The Optical Properties of Sea IceDonald K. Perovich May 1996

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AbstractSea ice is a translucent material with an intricate structure and complexoptical properties. Understanding the reflection, absorption, and transmis-sion of shortwave radiation by sea ice is important to a diverse array ofscientific problems, including those in ice thermodynamics and polar clima-tology. Radiative transfer in sea ice is a combination of absorption andscattering. Differences in the magnitude of sea ice optical properties are dueprimarily to differences in scattering. Spectral variations are mainly a result ofabsorption. Changes in such optical properties as the albedo, reflectance,transmittance, and extinction coefficient are directly related to changes in thestate and structure of the ice. Physical changes that enhance scattering, suchas the formation of air bubbles due to brine drainage, result in larger albedosand extinction coefficients. The albedo is quite sensitive to the surface state. Ifthe ice has a snow cover, albedos are large. In contrast, the presence ofliquid water on a bare ice surface causes a decrease in albedo, which ismore pronounced at longer wavelengths. Sea-ice optical properties dependon the volume of brine and air and on how the brine and air are distributed.

For conversion of SI units to non-SI units of measurement consult ASTMStandard E380-93, Standard Practice for Use of the International Systemof Units, published by the American Society for Testing and Materials,1916 Race St., Philadelphia, Pa. 19103.

Cover: Dr. T.C. Grenfell measuring melt pond albedos on first-year icenear Barrow, Alaska. A Kipp radiometer, which measures totalshortwave irradiance, is in the foreground. The cylindrical instru-ment on the tripod is a scanning spectroradiometer that measuresspectral irradiance from 400 to 2500 nm.

Monograph 96-1

The Optical Properties of Sea IceDonald K. Perovich May 1996

Prepared for

OFFICE OF NAVAL RESEARCH

Approved for public release; distribution is unlimited.

US Army Corps of Engineers Cold Regions Research & Engineering Laboratory

PREFACE

This monograph was prepared by Dr. Donald K. Perovich, Geophysicist, Snow and IceDivision, Research and Engineering Directorate, U.S. Army Cold Regions Research andEngineering Laboratory, Hanover, New Hampshire. Funding for this work was providedby the generous support of the Office of Naval Research under Contracts N0001495MP30002and N0001495MP30031.

The monograph was technically reviewed by J. Richter-Menge and G. Maykut.The author deeply thanks Dr. T.C. Grenfell for two decades of illuminating, insightful

and stimulating discussions on the optical properties of sea ice. The author also appreci-ates the helpful contributions of G. Cota, A. Gow, B. Light, and G. Maykut. Thanks to K.Jones, R. Maffione, S. Pegau, J. Richter-Menge and W. Tucker for helpful reviews of themanuscript.

The contents of this monograph are not to be used for advertising or promotionalpurposes. Citation of brand names does not constitute an official endorsement or approvalof the use of such commercial products.

ii

CONTENTSPage

Preface ................................................................................................................................. iiIntroduction ........................................................................................................................ 1Background ........................................................................................................................ 1Theory ................................................................................................................................. 4

Absorption ..................................................................................................................... 5Scattering ........................................................................................................................ 6

Observations ....................................................................................................................... 8Albedos ........................................................................................................................... 8Reflectance ..................................................................................................................... 11Transmission ................................................................................................................. 12Extinction coefficient .................................................................................................... 12Beam spread .................................................................................................................. 14

Models ................................................................................................................................. 15Summary and current areas of interest .......................................................................... 19Literature cited ................................................................................................................... 21Appendix A: List of symbols ........................................................................................... 25Abstract ............................................................................................................................... 27

ILLUSTRATIONS

Figure1. The optical portion of the electromagnetic spectrum ........................................ 32. Aerial photograph of typical Arctic summer scene taken from an altitude

of 600 m on 3 August 1994 at 78°N, 177°W ......................................................... 33. Range of observed values of total albedo for sea ice ......................................... 34. Schematic of radiative transfer in sea ice ............................................................ 45. Absorption coefficients of pure, bubble-free ice ................................................. 56. Absorption coefficients of biota found in congelation ice and frazil ice ........ 67. Observed and calculated phase functions for sea ice ........................................ 78. Laboratory observations of the increase in spectral albedo during

initial ice growth ..................................................................................................... 89. Spectral albedos for a possible evolutionary sequence of multiyear ice ........ 9

10. A spectral albedo sequence that first-year ice might follow througha melt cycle ............................................................................................................... 9

11. Observations of total albedo vs. brine volume for young ice .......................... 1012. Spectral albedos of Antarctic sea ice .................................................................... 1113. Bidirectional reflectance distribution function at 450 nm for snow-covered

ice and bare blue ice ............................................................................................... 1114. The influence of surface conditions on light transmission ............................... 1215. Observed spectral transmittances for 1.5-m-thick first-year ice ...................... 13

iii

Figure Page

16. Spectral extinction coefficients for nine distinct cases ....................................... 1317. Theoretical estimates of ultraviolet and visible light transmission through

sea ice in the Weddell Sea ...................................................................................... 1718. Calculated estimates of spectral albedo as a function of ice density and

growth rate ............................................................................................................... 1819. Seasonal changes in underice spectral irradiance calculated using a

bio-optical model .................................................................................................... 19

TABLES

Table1. Values of i0 and and κt ................................................................................................................................................................ 142. Summary of sea ice radiative transfer models ................................................... 16

iv

INTRODUCTION

Sea ice is a translucent material with an intri-cate structure and complex optical properties. Un-derstanding the reflection, absorption, and trans-mission of shortwave radiation by sea ice isimportant to a diverse array of scientific prob-lems. It is of fundamental concern in treating large-scale problems in ice thermodynamics and polarclimatology. The summer melt cycle of the Arcticsea ice cover is driven by shortwave radiation,making the interaction of shortwave radiationwith sea ice a critical component of the heat bal-ance of the ice cover (Maykut and Untersteiner1971, Maykut and Perovich 1987, Thorndike 1992,Ebert and Curry 1993). Of particular climatologi-cal concern is understanding the sea ice albedofeedback mechanism (Ingram et al. 1989). Duringthe summer the ice cover begins to melt due tothe input of solar radiation. This melting tends todecrease the surface albedo and increase the heatinput, thereby accelerating the melt process. Be-cause of the climatological interest in the heatbalance of sea ice, there is also a need for large-scale spatial and temporal information on ice packalbedos. Properly interpreted, the reflected radi-ance measured by visible and near-infrared satel-lite sensors can provide such information. In ad-dition, the amount and spectral composition ofshortwave radiation transmitted through sea icestrongly impacts primary productivity and bio-logical activity in and under a sea ice cover (SooHoo et al. 1987, Arrigo et al. 1993). Visible lightbenefits ice biota by contributing to photosynthe-sis, while ultraviolet light can damage organisms.

This monograph focuses on the optical proper-ties of sea ice. The goal is to provide an introduc-tory tutorial to the topic, not to be a completecompendium of work in the field. The physicalprinciples underlying radiative transfer in sea ice,including scattering and absorption, are discussed,

along with the importance to optics of the sea icephysical state and structure. Observational resultsare presented, with the emphasis placed on ex-plaining the wide variability in sea ice opticalproperties in terms of ice physical properties andradiative transfer theory. An overview is given ofexisting sea ice radiative transfer models present-ing their basic characteristics, solution schemes,strengths, and limitations. Finally, current researchareas and problems of interest in sea ice opticalproperties are discussed. Since the presence of asnow cover can greatly impact light reflection andtransmission through sea ice, some mention ismade of the optical properties of snow. An excel-lent review of the optical properties of snow isprovided by Warren (1982). The optical proper-ties of ice biota and particulates found in the ice(Arrigo et al. 1991, Roesler and Iturriaga 1994)are also discussed briefly because of their impacton radiative transfer in sea ice.

