant whereas the imaginary part is highly variable. The
imaginary part of the relative permittivity is also high for brine with respect to pure
ice (Hallikainen and Winebrenner, 1992).
The combination of these factors means that the relative permittivity of sea ice is a
function of the constituents, their density and orientation with respect to the direction
of propagation and also, weakly, a function of temperature.
It is this complexity that makes it difficult to construct physical models of the
emissivity of sea ice.
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David Pollard MSc Dissertation 2004
Figure 2.2 Nilas ice
Figure 2.3 Pancakes
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David Pollard MSc Dissertation 2004
Figure 2.4 First year ice
Figure 2.5 Multi year ice
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3 Data This chapter will describe the data that have been used to carry out this work. In the
following two sections I will describe the two main sets of data. These are a set of
emissivities measured over sea ice during an airborne research campaign, and
operational, remotely sensed sea ice products which are produced and distributed by
the operational satellite agencies.
The first section will describe the process of taking the measurements and calculating
the emissivity of sea ice along with a discussion of the assumptions that have been
made and the uncertainties associated with them.
The second section will take describe the main sea ice product algorithms and will
provide a critical comparison of their relative strengths and weaknesses.
3.1 Sea Ice Emissivity Measurements
Sea ice emissivity measurements were made using the Met Office C-130 research
aircraft during the POLEX-SEPOR (Polar Experiment – Surface Emission in Polar
Regions) campaign in March 2001. During this campaign five flights were conducted
over sea ice in order to carry out measurements that would allow the emissivity to be
calculated. Three of these flights were over first and multi year ice (FYI and MYI)
and reached a latitude of 85º N and longitudes of 15ºW, 0º and 15ºE. A further two
flights were carried out over the marginal ice zone around the island of Svalbard. The
tracks of these flights are shown in figure 3.1 and summarised in table 3.1.
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David Pollard MSc Dissertation 2004
Figure 3.1 Map overlayed with flight tracks of the sea ice flights conducted during the POLEX
campaign
Table 3.1 Summary of sea ice flights during POLEX campaign
Flight number Flight Track Date Surface types Geographical Extent
A823 A 11/03/01 Glacier & FYI 85N 0E
A824 B 13/03/01 Glacier & FYI 85N30E
A825 C 15/03/01 Marginal Ice Zone 77N 38E
A827 D 20/03/01 Glacier, FYI & MYI 85N 20W
A829 E 23/03/01 Marginal Ice Zone 75N 7E
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David Pollard MSc Dissertation 2004
3.1.1 Instrumentation
The key instrument aboard the C-130 for measuring emissivity was the MARSS
(Microwave Airborne Radiometer Scanning System). MARSS is a passive microwave
radiometer with five channels. Two of the channels are in the relatively transparent
regions at 89 and 157 GHz. The remaining three are centred on the water vapour
absorption line at 183 GHz. The radiometer is coupled to a scanning system which
has a three second along track scan, during which it takes measurements in 18 fields
of view, nine zenith and nine nadir, and two black body calibration targets, one heated
and one at ambient temperature (McGrath and Hewison, 2001).
In addition the C-130 also carried a number of complementary instruments. These
included; a Heimann infrared radiometer, visible and infrared broadband radiometers,
a suite of standard meteorological sensors and dropsondes.
3.1.2 Methodology
Figure 3.2 describes the measurement geometry that is used for the calculation of the
surface emissivity.
By applying the radiative transfer theory developed in the previous chapter, the nadir
brightness temperature, , measured at the aircraft can be given by: nT
( ) ττ ˆ1ˆ dsssan TeTeTT −+−= 3.1
where is the contribution due to thermal emission of the atmosphere below the
aircraft, the contribution from the surface is given by modified by the
transmittance of the atmospheric layer below the aircraft,
aT
ssTe
τ̂ . is the downwelling
radiation that is reflected by the surface.
dT
In order to facilitate the calculation of surface emissivity from quanities that can be
measured, it is necessary to make a number of assumptions.
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David Pollard MSc Dissertation 2004
seTs,
nT
aT
zTdT
h,mT
qpT ,,
τ̂
seTs,
nT
aT
zTdT
h,mT
qpT ,,
τ̂
Figure 3.2 Emissivity measuring geometry, showing the various contributions to the measured
nadir brightness temperature.
Firstly, it will be assumed that the surface is purely specular. While this is a good
approximation in the case of ocean surfaces, ice and snow tend to be Lamberitan, that
is the radiated energy varies with the cosine of the angle from the surface normal. We
are able to use this assumption because we will only be dealing with radiation
propagating in directions close to the surface normal, i.e. in the nadir and zenith
directions.
In order to be able to calculate the emissivity, it is apparent from 3.1 that we need to
know the downwelling radiation at the surface, and the atmospheric contribution to
the upwelling brightness temperature measured at the aircraft.
