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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

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.

ii


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.

iii


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

iv


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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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

1


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)

2


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.

3


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.

4


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:

5


⎟⎠⎞

⎜⎝⎛ −

=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


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.

7


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:

8


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

9


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:

10


( ) ( )∫+=∞ 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.

11


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.

12


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

13


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.

14


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.

15


Figure 2.2 Nilas ice

Figure 2.3 Pancakes

16


Figure 2.4 First year ice

Figure 2.5 Multi year ice

17


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.

18


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

19


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.

20


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.

21


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

22


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.

23


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,

24


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

25


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.

26


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.

27


Figure 3.4 NT sea ice concentration map for A827

28


Figure 3.5 ASI sea ice concentration map for A827

29


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.

30


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

31


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.

32


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.

33


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

34


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.

35


Figure 4.2 Emissivity spectra of first and multi year ice showing standard deviation and modelled

values

36


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.

37


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

38


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.

39


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.

40


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.

41


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

42


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.

43


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

44


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

45


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%

46


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

47


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

48


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.

49


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.

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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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