BACKGROUND

By “optical” we refer to the portion of the elec-tromagnetic spectrum that is coincident with thewavelength range of radiation from the sun, fromroughly 250 nm to 2500 nm (Fig. 1). The solarportion of the electromagnetic spectrum is alsoreferred to as shortwave radiation. The opticalregion can be divided into three segments: ultra-violet light from 250 to 400 nm, visible light from400 to 750 nm, and near-infrared light from 750 to2500 nm. The ultraviolet can be further dividedinto UV-C from 200 to 280 nm, UV-B from 280 to320 nm, and UV-A from 320 to 400 nm. Because ofstrong absorption in the atmosphere, essentiallyno UV-C reaches the Earth’s surface. It is in theUV-B where light levels are substantially enhancedby the depletion of stratospheric ozone (Frederickand Lubin 1988, Lubin et al. 1989, Tsay and

The Optical Properties of Sea Ice

DONALD K. PEROVICH

total, albedo αt is often a quantity of interest,since it is a measure of the total solar energyabsorbed by the ice and ocean (Maykut andUntersteiner 1971, Maykut and Perovich 1987). Itcan be expressed in terms of the spectral albedoand the spectral incident irradiance as

α

α λ λ λλ λt

d

d

0,

0,=

( ) ( )( )

∫∫

F d

F d . (1)

The total albedo depends on the spectral distri-bution of the incident irradiance as well as on thespectral albedo of the surface. Thus a change incloud conditions, and thereby the incident spec-tral irradiance, can result in changes in the totalalbedo (Grenfell and Maykut 1977).

For some problems a knowledge of the angu-lar distribution of the reflected radiance is needed.For example, in climate studies it would be use-ful to derive large-scale ice albedos from satellitedata. However, satellite sensors have narrow fieldsof view and measure reflected radiance. The keythen is to relate the radiance reflected at the view-ing angle of the instrument to the albedo of theice. In order to do this the angular distribution ofreflected radiance, characterized by the bidirec-tional reflectance distribution function (BRDF),must be known. The formal definition of the BRDFis (Nicodemus et al. 1977, Warren 1982, Perovich1994)

R

dI

dFθ θ φ φ λ

θ φ λθ θ φ λ0 0

0 0 0, , , ,

, ,

cos , ,( ) =

( )( ) ( )

where θ0 and φ0 are the solar zenith and azimuthangle, F(θ0, φ0, λ) is the incident spectral irradi-ance, and R has units of steradians–1. Formally Ris a derivative quantity, similar to a probabilitydensity function, defined in terms of infinitesi-mal angles. In practice, the definition is extendedto finite, measurable angles, so that dI→∆I anddF→∆F.

Light transmission through the ice is charac-terized by the transmittance T(λ), which is simi-lar to the albedo in that it is the fraction of theincident irradiance that is transmitted throughthe ice. Light attenuation in the ice is often repre-sented using an irradiance extinction coefficient

κ λ

λλ

zF z

dF z

dz,

,

,( ) = −( )

( )1

d

d

where Fd(z, λ) is the downwelling spectral irradi-ance at depth z in the ice.

Let us now examine the difficulties in deter-

Stamnes 1992, and Smith et al. 1992a) and canhave a deleterious impact on living organisms(Smith 1989, Smith et al. 1992b). The familiar spec-trum of visible light is also shown in Figure 1from violet (400 nm) to blue (450 nm) to green(550 nm) to yellow (600 nm) to red (650 nm).

“Properties” refers to the parameters that areused to describe the reflection, absorption andtransmission of solar radiation by sea ice. Theterminology of radiative transfer is intricate andvoluminous. It also has the unfortunate attributethat the same physical quantity may have a dif-ferent name, depending on whether an oceanog-rapher, an astrophysicist or a biologist is speak-ing. To avoid a Babel of jargon we shall limitourselves to the terms needed for a basic under-standing of the optical properties and shall fol-low the terminology conventions of the sea iceliterature.

The spectral radiance I(θ,φ,λ) is the power in aray of light in a particular direction, where θ isthe zenith angle (0 pointing downward, π point-ing upward), φ is the azimuth angle and λ is thewavelength. The spectral radiance is defined asthe radiant flux/nanometer per unit area per unitsolid angle in a particular direction and has unitsof W m–2 sr–1 nm–1. The spectral irradiance F(λ) issimply the radiance projected onto a plane sur-face and integrated over a hemisphere. Becauseof this projection the radiance is scaled by cos θ.The downwelling irradiance Fd(λ) is the radianceintegrated over downward directions (e.g., fromthe sky), and the upwelling irradiance Fu(λ) is theradiance integrated over upward directions (e.g.,from the surface). This can be expressed formallyas:

F I d d

F I d d

d

u

λ θ φ λ θ θ θ φ

λ θ φ λ θ θ θ φ

φ

π

θ

π

φ

π

θ π

π

( ) = ( )

( ) = ( )

= =

= =

∫ ∫

∫ ∫

0

2

0

2

0

2

2

/

/

, , cos sin

, , cos sin .

The most studied, and most used, optical prop-erty of sea ice is the albedo (α). The spectral al-bedo is simply defined as the fraction of the inci-dent irradiance that is reflected:

α λλ

λ( ) = ( )

( )

F

Fu 0,

d 0,

where the 0 designates the surface. In sea ice ther-modynamic studies the wavelength-integrated, or

2

of the ice. As Figure 2 indicates, sea ice exhibits agreat degree of horizontal variability with diversesurface conditions, including ponds, bare ice, andsnow-covered ice, and thicknesses that range fromopen water to pressure ridges over 10 m thick.

There is also vertical complexity,with ice properties such as tem-perature, salinity, brine volumeand air volume changing signifi-cantly from the ice surface to theice/water interface. The details ofsea ice physical properties andstructure are summarized inWeeks and Ackley (1982). What ismost germane to optics is that seaice has an intricate structure con-sisting of an ice matrix with in-clusions of air, brine, solid salts

Figure 3. Range of observed values of total albedo for sea ice. The albedosare from Burt (1954), Chernigovskiy (1963), Langleben (1971), Grenfelland Maykut (1977), and Grenfell and Perovich (1984).

0.68

0 0.06

0.15

0.21

0.29

0.40

0.52

0.

56

0.77

0.87

0.81

0.70 1.00

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t Pon

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Pon

ded

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yr)

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Pon

d

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ting

Blu

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e

Ref

roze

n M

elt P

ond

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e (1

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Sno

w

Win

dpac

ked

Sno

w

New

Sno

w

Bulk Albedo

3

mining the optical properties ofsea ice by posing a simply statedquestion: “What is the albedo ofsea ice?” Albedos are straight-forward to determine. A radi-ometer is used to measure theirradiance incident on a surfaceand reflected from the surface.The albedo is constrained to liebetween 0, if none of the inci-dent irradiance is reflected, and1, if all the incident is reflected.At first glance this appears to bean easy question to answer.