The latter can be modelled using a measured atmospheric profile and a suitable
radiative transfer model (such as Rosenkranz, 1998). In order to simplify this process,
the atmosphere below the aircraft is assumed to be a single, vertically homogeneous
layer with a mean radiating temperature of and transmittancemT τ̂ . The method used
to estimate these parameters uses a polynomial function based on the air temperature
at flight level and at the surface. This method provides reasonable values for and mT
τ̂ under most conditions. However, it may be limited in conditions where there is a
strong surface inversion.
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David Pollard MSc Dissertation 2004
Having estimated and mT τ̂ it is possible to calculate the upwelling atmospheric
contribution to the measured signal, : aT
( ) ma TT τ̂1−= 3.2
Similarly, the reflected downwelling brightness temperature, , can be estimated
from the measured zenith brightness temperature at the aircraft, , and from 3.2.
dT
zT aT
azd TTT += τ̂ 3.3
3.1 can be rewritten to give an expression for the emissivity:
( )ττ
ˆˆ
ds
dans TT
TTTe
−−−
= 3.4
nT can be measured directly at the aircraft, τ̂ can be modelled using atmospheric
profile measured by dropsondes and hence and can be estimated using
equations 3.2 and 3.3. Therefore the only remaining unknown is the surface
temperature.
aT dT
3.1.3 Estimation of skin temperature
The derivation of the surface temperature for the purposes of estimating the surface
emissivity poses a problem because microwaves are able to penetrate a number of
wavelengths into ice (Haggerty and Curry, 2001). For this reason it is not possible to
use the Heimann IR radiometer as this would only measure the temperature at the
physical surface of the ice. Therefore the effective microwave surface temperature
will be warmer than that measured in the infrared.
The surface temperatures used in this work have been derived using the method of
Selbach, 2003. This method allows the effective microwave surface temperature to be
estimated from brightness temperature measurements in the three channels centered
on the 183 GHz water vapour absorption line. The surface temperature is found by
minimising a cost function, , defined as the sum of the squared differences between cF
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David Pollard MSc Dissertation 2004
the observed nadir brightness temperatures, , and those modelled using radiative
transfer equations, , for the three channels.
OBSnT
RTEnT
( )∑ −=i
RTEin
OBSinc TTF
2
,, 3.5
where the index, , refers to the channel numbers. i
This method assumes that the surface emissivity is the same for all of the 183 GHz
channels, which is justified as the emissivity gradient in this region is of the order 10-4
GHz-1.
The method also assumes that the retrieved effective surface temperature will be the
same for all of the channels. However this is not the case as the lower frequency
channels will penetrate further into the ice and so their effective surface temperatures
will be higher. This effect has not been accounted for in the analysis and so will result
in a slight underestimation of the emissivity for these channels.
To try and assess the level to which this effect is likely to modify the retrieved
emissivity, representative values have been used in equation 3.4 and the surface
temperature varied in order to determine the emissivity sensitivity to surface
temperature. The representative values used here are the averaged values taken from
the low level runs over sea ice during flight A827. Table 3.2 summarises the typical
values used in equations 3.2 – 3.5 and the resulting sensitivity.
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David Pollard MSc Dissertation 2004
Table 3.2 Summary of emissivity sensitivity calculations
Channel τ̂ nT /K zT /K Senitivity/K-1
16 0.987 195.51 24.18 -0.004
17 0.978 194.49 25.42 -0.004
18 0.673 243.77 202.78 -0.046
19 0.779 234.83 142.04 -0.012
20 0.905 214.42 69.28 -0.005
The average surface temperature retrieved using 3.5 during this period was 240.08 K.
This sensitivity analysis shows that the channels that are most sensitive to surface
temperature are the 183 GHz channels for which we are retrieving the surface
temperature and so this sensitivity can be neglected. It is also possible to estimate the
magnitude of the underestimation of the emissivity due to an unrepresentative surface
temperature in the two lower frequency channels. At the time of year during which
the POLEX campaign was undertaken, a typical value for the thickness of the sea ice
would be approximately 2 m with a temperature gradient of 20 K between the top and
bottom surfaces (Perovich et. al., 1997). Using the microwave penetration depths
reported by Haggerty and Curry, 2001, then it is possible that the radiation from the
89 GHz channel is coming from a layer 0.025 m below that for 183 GHz. This would
imply that the error in the calculated emissivity introduced by making this assumption
would be less than 0.01 which again is of the order of the expected accuracy of the
retrieval technique and so it is reasonable not to correct for this error.
Figure 3.3 shows a time series of the surface temperatures retrieved from the Heimann
radiometer and using 3.5. This shows that in general, the Heimann gives a surface
temperature approximately 10 K lower than the microwave radiometer. This value is
larger than would be expected if the information reported by Perovich et. al, 1997,
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David Pollard MSc Dissertation 2004
and Haggerty and Curry, 2001, is used, so there is likely to be some other process at
work.
