UNIVERSITY OF READING. Department of Meteorology

Transcription

1 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

2 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 (R 2 = 0.97), and while this is not the case for the window channel at 89 GHz and the two higher frequencies (R 2 = 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 (R 2 = 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

3 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

4 Table of Contents 1 Introduction Motivation Aims and Outline of Dissertation Physical Basis Electromagnetic Quantities Radiative Transfer Gaseous Emission and Absorption Surface Emissivity Radiative Transfer Equations The Inverse Problem The nature of sea ice Electromagnetic properties of sea ice Data Sea Ice Emissivity Measurements Instrumentation Methodology Estimation of skin temperature Operational Sea Ice Products Results and Analysis Measured Sea Ice Emissivities...32 iv

5 4.2 Emissivity relationships Uncertainty Analysis Conclusions Future Work References Journal Articles Books Articles in Books...52 v

6 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

7 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 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

8 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

9 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

10 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: c ν = 2.1 λ 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

11 B ν = c 2 3 2hν hν exp 1 kt 2.2 where B ν is the black body spectral radiance which has units of [Wm -2 sr -1 Hz -1 ], T is the temperature of the emitting body in Kelvin, Boltzmann s constant. h is Planck s constant and k is In the case of microwave frequencies where hν kt << 1, expression 2.2 simplifies to the linear Rayleigh-Jeans approximation: 2 2 kt B = ν ν 2 c 2.3 Using this approximation, it is simple to define the brightness temperature, i.e. the temperature at which a black body would emit the observed radiance. This simplification is used almost exclusively in the description of microwave radiative transfer as it holds well over the complete range of frequencies used. However, it is apparent that this approximation breaks down for small values of T. The only point at which such low temperatures are encountered during the terrestrial application of microwave radiative transfer theory is when the cosmic microwave background temperature is defined. For this reason, a frequency dependent, effective cosmic microwave background temperature is used. 2.2 Radiative Transfer When propagating in free space electromagnetic radiation is unperturbed. However, when it encounters any medium the radiance will be modified by absorption by the medium and thermal emission from it and, in some cases, scattering by the particles within it. These processes, with the exception of scattering which is not relevant to this study, are described below Gaseous Emission and Absorption The emission and absorption spectra of gases are defined by line spectra corresponding to transitions between allowed energy levels. In the case of an atomic 6

12 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: E ν = 2.4 h 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

13 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: e 2.5 ( ν, θ ) + Γ + ϒ = 1 where e ) is the emissivity at frequency ν and incidence angle θ, Γ is the ( ν, θ reflectivity and ϒ is the transmittance of a layer of the medium. 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: e Bν, 2.6 ( ν θ ) = Bν bb The reflectivity, ( θ ) Γ, at polarisation p and incidence angle p θ for a specular surface is given by the Fresnel relations: 2 ( µε sin θ ) 2 ( µε sin θ ) µ cosθ Γ h ( θ ) = 2.7 µ cosθ + 2 ( µε sin θ ) 2 ( µε sin θ ) ε cosθ Γ v ( θ ) = 2.8 ε cosθ + 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 µ = 1 for most terrestrial matierials and so matierials can be described in terms of ε, which is a complex number: 2 2 8

14 ε = ε i ε 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 diν of a beam with intensity travelling through a finite path, s, of a gas with density ρ which, having defined an absorption coefficient,, is given by: k ν Iν di ν = k ρi ds 2.10 ν ν Integrating this expression along s gives Beer s law: I = s ν I ν 0 exp k ν ρds It is possible to consider an increment in the radiance by defining a quantity, j ν, in a similar manner to the absorption coefficient. However it is more convenient to consider a source term J ν which satisfies j = k J 2.12 ν ν ν Now, the net change in the radiance due to propagation along s can be given by di ν = k ρ I ds + k ρj ds 2.13 ν ν ν ν or k di ν ν ρds = I + J 2.14 ν ν 9

15 This expression can be generalized for radiation propagating vertically in a plane parallel medium where I and J are functions of the vertical coordinate z, and the direction of propagation defined by the zenith and azimuth angles θ and φ respectively. We can also define the optical depth τ = kν ρdz 2.15 z Thus equation 2.14 becomes where µ = cosθ. di ν ( z, θ, φ) µ = Iν ( z, θ, φ) + Jν ( z, θ, φ) 2.16 dτ 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: I = I S τ S ( τ ) + B( T( τ )) exp( τ ) exp dτ 2.17 S 0 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. ˆ and At this point it is convenient to define the atmospheric transmittance τ = exp( τ ) a vertical coordinate weighting function, W y = ln ( y) p which allow us to rewrite 2.17, with the inclusion of a dτˆ =, to give: dy 10