Figure 2 is an aerial photo-graph of a small, roughly one-quarter-square-kilometer, area ofa typical summer Arctic scene. The melt seasonhas begun and there is a tremendous amount ofspatial variability in ice surface conditions: snow-covered ice, bare white ice, blue melt ponds,dirty ice, and areas of open water. This vari-ability is also manifested in the wavelength-integrated albedo, which ranges from 0.05 foropen water, to 0.2 to 0.4 for ponded ice, to 0.5to 0.7 for bare ice, to 0.75 to 0.85 for snow-covered ice. Observations of wavelength-inte-grated albedo for a full range of sea ice typesand conditions are summarized in Figure 3.Considerable variability in albedo is apparent.Determining that the albedo falls between 0.05and 0.9 still does not provide an adequate an-swer to our question of “What is the albedo ofsea ice?” Indeed, while the question is simpleto state, it is extremely difficult to answer on alarge scale.

Considering the complicated and variablephysical structure of sea ice, variability in theoptical properties should not be surprising. Tounderstand and explain this variability, it is neces-sary to examine the physical state and structure

Figure 1. The optical portion of the electromagnetic spectrum. Visible light isfrom 400 nm (violet) to 750 nm (red).

Figure 2. Aerial photograph of typical Arctic summerscene taken from an altitude of 600 m on 3 August1994 at 78°N, 177°W. The horizontal extent is approx-imately 425 m.

and contaminants, and that it is a material thatexists at its salinity-determined melting point.Therefore, changes in temperature result inchanges in its physical properties and structure.One of the goals of this tutorial is to illustrate, atleast qualitatively, how changes in the ice physi-cal properties are related to changes in opticalproperties. To accomplish this, we must first ex-amine the theoretical underpinnings of radiativetransfer in sea ice.

THEORY

The interaction of solar radiation with sea iceis illustrated schematically in Figure 4. The inci-dent radiation field consists of a direct beam com-ponent from the sun and a diffuse componentfrom the sky and clouds. If it is completely cloudyand the solar disk is not visible, the incident ra-diation field is considered to be diffuse. Depend-ing on sky and surface conditions some portionof the incident radiation is specularly reflectedfrom the surface. A portion of the incident radia-tion is reflected from the ice, a portion absorbedin the ice, and a portion transmitted through theice. As we shall see, the relative sizes of theseportions are dependent on the physical proper-ties of the ice and on the wavelength of the light.

At optical wavelengths, radiative transfer insea ice is governed by two processes: absorptionand scattering. As a ray of light passes throughsea ice, some of the light is absorbed by the iceand some of it is scattered from the beam in dif-ferent directions. This is expressed more formally

as the equation of radiative transfer for a planeparallel medium (Chandrasekhar 1960):

−

( )= ( ) − ( )µ

τ µ φ λτ

τ µ φ λ τ µ φ λdI

dI S

, , ,, , , , , , (2)

where I = the radianceµ = the cosine of the zenith angle θφ = the azimuth angle.

Scattering is included in the S term, which is re-ferred to as the source function. τ is the nondi-mensional optical depth and is defined as

τ λ λ σ λ( ) = ( ) + ( )[ ]k z

where k is the absorption coefficient, σ is the scat-tering coefficient, and z is the physical depth. Thesingle scattering albedo

ϖ λ

σ λλ σ λ0 ( ) ( )

( ) ( )=+k

gives the fractional loss due to scattering (Chand-rasekhar 1960, Mobley 1994). ϖ0 ranges from 0 fora purely absorbing medium to 1 for a purely scat-tering medium. A plane parallel medium is hori-zontally homogeneous, but can have verticalvariations.

The compact form of eq 2 belies its true com-plexity. This complexity becomes evident if thereis scattering in the medium (ϖ0 > 0) and the sourcefunction is expressed in detail. For a plane-paral-lel medium with a direct incident beam, the sourcefunction is expressed as

S p Iτ µ φ λ ϖ

πµ µ φ φ τ µ φ λ

π, , , , , , , , ,( ) = ′ ′( ) ( )

−∫ ∫0

4 1

1

0

2

d d

Ep e′ − ( )

′ ′( ) − ( )µ φλ

µ µ φ φ τ λ µ0

40, , , ,/

where p(µ,µ′,φ,φ′) is the phase function and E0 isthe radiance of the direct beam component of theincident radiation field. With scattering included,eq 2 is an integro-differential equation and is notreadily amenable to solution. However, while itis difficult to solve the equation, it is still straight-forward to understand qualitatively. The doubleintegral term is used for diffuse radiative pro-cesses only and represents scattering of the radi-ance field I(τ,µ′,φ′,λ) from different directions intothe direction of the solution (µ,θ). How much ofthis light is scattered from one direction to an-other is defined by the phase function p(µ,µ′,φ,φ′).The phase function is normalized so that its in-Figure 4. Schematic of radiative transfer in sea ice.

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radiance, I (z, λ), are even more pronounced,being exponentially greater than the changes inabsorption coefficient.

Examining the e-folding length gives a betterunderstanding of the absorption coefficients. Thee-folding length is the amount of ice needed toreduce the incident light (I (0, λ)) by 1/e (i.e., thetransmitted light is 37% of the incident). e-foldinglengths for ice decrease sharply from 24 m at 470nm, to 8 m at 600 nm, to 2 m at 700 nm, to 0.05 mat 1000 nm, to 0.006 m at 1400 nm. This indicatesthat ice is quite transparent in the blue, while ittakes only a few centimeters of ice to absorb mostof the light beyond 1000 nm.

As Figure 5 indicates, absorption coefficientsfor clean Arctic water are similar in magnitudeand spectral shape to values for pure ice. An ab-sorption coefficient for sea ice ksi is determinedby combining the absorption coefficients for theconstituent components of brine and ice using

k k ksi i i b b= +ν ν (4)

where νi and νb represent the volume fraction ofice and brine, and ki and kb are the absorption

Figure 5. Absorption coefficients of pure, bubble-freeice (Grenfell and Perovich 1981, Perovich and Govoni1991) and clear sea water (Tyler and Smith 1970, Smithand Baker 1981).

103

102

101

100

10– 1

10– 2

200 400 600 800 1000 1200 1400Wavelength (nm)

Abs

orbt

ion

Coe

ffici

ent (

m

)–

1

Pure, Bubble-freeIce

ClearSeawater

tegral over angle is equal to one. The second termprovides the contribution of scattered light fromthe attenuated direct beam E0(λ). This term isneeded only if there is direct incident irradianceas well as a diffuse component.

AbsorptionIt is time to examine absorption and scattering

in sea ice in detail, starting with absorption be-cause it is the simpler of the two processes. Con-sider the case of absorption only for a direct beamof light normally incident on a medium. Sincethere is no scattering, S = 0 and σ = 0. For normalincidence, θ = 0, which means µ = 1. Equation 2then reduces to

− ( )( ) = ( )dI z

k dzI z

,,

λλ

λ

which, when solved, gives the familiar exponen-tial decay law

I z I e kz, ,λ λ( ) = ( ) −0 (3)

also known as Beer’s law or the Bouguer-Lam-bert law. Radiative transfer in a purely absorbingmedium is quite simple to describe. The radiancedecreases exponentially with depth in the me-dium, with the rate of decrease dependent on theabsorption coefficient. What needs to be knownare the absorption coefficients for the primarycomponents of sea ice: ice, brine and air. Equa-tion 3 implies that absorption coefficients can bedetermined by measuring the incident radiance,the transmitted radiance, and the thickness of ahomogeneous sample that is free of scatterers(Grenfell and Perovich 1981).