This could be due to scattering by small ice particles in the inversion layer below the
aircraft having the effect of cooling the temperature measured by the Heimann
radiometer.
There may also be a covering of snow on the sea ice which would have the effect of
insulating the sea ice. This layer of snow would be transparent to microwaves, but the
Heimann radiometer would measure the brightness temperature at the snow surface.
It is a significant shortcoming of the POLEX campaign that no coincident, in-situ
measurements of surface parameters, such as snow depth and sea ice temperature
profiles, are available. However the method described above for the estimation of the
effective microwave surface temperature goes some way towards providing a work-
around for this problem.
Figure 3.3 Comparison of the surface temperatures measured by the Heimann IR radiometer
and using the microwave cost function for flight A823
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David Pollard MSc Dissertation 2004
3.2 Operational Sea Ice Products
A number of operational sea ice products are produced using various algorithms to
interpret Special Sensor Microwave Imager (SSM/I) measurements. SSM/I is a series
of conical scanning microwave imagers, that have been flown on the Defence
Meteorological Satellite Program series of polar orbiting platforms since 1987. SSM/I
has dual polarised channels at 19, 37 and 85 GHz and a single polarised channel at 22
GHz.
Early sea ice algorithms (Cavalieri, 1994 and Comiso, 1995) used the polarisation
ratio at 19 GHz, , and the spectral gradient between 19 and 37 GHz,
, defined as
( )19PR( VVGR 1937 )
( ) ( ) ( )( ) ( )HTVTHTVTPR
BB
BB
1919191919
+−
= 3.6
and
( ) ( ) ( )( ) ( )VTVTVTVTVVGR
BB
BB
193719371937
+−
= 3.7
where is the measured brightness temperature at a particular channel and V and BT
H denote the polarisation.
The gradient ratio gives a surface temperature independent indication of the ice
concentration, while the polarisation ratio contains some information about the type of
ice that is being measured.
Unfortunately, the long wavelength associated with the channels used for these
algorithms means that the resolution at the surface is rather course and ice parameters
can only be retrieved on a 25 km grid (Kern et. al., 2003). For this reason, there have
been more recent attempts to utilise the 85 GHz channel of SSM/I for sea ice
measurements (Markus and Cavalieri, 2000; Kaleschke et. al., 2001; Kern et. al
2003). The use of this channel allows an improvement in resolution to 12.5 km.
However, this channel will be affected by the atmosphere, and so this must be
corrected. This is done by using radiative transfer models to calculate look up tables
of the atmospheric effects for various weather conditions and ice concentrations.
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David Pollard MSc Dissertation 2004
It is the latter, 12.5 km resolution sea ice products that will be used for this study.
The sea ice products from two algorithms have been obtained for the days that
coincide with the POLEX sea ice flights. These are the NASA-TEAM algorithm,
which gives the total sea ice concentration (NT) as well as a multi year ice
concentration (MY) (Markus and Cavalieri, 2000), and the ARTIST (ASI) algorithm
(Kaleschke et. al., 2001) which is a hybrid of the NASA-TEAM algorithm and the
algorithm of Svendsen et al, 1987.
Figures 3.4 and 3.5 show the sea ice concentration maps for the NT and ASI
algorithms respectively for the day of flight A827. It can be seen that the overall sea
ice distribution for both products is broadly similar, although the NT algorithm
appears slightly more ‘blurred’ at the ice edge.
In order to be able to use these ice products with the aircraft data, it was necessary to
geo-locate the sea ice products with the aircraft measurements. In order to do this, the
aircraft global positioning system (GPS) data for the low-level runs over sea ice was
used to select the corresponding pixels from the sea ice concentration maps. In this
manner a time series of the various sea ice products coinciding with the time series of
aircraft data was created for each flight. It was decided to map the sea ice data to the
aircraft data rather than the other way around in order not to average out the aircraft
data, and therefore artificially remove noise as well as to maximise the data set
available. The five resulting time series were then concatenated to give a single data
set to work with.
Once this new data set had been created, it was possible to perform a more rigorous
comparison of the NT and ASI products. Figure 3.6 shows a plot of the NT sea ice
concentration versus the ASI equivalent. The plot shows that the two products agree
reasonably at high ice concentrations, but that the NT algorithm produces higher
concentrations than ASI for low concentrations.
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David Pollard MSc Dissertation 2004
Figure 3.4 NT sea ice concentration map for A827
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David Pollard MSc Dissertation 2004
Figure 3.5 ASI sea ice concentration map for A827
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David Pollard MSc Dissertation 2004
Figure 3.6 Comparison of sea ice concentrations given by NT and ASI algorithms for all POLEX
flights
It is also possible to compare the sea ice products with observations made by the
aircraft scientist during the flight. Table 3.3 shows such a comparison for various
sections of flight A827. Flight A827 has been selected for this comparison because it
was the flight that encountered the most multi year ice. Table 3.3 shows a generally
good agreement between the algorithms and observations for most conditions, with
the exception of no ice and low ice conditions where NT overestimates the
concentration. This is consistent with figure 3.6.