16 I ( ) W ( y) = I Sτˆ S + B T dy 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: T ( y) W ( y) = estsτˆ s + Ta dy 2.19 where T is the brightness temperature measured at the top of the atmosphere, e is the surface emissivity, T the surface temperature and (y) is the atmospheric s temperature profile. 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. T a s 11

17 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

18 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 J( x): J T 1 T 1 ( x) = ( x x ) B ( x x ) + ( y H( x) ) R ( y H( x) ) b b 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, x, and the observations, y, 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). 13

19 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

20 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 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

21 Figure 2.2 Nilas ice Figure 2.3 Pancakes 16

22 Figure 2.4 First year ice Figure 2.5 Multi year ice 17

23 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 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

24 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

25 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 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: T n T n ( 1 e ) T ˆ τ = T e T ˆ τ a s s s d where T a is the contribution due to thermal emission of the atmosphere below the aircraft, the contribution from the surface is given by e s T s modified by the transmittance of the atmospheric layer below the aircraft, τˆ. T d is the downwelling radiation that is reflected by the surface. 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

26 Td Tz T, p, q Tn Tm, τˆ Ta h Ts,es 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 Tm and transmittanceτˆ. 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 τˆ under most conditions. However, it may be limited in conditions where there is a strong surface inversion. 21 T m and

27 Having estimated Tm and τˆ it is possible to calculate the upwelling atmospheric contribution to the measured signal, T a : T a ( 1 τˆ ) T m = 3.2 Similarly, the reflected downwelling brightness temperature, T d, can be estimated from the measured zenith brightness temperature at the aircraft, T, and T from 3.2. z a T = T τˆ + T 3.3 d z a 3.1 can be rewritten to give an expression for the emissivity: e s T ˆ n Ta Tdτ = 3.4 ( T T )τ ˆ s d T n can be measured directly at the aircraft, τˆ can be modelled using atmospheric profile measured by dropsondes and hence T and T can be estimated using equations 3.2 and 3.3. Therefore the only remaining unknown is the surface temperature 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, 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, a, defined as the sum of the squared differences between F c d 22

28 the observed nadir brightness temperatures, transfer equations, RTE T n OBS T n, for the three channels., and those modelled using radiative F c OBS RTE ( T T ) = n, i n, i 3.5 i 2 where the index, i, refers to the channel numbers. 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 and the resulting sensitivity. 23

29 Table 3.2 Summary of emissivity sensitivity calculations Channel τˆ T n /K T z /K Senitivity/K The average surface temperature retrieved using 3.5 during this period was 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 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

30 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 workaround 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

31 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 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, PR( 19) GR( 37 V19V ), defined as PR, and the spectral gradient between 19 and 37 GHz, ( 19) ( 19V ) TB ( 19H ) ( 19V ) + T ( 19H ) TB = 3.6 T B B and GR ( 37V19V ) ( 37V ) TB ( 19V ) ( 37V ) + T ( 19V ) TB = 3.7 T B B where T B is the measured brightness temperature at a particular channel and V and 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

32 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, 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

33 Figure 3.4 NT sea ice concentration map for A827 28

34 Figure 3.5 ASI sea ice concentration map for A827 29

35 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

36 Table 3.3 Comparison of SSM/I sea ice products with aircraft scientist observations during flight A827 Start Time End Time Surface Characteristics SSM/I Derived Ice Concentrations ASI NT MY 09:51:21 09:56:46 Open Water :57:47 10:01:30 Open Water < 5% ice :27:25 10:47:45 CCPI (FYI) :49:00 10:58:15 CCPI (some MYI) :47:00 11:49:00 Possible MYI :20:00 12:30:00 70% MYI, 30% FYI :30:00 12:42:00 85% MYI, 15% FYI :46:00 12:56:00 Mostly MYI

37 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

38 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

39 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

40 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

41 Figure 4.2 Emissivity spectra of first and multi year ice showing standard deviation and modelled values 36

42 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

43 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: e =.06854e with an r 2 value of Table 4.1 Results of attempting to fit a trend to variation of emissivity to FYI concentration Frequency / GHz Gradient Intercept R E E E E-3 38

44 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 R 2 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

45 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

46 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

47 Figure 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 R 2 Open Water First year ice Multi year ice