Absorption in the air inclusions in sea ice isnegligible, so absorption coefficients for air areassumed to be zero. Spectral absorption coeffi-cients from the ultraviolet to the near-infraredfor ice and seawater are shown in Figure 5. Ab-sorption coefficients for ice were determinedusing pure, bubble-free, fresh ice (Grenfell andPerovich 1984, Perovich and Govoni 1991), andabsorption coefficients for brine taken from mea-surements of clear Arctic water (Tyler and Smith1970, Smith and Baker 1981). The minimum ab-sorption and therefore maximum transmissionfor ice is in the blue part of the electromagneticspectrum at 470 nm. Spectral changes in ab-sorption coefficient are extremely large, span-ning several orders of magnitude from 250 to1400 nm. Spectral differences in the transmitted

5

coefficients of ice and brine (Grenfell 1983). Ab-sorption by air is assumed to be negligible.

Equation 4 provides a simple means of gener-ating an absorption coefficient for sea ice fromphysically determinable quantities and knownvalues of ice and brine absorption coefficients.Unfortunately, in nature, sea ice is often morethan a combination of ice, brine and air. For ex-ample, particulates, sediments, ice biota and dis-solved organics can be present. If these impuri-ties are present in sufficient quantity, then theirabsorptive properties must also be considered. Ingeneral these impurities are strongly absorbingand weakly scattering. Absorption coefficients forsediments and ice biota vary depending on theircomposition. Examples of absorption coefficientsfor ice biota (Arrigo et al. 1991) are shown inFigure 6. The spectral shapes of these absorptioncoefficients are quite different than those of ice orbrine. If sediment or ice biota are present in suffi-cient quantity, they should be explicitly treated inthe theoretical formulation by modifying eq 4.

ScatteringSea ice is not a monolithic slab of pure ice. It

has an intricate structure consisting of an ice ma-

trix with inclusions of brine, air and perhaps solidsalts. Since these inclusions have different indicesof refraction than the surrounding ice, they scat-ter light. The larger the difference in index ofrefraction between the inclusion and the ice, thestronger the scattering. Sea ice has an abundanceof brine pockets and air bubbles and therefore isa highly scattering medium. In certain cases, par-ticulates, sediment, and ice biota contribute toscattering, but air bubbles and brine pockets arethe primary scatterers in sea ice and are the focusof this discussion.

Scattering results from differences in the realindices of refraction (n) between ice (n ~ 1.31) andthe inclusions. With a greater difference in indexof refraction, air bubbles (n ~ 1.0) are more strong-ly scattering than brine pockets. The real part ofthe index of refraction for brine depends on tem-perature, increasing from 1.34 at –2°C to 1.40 at–32°C (Maykut and Light 1995). If the ice is coldenough that solid salts form, scattering increasessignificantly, since these salts are very effectivescatterers (Perovich and Grenfell 1981). The scat-tering coefficient depends not only on the amountof brine and air, but on how it is distributed. Thiscomplicates matters since the readily determinedbrine and air volumes are not sufficient to definescattering. The more difficult to obtain size distri-bution of the inclusions is also needed. More in-clusions in the ice results in more scattering andconsequently a larger scattering coefficient. Scat-tering coefficients in sea ice are large, with valuestypically greater than 10 m–1 for warm ice andgreater than 200 m–1 for ice with abundant airbubbles or ice colder than –24°C with precipi-tated hydrohalite present (Perovich and Grenfell1982).

Scattering is defined by two parameters: thescattering coefficient and the phase function. Thescattering coefficient (σ) is analogous to the ab-sorption coefficient and is a measure of theamount of scattering per unit length. The phasefunction [p(µ,µ′,φ, φ′)] describes the angular de-pendence of scattering and usually is normalizedso that its integral over the full range of µ and φ isequal to one.

Because scattering depends on the intricate andhighly variable microstructure of sea ice, it is notpossible to formulate a simple, all-encompassingequation to define the scattering coefficient andthe phase function, as we could for the absorp-tion coefficient. Complicating matters even fur-ther is the fact that in a highly scattering mediumsuch as sea ice, scattering coefficients and phase

Figure 6. Absorption coefficients of biota found incongelation ice and frazil ice (from Arrigo et al. 1991).

10 x 10– 3

8

6

4

2

0400 500 600 700

Wavelength (nm)

Congelation IceCommunity

Platelet IceCommunity

Spe

cific

Abs

orbt

ion

Coe

ffici

ent

[m (

mg

chlo

roph

yll a

m

)]

– 3

1

6

functions are extremely difficult to measure. Thereis, however, one simplifying aspect to scatteringin sea ice in the optical regime: it can be assumedto be independent of wavelength. The wavelengthdependence of the real portion of the index ofrefraction for ice, brine and air is very weak atoptical wavelengths and typically is assumed tobe constant with wavelength (Grenfell 1983, 1991).Optical wavelengths are on the order of tenths ofa micrometer to micrometers. The inclusions insea ice have sizes on the order of tenths of amillimeter for brine pockets to millimeters for airbubbles. Since the scatterers are much bigger thanthe wavelength and the scatterers are far apart,contributions due to diffraction and interferencecan be ignored (Grenfell 1983, Bohren and Huff-man 1983). The result of the weak wavelengthdependence of n, and the fact that the size of thescatterers is much larger than the wavelength, isthat scattering coefficients and phase functionsfor sea ice can be assumed to be constant withwavelength (Grenfell 1983, 1991, Perovich 1993).A similar argument is made when analyzing

scattering in snow (Bohren and Barkstrom 1974,Wiscombe and Warren 1980). A thorough generaldiscussion of scattering can be found in van deHulst (1981) and Bohren and Huffman (1983).

Observations of scattering parameters are lim-ited. Perovich and Grenfell (1982) estimated scat-tering coefficients for young ice from observa-tions of albedo and transmittance. They foundthat scattering coefficients ranged from 8.9 m–1

for melting young ice to 19.6 m–1 for cold youngice to 420 m–1 for very cold young ice with pre-cipitated solid salts present. Grenfell and Hedrick(1983) used small samples of young ice to mea-sure phase functions for sea ice. Phase functionsfor columnar ice samples grown at –10°C and–30°C are shown in Figure 7. The phase functionis strongly forward-peaked, with forward scat-tering being more than a factor of 50 greater thanside or backward scattering. However, althoughsmall samples were used, there was still multiplescattering, and consequently the results representonly an approximation to the true single scatter-ing albedo and phase function. Multiple scatter-ing tends to smooth and reduce the angular de-pendence of the measured phase function.

Numerical calculations have been used tosupplement the relatively sparse observationaldata (Grenfell 1983, 1991). Phase functions arecalculated using a Mie scattering model with theindices of refraction for ice and brine and inclu-sion size distributions as input parameters (Bohrenand Huffman 1983). A calculated phase functionfor sea ice at –30°C with brine pockets with aradius of 0.02 mm (Light 1995) is compared toobserved values in Figure 7. As expected, the cal-culated phase function is more strongly forward-peaked than the multiply-scattered observed.