For this reason, in the rest of this work, the ASI algorithm will be used for total ice
concentration in preference to NT, while the MY product will be used to give the
multi year ice concentration.
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David Pollard MSc Dissertation 2004
Table 3.3 Comparison of SSM/I sea ice products with aircraft scientist observations
during flight A827
SSM/I Derived Ice
Concentrations
Start Time End Time Surface Characteristics
ASI NT MY
09:51:21 09:56:46 Open Water 0.00 0.32 0.09
09:57:47 10:01:30 Open Water < 5% ice 0.00 0.13 0.06
10:27:25 10:47:45 CCPI (FYI) 0.88 0.88 0.31
10:49:00 10:58:15 CCPI (some MYI) 0.96 0.93 0.37
11:47:00 11:49:00 Possible MYI 0.99 0.97 0.66
12:20:00 12:30:00 70% MYI, 30% FYI 1.00 1.00 0.70
12:30:00 12:42:00 85% MYI, 15% FYI 0.99 1.00 0.83
12:46:00 12:56:00 Mostly MYI 1.00 1.00 0.95
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David Pollard MSc Dissertation 2004
4 Results and Analysis As stated in the first chapter of this document, the aim of this work is to attempt to
develop a simple method for determining the emissivity of sea ice at various
frequencies using information about the ice given by operationally produced sea ice
products. It is in this context that the results will be presented in this chapter. In the
first section a brief overview of the nature of the measured emissivities will be given,
and a comparison made between the measurements and the modelled emissivities
given by the FASTEM model.
The following section will attempt to demonstrate relationships within the emissivity
data and in conjunction with the sea ice products that might be utilised in a simple,
empircal model of surface emissivity.
The final section of this chapter will describe an attempt to carry out a statistical
uncertainty analysis of all possible combinations of the relationships that have been
found.
4.1 Measured Sea Ice Emissivities
Figure 4.1 shows a time series of emissivities measured during the low level segment
of flight A827 as well as the corresponding sea ice concentrations from the ASI and
MY products. The first thing to note about the time series is the amount of variability
in the measured emissivities. This variability is significantly greater than the expected
1% uncertainty in the measured emissivity and is due to the spatial variability of the
sea ice and demonstrates the problems associated with determining the emissivity that
should be used when performing retrievals from satellite measurements.
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David Pollard MSc Dissertation 2004
Figure 4.1 Time series of emissivities (top panel), emissivities averaged over SSM/I pixels and
description of under lying surface (middle panel) and SSM/I derived ice concentrations (bottom
panel) for low level section of flight A827
At the beginning of the time series shown in figure 4.1 the aircraft is over a glacier. It
then flies out over open water, where the emissivities are lower and less variable,
before encountering the marginal ice zone at approximately 10:30 marked by a rise in
the measured emissivities and increased variability. After crossing the ice edge, there
is a region of FYI and Nilas, before a more uniform region of FYI, which appears to
have a slightly lower emissivity than the preceding region of mixed ice. At the very
end of the run a region of MYI was encountered where there is a further reduction in
the measured emissivity.
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David Pollard MSc Dissertation 2004
As we are interested in the emissivity that would be seen by microwave radiometers
flying on satellites, which obviously have a much courser resolution, the middle panel
of figure 4.1 shows the measured emissivity averaged over individual sea ice product
pixels. These pixels correspond to the resolution of the SSM/I 85 GHz channel which
is approximately the same as the resolution of the AMSU-B instrument. It can be seen
that applying this averaging immediately removes a large proportion of the variability
in the data, which is likely to be due to small scale spatial inhomogeneities within the
ice.
Flight A827 was chosen as an illustration of the emissivity measurements because it
was the flight which encountered the greatest variety of ice types, and the most MYI.
The emissivties measured during A827 are typical of those measured during the other
flights and for all subsequent work a data set of measurements from all of the sea ice
flights will be used.
4.2 Emissivity relationships
The aim of this work is to investigate a method of determining sea ice emissivity at
the frequencies used for humidity sounding, by exploiting relationships between
emissivity and the ice type and concentration given by operational sea ice products
described in section 3.2. This section will begin to investigate the ways, if any, in
which the measured emissivities vary in relation to the collocated sea ice products.
To begin with, using the data set described above, the emissivities were sorted in
order to give characteristic spectra for the two ice types which can be resolved from
the operational sea ice products. These are multi year ice (MYI) (based on the MY
product) and first year ice (FYI), which for the purposes of this work will encompass
any ice that is not MYI. Although this is not an accurate representation of the
diversity of ice type encountered, is a reasonable simplification based on the available
information.