Though we do not have a quantitative under-standing of the relationship between scatteringand ice physical properties, a qualitative grasp issufficient for our purposes. To interpret observa-tions of optical properties the important theoreti-cal points are 1) absorption coefficients for iceand brine depend strongly on wavelength, 2) scat-tering coefficients and phase functions for sea iceare constant with wavelength, 3) increasing thenumber of inclusions in sea ice increases theamount of scattering, 4) air bubbles scatter morestrongly than brine pockets, and 5) scattering insea ice is strongly forward peaked. With thistheoretical foundation regarding the underly-ing physics of radiative transfer in sea ice, it istime to revisit the question of “What is the albedoof sea ice?”

105

104

103

102

101

100

0° 30° 60° 90° 120° 150° 180°Angle

10– 1

Pha

se F

unct

ion

c

a

b

Figure 7. Observed (Grenfell and Hedrick 1983) andcalculated (from Light 1995) phase functions for seaice. 0° is forward scattering and 180° is backward scat-tering: a) observations of ice grown at –30°C, b) obser-vations of ice grown at –10°C, and c) calculated esti-mates for ice at –30°C.

7

OBSERVATIONS

There is a large observational dataset of sea iceoptical properties, particularly of sea ice albedos(Perovich et al. 1986). In this section we presentan overview of these observations in the contextof illustrating how the optical properties of seaice are affected by the physical properties. Weinvestigate the effects of ice type, surface condi-tions, ice thickness, ice brine volume, and impu-rities on albedo, reflectance, transmittance, andextinction coefficient. The simplifying beauty ofoptical property observations is that, at least from400 nm to 750 nm, what you see is what you get.If the ice looks white, then its albedo will be highand relatively constant with wavelength. Simi-larly, the spectral albedo of a blue-looking meltpond will have a peak between 400 and 500 nm.

AlbedosAlbedos are sensitive to thickness during the

initial stages of ice growth. Weller (1972) mea-sured total albedos in a freezing lead and found arapid rise in albedo from 0.08 to 0.40 as the icegrew from open water to a thickness of 0.30 m,followed by a more gradual, asymptotic increaseas the ice continued to grow. For ice thicker thanapproximately 0.8 m total, albedo shows littlechange with thickness (Maykut 1982).

Spectral changes in albedo during initial icegrowth are plotted in Figure 8. The ice was grownin the laboratory at a constant air temperature of–20°C and had a columnar crystal structure(Perovich 1979). Albedo increased with thicknessat all wavelengths. As the ice grows thicker, op-portunities for backscattering in the ice are addedand at first albedos rise rapidly. However, thepath length of the backscattered light also in-creases, until finally only a negligible amount oflight penetrates to the bottom of the ice, isbackscattered, and emerges from the ice surfacewithout being absorbed. At this point increasingthe ice thickness no longer directly affects thealbedo and the ice is optically thick. As Figure 8indicates, this asymptotic ice thickness is smallerat longer wavelengths. At shorter wavelengthsalbedos are still increasing when the ice is 0.25 mthick, while at longer wavelengths (beyond 700nm), the asymptotic nature of the albedo increaseis evident. This is a direct result of the increase inabsorption as wavelength increases. This is consis-tent with our earlier comment: spectral variationsin optical properties are due to absorption. A closerlook at Figure 8 shows that the rapid rise in al-

bedo did not begin until the ice was 0.05 m thick.During the first 0.05 m of growth, the ice in thisexperiment had not yet begun to cool and brinevolumes were quite large. Because of this therewas little scattering in the ice. As the ice cooledand the large brine pockets fragmented into manysmaller pockets, there was more scattering andthe albedo increased. This observation illustratesagain that the optical properties of sea ice areoften more complicated than we would expect.

Of course, even for thick ice, sea ice albedosvary. From the previous discussion we can seethat albedo is sensitive to the ice surface condi-tions. Spectral albedos for multiyear ice are plot-ted in Figure 9 (taken from Grenfell and Maykut1977). These albedos represent a possible evolu-tionary sequence from spring to summer as meltoccurs, and the ice cover changes from snow-covered ice to bare ice or frozen ponds to meltingice to ponded ice. Snow albedos (curve a) arelarge (~0.9) and nearly constant with wavelengthin the visible; the snow appears bright and white.Scattering coefficients for snow are so large that,in the visible, absorption has little impact on thealbedo and there is no wavelength dependence.

0.8

0.6

0.4

0.2

0 5 10 15Ice Thickness (cm)

20 25

1.0

Bul

k A

lbed

o

Wavelength = 400 nm

500

600

700

800

900

1000

Figure 8. Laboratory observations of the increase inspectral albedo during initial ice growth (Perovich1979). The ice was grown at an air temperature of–20°C.

8

cally has a drained bubbly surface layer withplenty of air bubbles which, while not as stronglyscattering as snow, still contributes considerablescattering. The result is an overall decrease inalbedo of approximately 10% and a slight wave-length dependence. As the ice warms and beginsto melt (curve c), albedos continue to decreasewith a more evident wavelength dependence. Thisis due to a decrease in scattering as the ice meltsand some of the air voids fill with water. In someareas of the ice cover, water collects on the sur-face, forming melt ponds (curve d). As the meltseason progresses these ponds can get deeper(curve e). Albedos of ponded ice are character-ized by a maximum in the 400–500 nm regionand a precipitous decrease between 500 and 800.The melt ponds look blue. This spectral behavioris due to the transparency of the water at shorterwavelengths; albedos below 500 nm are deter-mined primarily by the scattering properties ofthe underlying ice. From 500 to 800 nm the al-bedo becomes increasingly insensitive to the un-derlying ice as the absorption in the water be-comes the dominant factor. Above 800 nmabsorption in the water is so great that pond albe-dos are essentially determined by Fresnel reflec-tion at the surface and are independent of wave-length. These results indicate that both themagnitude and the shape of the spectral albedosare extremely sensitive to the amount of liquidwater present in the upper part of the ice.

When skies are clear, the wavelength intervalfrom 1000 to 2500 nm can contain up to 25% of thetotal incident shortwave energy (Grenfell and

Perovich 1984), so albedos in this re-gion can have a significant impact onthe heat and mass balance of the ice.Figure 10 shows a spectral albedo se-quence that first-year ice might followas it progresses through a melt cyclefrom (a) ice covered by cold dry snow,(b) to ice covered by melting snow, (c) tobare ice with a crumbly surface layer,and (d) to melting first-year blue ice.Concentrating on wavelengths beyond1000 nm, a continual downward trendis evident, with albedo reaching a mini-mum at about 1500 nm. Local maximaare located at 1350, 1900 and 2300 nmand correspond to minima in the ab-sorption spectrum for ice. In general,sea ice and snow albedos at longerwavelengths are significantly smallerthan values at visible wavelengths.

Figure 10. A spectral albedo sequence that first-year ice mightfollow through a melt cycle (Grenfell and Perovich 1984): a) ice cov-ered by cold dry snow, to b) ice covered by melting snow, to c) bareice with a crumbly surface layer, to (d) melting first-year blue ice.

1.0

0.8

0.6

0.4

0.2

0400 800 1200 1600 2000 2400

Wavelength (nm)

Alb

edo

a

b

c

d

A 0.1-m-thick layer of wind-packed Arctic snowis sufficient to eliminate any contribution to thealbedo from the underlying ice.