Emissivity spectra were produced for these two ice types by selecting only data points
where the ice concentrations were high, in order to minimise contamination from
open water. Additionally, for the FYI classification points which contained MYI were
also removed. The thresholds applied were ASI > 0.9 and MY < 0.1 for the FYI
classification and MY > 0.8 for the MYI classification. A lower threshold was chosen
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David Pollard MSc Dissertation 2004
for the MYI classification because of the scarcity of multi-year ice encountered during
the POLEX campaign. This is a reasonable compromise because MYI is less likely to
be contaminated by open water than FYI.
Figure 4.2 shows the resulting, averaged emissivity spectra for FYI and MYI along
with error bars showing the standard deviations, the dashed lines represent the
FASTEM values for these ice types.
It is evident that the two ice classifications have different emissivity spectra, despite
the large dispersion of the emissivities about the mean. The shapes of the spectra
show reasonable agreement with those given using FASTEM. However there appears
to be a bias in the FASTEM values although they are within a standard deviation of
the mean. In general the multi year ice has a lower emissivity than first year ice,
particularly at 89 GHz.
The difference between the emissivity spectra for FYI and MYI might suggest that it
is possible to model the emissivity of a given scene by using a combination of the
emissivity of the relevant ice type and the emissivity of open water for the prevailing
conditions, weighted by the ice concentration given by the operational sea ice
products.
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David Pollard MSc Dissertation 2004
Figure 4.2 Emissivity spectra of first and multi year ice showing standard deviation and modelled
values
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David Pollard MSc Dissertation 2004
Figure 4.3 Variation of emissivity with ASI concentration at 89, 157 and 183 GHz (MYI
removed)
Figure 4.3 shows an attempt to do this using the ASI product for all measurements
taken during the POLEX sea ice flights. The figure shows the measured emissivity
plotted against the ice concentration for the three frequencies of interest, along with
the emissivity averaged over various levels of sea ice concentration in ten bins (blue
lines) and their associated standard deviations (error bars). In order to model the
emissivity directly as a function of ice concentration, then it would be necessary to
use some mathematical representation of the averaged emissivities as a function of
concentration. Table 4.1 shows the results of attempting a linear fit to the emissivities
as a function of ice concentration in the absence of multi year ice.
However, such a method would be extremely uncertain due to the large spread of
emissivity values from the mean and so would not be worth attempting, with the
possible exception of 89 GHz which shows a weak trend with FYI concentration.
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David Pollard MSc Dissertation 2004
The considerable variability in the emissivity measurements means that it is unlikely
that it will be possible to model the emissivities simply as a function of the ice type
and concentration products and so additional constraints must also be used.
However, figure 4.3 does show that the emissivities at 157 and 183 GHz do have a
similar distribution and this might suggest that the emissivities in the different
channels may be correlated. As figure 4.4 shows, there is a very strong correlation
between the emissivity at 157 and 183 GHz, independent of the surface type. This
finding should not be unexpected as the two frequencies are reasonable close
spectrally and hence the physics responsible for the surface emissivity will be similar.
Performing a linear regression on these data points gives the relationship as follows:
0.069380206854.1 183157 −= ee 4.1
with an r2 value of 0.977.
Table 4.1 Results of attempting to fit a trend to variation of emissivity to FYI
concentration
Frequency / GHz Gradient Intercept R2
89 0.152277 0.717140 0.242321
157 7.22251E-3 0.778685 5.82354E-4
183 9.41878E-3 0.791226 1.16147E-3
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David Pollard MSc Dissertation 2004
Figure 4.4 Relationship between measured emissivity at 157 and 183 GHz, solid line shows 1:1
relationship
The result of attempting to find a similar relationship between the emissivities at 89
and 183 GHz is shown in figure 4.5.
It is obvious that the relationship here is considerably poorer than before. This again
is not unexpected as the difference in the frequencies implies that the physics
underlying the surface emissivity will be different. Performing a linear regression on
this data yields an R2 value of only 0.5. However, there does appear to be some
clustering of points which might indicate a surface type dependence and there is less
spread in the values for higher emissivities.
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David Pollard MSc Dissertation 2004
Figure 4.5 Relationship between measured emissivity at 89 and 183 GHz, solid line shows 1:1
relationship
In order to investigate the possible surface type dependence, the surface
classifications used above to generate figure 4.2 have been used, with an additional
classification of open water (ASI < 0.1) and all of the points which satisfy these
condition have been colour coded in figure 4.6. This shows that there are indeed clear
groupings for the three surface classifications. Table 4.2 shows the results of
performing linear regressions on the data for the three classifications.
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David Pollard MSc Dissertation 2004
Figure 4.6 Emissivity relationship between 89 and 183 GHz showing surface classifications: Open
water (blue), FYI (green) and MYI (red)
The linear regression analysis shows that there is an improvement in the accuracy of a
linear relationship between the emissivities at 89 and 183 GHz, if only measurements
where the FYI concentration is above 0.9 are used. However, this is not the case for
multi year ice based on this data set.
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David Pollard MSc Dissertation 2004
Figure 4.7 89 and 183 GHz emissivity relationship showing fitted linear curves for various FYI
concentrations.
Table 4.2 Results of linear regression between 89 and 183 GHz emissivity for various
surface classifications.
Classification Gradient Intercept R2
Open Water 1.59841 -0.528858 0.7927
First year ice 0.588084 0.393202 0.6624
Multi year ice 1.52515 -0.425892 0.4870
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David Pollard MSc Dissertation 2004
Further investigation shows that as the points plotted on figure 4.6 appear to fall on a
line that moves between that fitted to open water values and the one for FYI values in
an apparently linear fashion.
To test this, the measurements where split into ten bins based on the FYI
concentration (i.e. the ASI concentration in the absence of MYI) and linear
relationships fitted to each of these bins. The results of this process are plotted in
figure 4.7. While figure 4.8 shows the coefficients and R2 values of these fitted
curves.
By then fitting a linear relationship to the variation of these coefficients with FYI
concentration, it is possible to generate an expression for the relationship between the
emissivity at 89 and 183 GHz in the presence of FYI (or for more practical purposes,
in the absence of MYI) this relationship is:
( ) ( )669397.015099.176084.129012.1 18389 −++−= FYIeFYIe 4.2
Where FYI is equivalent to ASI where no MYI is present.
The same process can be carried out for the relationship between the 89 and 157GHz
emissivities, which results in the following expression:
( ) ( )572474.007302.166714.121369.1 15789 −++−= FYIeFYIe 4.3
This process has also been carried out using ASI concentrations rather than FYI (i.e.
without filtering out MYI) with a similar result, however as shown in figure 4.2
above, MYI does have a significantly different emissivity spectra to FYI. It is
therefore likely that this similar result for the emissivity relationships is due to the
small number of measurements in which there are significant MYI concentrations and
therefore the analysis has not been perturbed as significantly as it would have been if
there had been a comparable number of observations of MYI.
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David Pollard MSc Dissertation 2004
Figure 4.8 Showing the linear fitting coefficients for the relationships between FYI
concentrations and the correlation between 89 and 183 GHz emissivities, gradient (left),
intercept (middle) and R2 (right).
It is also for this reason that the process of determining emissivity relations has not
been carried out for MYI on its own (i.e. for measurements where ASI is
approximately equal to MYI to avoid contamination by FYI) due to the lack of
measurements with intermediate MYI concentrations.
As well as the relationships given in 4.2 – 4.3 it is also possible to use a combination
of two relationships in order to find the emissivity at the remaining frequency. This
could be achieved by either taking the average value given by two relationships, or
weighting them in some way.
4.3 Uncertainty Analysis
It has not been practical to perform a rigorous, mathematical uncertainty analysis on
the resulting emissivity relations, which are described in equations 4.1 – 4.3. This is
due to not being able to prescribe an uncertainty to the sea ice products, and the
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David Pollard MSc Dissertation 2004
mathematical complexities of propagating uncertainties through successive linear
regressions.
However, it is desirable to develop an understanding of the accuracy with which the
relationships are able to predict emissivities. In order to achieve this, the relationships
have been applied to the dataset and compared to the measured values. The results of
this analysis show that the relationships using the 89 GHz emissivity and FYI
concentration to predict the emissivities at 157 and 183 GHz are able to do so with an
RMS error of 16% and 6.7% respectively, while using the emissivity at 157GHz on its
own can predict the emissivity at 187 GHz with an RMS error of 1.2%. A complete
list of the RMS errors for all of the relationships is shown in table 4.3
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David Pollard MSc Dissertation 2004
Table 4.3 RMS errors for various emissivity relationships
Modelled Emissivity Information Used RMS Error
FYI 7.1%
157, FYI 4.1%
183, FYI 4.3% 89
157, 183, FYI 4.2%
FYI 8.6%
89, FYI 16.0%
183 1.2% 157
89, 183, FYI 8.1%
FYI 7.8%
89, FYI 6.7%
157 1.2% 183
89, 157, ASI 3.6%
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David Pollard MSc Dissertation 2004
5 Conclusions The initial aim of this dissertation was to see if it could be possible to use information
about ice concentration and type that is derived from operational satellite instruments
in order to define the surface emissivity. This is necessary in order to be able to carry
out retrievals of humidity profile information in Polar Regions.
In order to achieve this, two data sets were used. These were airborne measurements
of the surface emissivity and the operational sea ice products themselves.
The airborne emissivity measurements taken during the POLEX-SEPOR campaign
provide a very useful set of data, although they are not without their problems which
must be overcome.