Spectral albedos decrease as the surfacechanges from snow-covered ice to cold, baremultiyear ice (curve b). White multiyear ice typi-

Figure 9. Spectral albedos for a possible evolu-tionary sequence of multiyear ice (Grenfell andMaykut 1977): a) snow-covered ice, b) cold bareice, c) melting bare ice, d) early-season meltpond and e) mature melt pond.

0.8

0.6

0.4

0.2

0400 500 600 700 800

Wavelength (nm)

1.0a

b

c

d

eAlb

edo

9

Comparing albedos in Figures 9 and 10 dem-onstrates that, for equivalent conditions, multiyearice albedos are typically larger than first-year icevalues. Multiyear ice has undergone a summermelt season, with the attendant surface meltingand brine drainage. This results in a well-devel-oped surface-scattering layer with many airbubbles.

As a result of the decrease in albedo at longerwavelengths, total albedos (αt) are greater undercloudy skies than under clear skies. The total al-bedo depends on the spectral albedo and the spec-tral incident irradiance (eq 1). Clouds absorb morestrongly in the infrared than in the visible. There-fore on cloudy days a greater portion of the inci-dent irradiance is at visible wavelengths, wherethe albedo is larger. Total albedos under cloudyskies are typically 8–12% larger than clear skyvalues (Grenfell and Maykut 1977, Grenfell andPerovich 1984). When the incident direct beamcomponent is significant, both spectral and totalalbedos increase as the solar zenith angle increases(sun closer to the horizon) due to enhanced specu-lar reflection (Perovich and Grenfell 1982) and toforward scattering allowing the photons to es-cape the medium faster.

Surface conditions have a strong impact onalbedo, but the internal state and structure of theice are also significant. As we have seen, the pres-ence of air bubbles in the upper portion of the iceenhances albedo. Brine volume is another impor-tant ice physical property that we might expect tohave some impact on albedo. Perovich andGrenfell (1981) investigated the influence of brinevolume on albedo for young ice. Results fromthree laboratory experiments are summarized inFigure 11. In each experiment the ice was grownat a selected air temperature (–37°, –30° and–10°C), and therefore a different growth rate, to athickness of approximately 0.25 m. Brine volumewas then varied by warming the ice. For eachexperiment there is a continual decrease in al-bedo as brine volume increases. As the ice warmedand the brine volume increased, individual brinepockets coalesced, forming larger but fewer in-clusions. Thus, the result of the warming was areduction in the number of brine pockets and inthe amount of scattering. Comparing between ex-periments, we also see that at a given brine vol-ume there is considerable variability in the ob-served albedo, with faster grown ice (lower airtemperature) having larger albedos (Perovich andGrenfell 1981). More rapidly grown ice has smallerplatelet and crystal sizes and more brine inclu-

sions (Weeks and Hamilton 1962, Lofgren andWeeks 1969, Weeks and Ackley 1982). This leadsto the important conclusion that not only is thevolume of brine important, but how it is distrib-uted is also significant. For a given volume ofbrine, there is more scattering if that brine is dis-tributed into many small brine inclusions, ratherthan a single large one. The same conclusion istrue for air bubbles.

All of the albedos presented so far have beenfor Arctic sea ice. Are albedos for Antarctic icedifferent? Spectral albedos for young sea icegrown off of East Antarctica are plotted in Figure12 (Allison et al. 1993). These albedos show thesame general properties as Arctic sea ice results;an increase as the ice grows thicker and a gradualwavelength dependence with larger albedos atshorter wavelengths (Schlosser 1988, Allison etal. 1993). There are differences in ice structurebetween Antarctic and Arctic sea ice. Antarcticsea ice has much more frazil ice than Arctic seaice and is somewhat more saline (Gow and Tucker1990). Surface conditions also differ with signifi-cant amounts of flooded snow-covered ice butvery little ponded ice in the Antarctic (Andreasand Ackley 1982). Because of this there may bedifferences in optical properties between Antarc-tic and Arctic sea ice, but any differences between

Figure 11. Observations of total albedo vs. brine volumefor young ice (from Perovich and Grenfell 1981). Threeexperiments were performed where the ice was grown toapproximately 0.25 m thick and then warmed, in stages,to –2°C.

Air TemperatureDuring Growth = – 37 °C

– 30

– 10

1.0

0.8

0.6

0.4

0.2

0 5 10 15 20 25Brine Volume (%)

Alb

edo

10

instruments mounted on aircraft or satellites typi-cally have narrow fields of view and measurereflected radiance, rather than irradiance. To con-vert these observations of radiance to an estimateof irradiance, information on the bidirectional re-flectance distribution function (BRDF) is needed.Under cloudy conditions the incident radiationfield is diffuse, so the light reflected from thesurface is also diffuse. Reflected radiance is es-sentially the same in any direction and the re-flected irradiance is easily computed. When it issunny, though, the incident radiation consists ofa diffuse sky component plus a very strong solardirect beam, and the incident radiance field isstrongly anisotropic. For these incident conditionsthe angular distribution of reflected radiance canbe complex. Angular reflectances (reflected radi-ance normalized to a white reference standard)measured under sunny skies for snow-coveredice and bare blue ice are plotted in Figure 13.Snow-covered ice reflectances are fairly constantwith angle, except for a 30% increase at the angleof reflection of the solar beam. The peak in reflec-tance at the angle of reflection is even more pro-nounced in the bare blue ice case, with an in-crease to nearly twice the value of the albedo. Atother angles, blue ice reflectances are equal to orslightly less than the albedo. The differences be-tween R and α show the importance of the BRDFin determining albedos from observations of re-flected radiance. The presence of any systematictopographic features, such as sastrugi, will fur-ther complicate the BRDF.

the two cases are smaller than differences withinthe two.

ReflectanceWhen considering light reflected from sea ice,

the albedo is the parameter of prime climatologi-cal importance. However, optical remote sensing

Figure 12. Spectral albedos of Antarctic sea ice (fromAllison et al. 1993).

0.8

0.6

0.4

0.2

0400 600 800

Wavelength (nm)1000

1.0

Alb

edo

Fast Icew/30 cm Snow

Young, Gray Icew/2 cm Snow

Young,Gray Ice

Nilas 3-4 cm

Open Water

Azimuth– 180° – 120° – 60° 0° 60° 120° 180°

Zenith = 60°

2.0

1.5

1.0

0.5

0– 180 – 120° – 60° 0° 60 120 180°

Azimuth

Zenith = 30°

Ref

lect

ance

Fac

tor

Snow

Blue Iceα

Ro

Figure 13. Bidirectionalreflectance distributionfunction at 450 nm forsnow-covered ice and bareblue ice (from Perovich1994). R0 is the normal-ized reflected radiance atnadir and α is the albedo.The measurements weremade at a solar zenithangle of 60° under clearskies.

11

The peak in reflectance is largely due to specu-lar reflection of the direct solar beam. Specularreflection is light reflected from the surface of themedium in the direction of the angle of reflec-tion. Its magnitude depends on the angle of inci-dence and the index of refraction according to:

I Ir 0θ θ

θ φθ φ

θ φθ φ

( ) = ( ) −( )+( ) +

−( )+( )

12

2

2

2

2sin *sin *

tan *tan *

where I0(θ) = the incident direct solar beam ra-diance,

Ir(θ) = the reflected radianceθ = the zenith angle of incident and

reflected radianceθ∗= [n arcsin(θ)]–1

n = the index of refraction of the me-dium (Born and Wolfe 1965).