The first and most serious of these is the lack of ‘ground truth’ observations of the
physical structure of the ice and the profile of temperature through the ice as well as
the depth, if any, of the overlying snow pack. This in turn leads to a problem in
defining the surface temperature that should be used in the calculation of emissivty
from the measured brightness temperature, due to the varying penetration of
microwaves at different frequencies into the ice. This may lead to some bias in the
measured emissivities, but the bias will be consistent across the channels and so the
relationships derived will still be valid.
The operational sea ice products themselves are not ideal for defining the type of ice
due to the lack of information available. This has meant that it is only possible to
define two different ice types. It has also been shown that the concentration values
given by some of these products can sometimes be overestimates in regions of low ice
concentrations and so care has to be taken over the choice of algorithm that is used.
These products do have significant advantages despite their limitations, these are their
timely availability and excellent coverage over the regions of interest. It is also
advantageous that these products are made available at roughly the same resolution as
the AMSU-B instrument for which this work is ultimately aimed.
It was originally hoped that the ice type and concentration information available
would be sufficient to predict the emissivity. This did not turn out to be the case as the
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David Pollard MSc Dissertation 2004
emissivities turned out to be uncorrelated with the sea ice products available, with the
exception of the 89 GHz channel for which was only weakly correlated.
However, it was shown that using both sea ice information and the emissivity at some
other frequency gave a much better correlation.
The question that is now posed, is whether or not these findings are useful in the
context of being able to retrieve humidity information from AMSU-B soundings?
There are three possible ways in which the results obtained here might be used for
humidity soundings.
The first and simplest might be to use the relationship between the FYI concentration
and 89 GHz emissivity to derive this emissivity and then use the relationships
between 89 GHz and the other two frequencies to find these emissivities. However,
the uncertainties associated with this method would be unacceptably high for one
dimensional variational assimilation to yield any useable increments to the
background state.
Secondly, in cases where the atmosphere is relatively dry, it may be possible to
retrieve the surface emissivity in the relatively transparent channel at 89 GHz and
possibly at 157 GHz using the background state and a radiative transfer model to
remove the atmospheric influence. Such a method has been successfully applied in the
past (Prigent et. al., 1997) using analysis data in order to give the atmospheric
correction. It would then be possible to use the derived relationships to determine the
emissivity at 183 GHz. If the technique could be applied using both the 89 and 157
GHz channels then the emissivity at 183 GHz could either be a simple average of the
two values, or an average weighted by some measure of the confidence in the
measurements at the two low frequency channels, for example the liquid water
content. The limitations of this technique would be that some of the information
contained in the microwave soundings would have to be used to determine the
emissivity and so the limited information remaining will mean that only small
increments can be made to the background state. Therefore such a system would be of
limited use when the state of the atmosphere differs significantly from the background
state. This technique would also run into the problems associated with defining the
effective microwave surface temperature that were described in section 3.1.3
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David Pollard MSc Dissertation 2004
The final method would be to define the emissivity and surface temperature as
variables in the variational retrieval process using the relationships defined above as
constraining information, and the results of the uncertainty analysis to produce the
necessary error covariance matrix. Initially this would not show significant benefit.
However, after a number of successive applications of the 1D-VAR retrieval during
the operational assimilations scheme, it would be possible to build up a microwave
surface temperature and emissivity background state. Due to the lower temporal
variability of the surface as compared to the atmosphere this in turn would allow more
of the information from the microwave soundings to be used to generate increments to
the atmospheric background state.
5.1 Future Work
There are two areas of work that follow on from the results obtained during this study.
The first would be to consolidate the analysis carried out here by using a larger data
set, obtained in a similar way but including a greater variety of ice types, specifically
more multi year ice, and observations made at different times of year to investigate
seasonal variability.
It would also be of benefit if any future campaigns to measure the emissivity of sea
ice were to include a ‘ground truth’ component that would allow the assumptions
made in estimating the effective microwave surface temperature to be more rigorously
tested.
The second area of work would be to develop a variational scheme for the retrieval of
microwave emissivities and skin temperatures, and its validation. It would then be
necessary to conduct an observing system experiment to investigate whether such a
system would have a positive impact on forecast accuracy before such a scheme can
be incorporated into an operational assimilation scheme.
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David Pollard MSc Dissertation 2004
6 References
6.1 Journal Articles
BROMWICH, D. H., (1997). Introduction to special section: Synotic and mesoscale
weather systems in the polar regions. J. Geophys. Res., 102 D12, 13727-13729.
CAVALIERI, D. J., (1994). A microwave technique for mapping thin sea ice. J.
Geophys. Res., 99 C6, 12561-12572.
COMISO, J. C., (1995). SSM/I sea ice concentrations using the bootstrap algorithm,
NASA Ref. Pub., 1380, 49-.
ENGLISH, S. J., (1999). Estimation of temperature and humidity profile information
from microwave radiances over different surface types. J. Appl. Met., 38, 1526-1541.