As the zenith angle increases (sun gets closer tothe horizon), the specular reflection increases. Thespecular component is larger for smooth surfacessuch as blue ice or melt ponds and smaller forrough surfaces such as snow or drained whiteice.

TransmissionThe magnitude and spectral distribution of

light transmitted through the ice cover dependson the physical composition of the ice, the thick-ness of the ice, and the surface conditions. Asthickness increases, light transmission through theice drops off roughly exponentially. The influ-ence of surface conditions on light transmissionthrough the ice is illustrated in Figure 14 (Maykutand Grenfell 1975). Even a thin (0.25-m) layer ofhighly scattering snow can reduce transmittancesthrough the ice cover to less than 1% (curve a). Asthe snow melts, scattering decreases and the trans-mittance increases (curve b) until the snow is gone(curve c). The presence of melt ponds greatly re-duces scattering in the upper portion of the iceand enhances transmission in the visible (curved). Light levels beneath ponded first-year ice areat least a factor of three greater than those be-neath white ice of the same thickness (Grenfelland Maykut 1977).

Sea ice can be a prime habitat for biologicalorganisms. The growth of these organisms is in-fluenced by the amount of light available in andunder the ice (Soo Hoo et al. 1987, Cota and Horne1989, Arrigo et al. 1991). Just as the ice biota areaffected by the light levels, they in turn can re-

duce light transmission and change its spectralcomposition (Maykut and Grenfell 1975, Soo Hooet al. 1987, Perovich et al. 1993). As an example ofthis, spectral transmittances for 1.5-m-thick first-year ice with a 0.05-m snow cover and with a0.19-m snow cover are plotted in Figure 15. Sur-prisingly, the transmission is less under the thin-ner snow cover. This is a direct result of a 50%higher algal biomass (157 vs. 117 mg chlorophyllm–2) at the thin snow site. In addition to the over-all reduction, the presence of the additional bio-mass results in enhanced losses in the blue end ofthe spectrum and a pronounced drop in transmit-tance at 670 nm.

Extinction coefficientA more fundamental way to characterize light

penetration through sea ice is by an extinctioncoefficient (κλ). The extinction coefficient is a mea-sure of loss due to scattering and absorption andis typically determined from measurements ofincident, reflected and transmitted light. Trans-mission measurements are difficult and demand-ing, and consequently there have been far fewer

Figure 14. The influence of surface conditionson light transmission (from Maykut and Grenfell1977). In all cases the ice thickness was 1.85 m.Surface conditions were a) blue ice covered by0.25 m of melting snow, b) blue ice covered by0.12 m of melting snow, c) white ice and d) blueice covered by a 0.05-m melt pond.

Tra

nsm

ittan

ce

0.20

0.16

0.12

0.08

0.04

0400 500 600 700 800

Wavelength (nm)

a

b

c

d

12

observations of extinction coefficient than of al-bedo. Most of the reported sea ice spectral extinc-tion coefficients have been calculated using a two-stream radiative transfer model (Grenfell andMaykut 1977, Perovich and Grenfell 1981).

Figure 16 summarizes spectral extinction coef-ficients culled from a number of sources for ninedistinct cases: dry snow, melting snow, ice belowthe eutectic point with solid salts present, thesurface scattering layer of white ice, the interiorof white ice, cold blue ice, melting blue ice, bubble-free fresh ice, and clear Arctic water (Grenfell andMaykut 1977, Perovich and Grenfell 1981, Smithand Baker 1981). The range of over one to twoorders of magnitude in the extinction coefficientsshows the tremendous variation in attenuationbetween different snow and ice types. Sea ice andsnow curves all show relatively constant valuesin the 400- to 500-nm region, followed by stronglyincreased attenuation at longer wavelengths.Again, as was the case for albedo, the magnitudeof the extinction coefficient is largely a functionof the amount of scattering, while the wavelengthdependence is determined by absorption. Thegreatest attenuation occurs in cold snow, where

spectral extinction coefficients are about 20 timeslarger than those of melting blue ice.

Coefficients in melting snow are above halfthose in cold dry snow. Extinction coefficients forvery cold ice below the eutectic point are quitelarge, comparable to values for snow. In this casesolid salts precipitate in the interior of the sea ice.These precipitated salts are small and plentifuland, with an index of refraction of approximately1.5, are effective scatterers. The drained surfacelayer of multiyear ice (white ice scattering) con-tains an abundance of air inclusions which formedas a result of brine drainage. These air inclusionscause considerable scattering, and extinction co-efficients are large. In the interior of white icethere are fewer air bubbles, and extinction coeffi-cients are correspondingly smaller. In the blue icecases the inclusions are primarily brine pockets,

500 600 700

Wavelength (nm)

400 800

100

a

b

c

d

e

g

h

i

Ext

inct

ion

Coe

ffici

ent (

m

)–

1

10– 1

10– 2

10– 3

10– 4

Figure 15. Observed spectral transmittances for 1.5-m-thick first-year ice with a) 0.05-m snow cover plus157 mg chlorophyll m–2 biomass and b) 0.19 m snowcover plus 117 mg chlorophyll m–2.

Figure 16. Spectral extinction coefficients for ninedistinct cases: a) dry snow (Grenfell and Maykut1977), b) ice below the eutectic point with solid saltspresent (Perovich and Grenfell 1981), c) melting snow(Grenfell and Maykut 1977), d) surface scatteringlayer of white ice (Grenfell and Maykut 1977), e) theinterior of white ice (Grenfell and Maykut 1977), f)cold blue ice (Grenfell and Maykut 1977), g) meltingblue ice (Grenfell and Maykut 1977), h) bubble-freefresh ice (Grenfell and Perovich 1981), and i) clearArctic water (Smith and Baker 1981).

400 500 600 700

Wavelength (nm)

10– 2

10– 3

10– 4

b

a

Tra

nsm

ittan

ce

13

rather than air bubbles, and the amount of scat-tering is less and extinction coefficients are re-duced. The much smaller values of extinction co-efficient for bubble-free ice and clear Arctic waterillustrate how significant scattering is in sea ice.The importance of scattering is illustrated by therough rule of thumb that extinction through 1 cmof snow is approximately the same as through 10cm of ice or 100 cm of water.

As was the case for albedo (Fig. 11), extinctioncoefficients also depend on the internal structureof the ice (Zaneveld 1966, Grenfell and Maykut1977, Perovich and Grenfell 1981, Gilbert andBuntzen 1986). Extinction coefficients decreaseduring warming as the brine volume increasesand the number of inclusions decrease. Also, at agiven brine volume extinction coefficients arelarger for faster grown ice, which has more inclu-sions. In these experiments the ice was changinginternally, but the only change in surface condi-tions was a slight wetting as the air temperatureapproached 0°C. The results would be quite dif-ferent if there were brine drainage from the sur-face layer of the ice as a result of the warming. Inthat case the resulting air voids would form ahighly scattering surface layer, and albedos andextinction coefficients would increase. This wouldbe expected in thicker ice with more freeboard.Such an effect has been observed in the Antarctic,where low humidities keep the ice surface free ofwater during melt (Andreas and Ackley 1981).Observations made in McMurdo Sound, Antarc-tica (Trodahl et al. 1987, Buckley and Trodahl 1987,Trodahl and Buckley 1990), have shown that asthe ice warms, a drained surface layer forms re-sulting in an increase in backscatter and a de-crease in transmittance.