ENGLISH, S. J., RENSHAW, R. J., DIBBEN, P. C., SMITH, A. J., RAYER, P. J.,
POULSEN, C., SAUNDERS, F. W., EYRE, J. R., (2000). A comparison of the
impact of TOVS and ATOVS satellite sounding data on the accuracy of numerical
weather forecasts. Q. J. R. Meterorol. Soc., 126, 2911-2931.
FUHROP, R., GRENFELL, T. C., HEYGSTER, G., JOHNSEN, K. P., SCHLUSSEL,
P., SCHRADER, M., SIMMER, C,. (1998). A combined radiative transfer model for
sea ice, open ocean, and atmosphere. Radio Science, 33, 303-316.
HAGGERTY, J. A., CURRY, J. A., (2001). Variability of sea ice emissivity
estimated from airborne passive microwave measurements during FIRE SHEBA. J.
Goephys. Res., 106 D14, 15265-15277.
HEWISON, T. J., ENGLISH, S. J., (1999). Airborne retrievals of snow and ice
surface emissivity at millimetre wavelengths. IEEE Trans. Geosci. Rem. Sens., 37,
1871-1879.
KALESCHKE, L., HEYGSTER, G., LÜPKES, C., BOCHERT, A., HARTMANN, J.,
HAARPAINTER, J., VIHAMA, T., (2000). SSM/I Ice remote sensing for mesoscale
ocean-atmosphere interaction analysis. Can. J. Rem. Sens., 27, 526-537.
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KERN, S., KALESCHKE, L., CLAUSI, D. A., (2003). A Comparison of two 85 GHz
SSM/I ice concentration algorithms with AVHRR and ERS-2 SAR imagery. IEEE
Trans. Geosci. Rem. Sens., 41, 2294-2306.
KEY, J. R., SCHWEIGER, A. J., STONE, R. S., (1997). Expected uncertainty in
satellite-derived estimates of the surface radiation budget at high latitudes. J.
Geophys. Res., 102 C7, 15837-15847.
MCGRATH A. J., HEWISON T. J., (2001). Measuring the accuracy of a Microwave
Airborne Radiometer (MARSS). Journal of Atmospheric and Oceanographic
Technologies, 18, 2003-2012.
MARKUS, T., CAVALIERI, D. J., (2000). An enhancement of the NASA team sea
ice algorithm. IEEE Trans. Geosci. Rem. Sens., 38, 1387-198.
PEROVICH, D. K., ELDER, B. C., RICHTER-MENGE, J. A., (1997). Observations
of the annual cycle of sea ice temperature and mass balance. Geophys. Res. Lett., 24,
555-558.
PRIGENT, C., ROSSOW, W. B., MATTHEWS, E., (1997). Microwave land surface
emissivities estimated from SSM/I observations, J. Geophys. Res., 102 D18, 21867-
21890.
ROSENKRANZ, P. W., (1998). Water vapour microwave continuum absorbtion: A
comparison of measurements and model. Radio Science, 33, 919-928.
SVENDSEN, E., MÄTZLER, C., GRENFELL, T. C., (1987). A model for retrieving
total sea ice concentration from a spaceborne dual-polarized passive microwave
instrument operating near 90 GHz, Int. J. Rem. Sens., 8, 1479-1487.
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6.2 Books
MASSOM, R., (1991).Satellite Remote Sensing of Polar Regions. Belhaven Press.
PRZYBYLAK, R., (2003). The Climate of the Arctic. Kluwer Academic Publishers.
SELBACH, N., (2003) Determination of total water vapour and surface emissivity of
sea ice at 89GHz, 157 GHz and 183 GHz in the arctic winter, ser,. Berichte aus dem
Institut fur Umweltphysik. Berlin: Logos-Verlog, 21.
WMO, (1989). WMO sea ice nomenclature. WMO.
6.3 Articles in Books
HALLIKAINEN, M., WINEBRENNER, D. P., (1992). The physical basis for sea ice
remote sensing. Pages 29-46 in Carsey, F. D. (Ed.). Microwave remote sensing of sea
ice. American Geophysical Union.
TUCKER, W. B., PEROVICH, D. K., GOW, A. J., WEEKS, W. F., DRINKWATER,
M. R., (1992) Physical properties of sea ice relevant to remote sensing. Pages 9-28 in
Carsey, F. D. (Ed.). Microwave remote sensing of sea ice. American Geophysical
Union.
52
IntroductionMotivationAims and Outline of Dissertation
Physical BasisElectromagnetic QuantitiesRadiative TransferGaseous Emission and AbsorptionSurface EmissivityRadiative Transfer Equations
The Inverse ProblemThe nature of sea iceElectromagnetic properties of sea ice
DataSea Ice Emissivity MeasurementsInstrumentationMethodologyEstimation of skin temperature
Operational Sea Ice Products
Results and AnalysisMeasured Sea Ice EmissivitiesEmissivity relationshipsUncertainty Analysis
ConclusionsFuture Work
ReferencesJournal ArticlesBooksArticles in Books
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