Observations of total light transmission havebeen used to determine wavelength-integrated,or total, extinction coefficients (κt). Values for seaice are in the 1.1 to 1.5 m–1 range (Untersteiner1961, Chernogovskiy 1963, Thomas 1963, Wellerand Schwerdtfeger 1967). Extinction coefficientsfor snow are much larger, varying from 4.3 m–1

for dense Antarctic snow (Weller and Schwerdt-feger 1967) to as high as 40 m–1 in freshly fallensnow (Thomas 1963). Though total extinction co-efficients are simpler to measure and simpler touse computationally than spectral values, theyare severely limited. The total extinction coeffi-cient combines contributions from different wave-lengths and therefore depends on the spectral dis-tribution of transmitted irradiance, which in turndepends on the spectral incident irradiance, the

Table 1. Values of i0 and κt(Grenfell and Maykut 1977).

Case i0 κt (m–1)

ClearBlue ice 0.43 1.5White ice 0.18 1.6

CloudyBlue ice 0.63 1.4White ice 0.35 1.5

spectral albedo and the spectral extinction coeffi-cient. Since all of these quantities vary with wave-length, the total extinction coefficient does notdepend entirely on the properties of the ice. Aswas the case for total albedo, the total extinctioncoefficient depends on sky conditions. On sunnydays the incident irradiance has a larger longwavecomponent, which is absorbed rapidly in the ice,resulting in higher values of κt. More significantly,κt exhibits a strong depth dependence near thesurface. Observations have shown that the spec-tral transmittance changes greatly near the sur-face of the ice due to the rapid extinction of thelonger wavelengths. Correspondingly, κt is largenear the ice surface and decreases by more thanan order of magnitude in the top 0.1 m of the ice(Grenfell and Maykut 1977). Below 0.1 m, onlyvisible light remains, where the spectral depen-dence of κλ is weaker, and changes in κt withdepth are small. Total extinction coefficients havebeen used in sea ice thermodynamic models(Maykut and Untersteiner 1971) to calculate thesurface heat balance and solar heating in the iceinterior. To do this Maykut and Untersteiner (1971)modified the exponential decay law to the form:

F z i F e zzd d

t for m( ) = ( ) >−0 0 0 1κ .

where i0 is the fraction of the wavelength-inte-grated incident irradiance transmitted through thetop 0.1 m of the ice and κt is the total extinctioncoefficient in the ice below 0.1 m. Values of κtbelow 0.1 m and i0 determined from field obser-vations (Grenfell and Maykut 1977) are summa-rized in Table 1. There is more scattering in whiteice than blue ice, resulting in a smaller i0 and alarger κt.

Beam spreadWhile much of the observational emphasis has

been on measurements of transmitted solar irra-diance to determine transmittance and extinctioncoefficient, measurements using artificial light

14

sources have also been made. In particular, stud-ies were conducted examining the spreading of acollimated beam as it passes through sea ice(Trodahl et al. 1987, Gilbert and Schoonmaker1990, Voss and Schoonmaker 1992, Voss et al.1992). In these experiments a collimated beam oflight was incident on either the surface or bottomof the ice and the spatial distribution of the emer-gent irradiance was measured. Examining thepeak magnitude and the spatial distribution ofirradiance provide information on scattering andabsorption in the ice. Laboratory studies indicatethat scattering in the ice is quite strong, with theradiation field quickly becoming diffuse, and thatthere is increased attenuation and scattering forcolder ice (Gilbert and Schoonmaker 1990, Vossand Schoonmaker 1992). Beam spread measure-ments, when combined with radiative transfermodels, show promise as a means of determiningscattering coefficients and phase functions frommultiply scattering sea ice.

MODELS

It is evident from the observational data thatthe optical properties of sea ice vary greatly. Theoptical properties vary spatially over scales ofonly a few meters and they vary temporally asthe ice cover melts in the summer and freezes inthe fall. An analysis of optical observations hasdemonstrated that the optical properties of seaice are directly affected by the state and structureof the ice. Models are essential in interpretingobservations and in progressing from a phenom-enological collection of observations to a physi-cally based understanding of radiative transfer insea ice.

The variability in optical properties also cre-ates difficulties in extrapolating observations. In-dividual observations provide information on theoptical properties at a particular location at a par-ticular time, but for many problems more generalinformation is needed on how the optical proper-ties of a region evolve with time. In principle, thisinformation can be obtained observationally, butfor a large-scale, long-term study this is not prac-tical. For such studies, models are an essentialtool.

Radiative transfer models have been appliedto a wide range of problems, including estimat-ing the absorption of solar radiation in sea ice(Maykut and Untersteiner 1971), studying the re-lationship between changes in ice physical prop-

erties and changes in optical properties (Grenfell1983, 1991), analyzing the spread of a beam oflight as it passes through ice (Trodahl et al. 1987),investigating bio-optical interactions (Arrigo etal. 1991), examining the transmission of visibleand ultraviolet light through sea ice (Perovich1990, 1991, 1993) and assessing radiative interac-tions between the atmosphere, ice and ocean (Jinet al. 1994).

These radiative transfer models for sea icerange in complexity from a simple wavelength-integrated parameterization of an exponentialdecay law to numerically intricate solutions ofthe radiance field in the ice. There are severaldifferent models with a variety of solutionschemes and different input and output param-eters; however, the same physics underlies all ofthese models. They may use different techniquesbut they all treat the basic physical properties ofabsorption and scattering of light in the ice. Be-cause of their diversity, these models all haveattributes that endorse them for some applica-tions and restrict them for others. A sampling ofsea ice radiative transfer models is presented inTable 2.

One of the distinguishing features of radiativetransfer models is the number of “streams” theyconsider. The number of streams refers to the num-ber of moments from which the radiance is calcu-lated. Quite common are two-stream models,where the upwelling and downwelling irradiancesare computed. More streams means more angu-lar detail in the calculated radiance field. The costof this additional detail is more complexity in thecomputations and often a requirement for moredetailed information on the optical properties ofthe ice.

The simplest sea ice radiative transfer model isthe exponential decay relationship

F z F e z, λ α λλκ λ( ) = −( ) ( ) −1 0 (5)

where F0(λ) is the incident solar irradiance. Thisformulation has the advantage of being simplecomputationally. However, there is an implicitassumption that the medium is infinitely thick,and consequently, the exponential decay law doesa poor job of representing radiative transfer inthin ice (Grenfell 1979).

Grenfell (1979) developed a two-stream, three-layer model, based on the work of Dunkle andBevans (1957), that improved the treatment ofthin ice with only a modest increase in computa-tional complexity. The general solution for the

15

Table 2. Summary of sea ice radiative transfer models.

Spectral Number Solution OutputModel Streams range (nm) of layers scheme parameters Comments

Grenfell (1979) 2 400–2150 3 Analytic Fd, Fu, α, T Examined thin ice, devel-oped parameterizationsfor α and T as a functionof thickness, isotropicscattering

Perovich and Grenfell (1982) 14 400–1000 2 DOM*-analytic I(θ), Fd, Fu, α, T Anistropic scattering, esti-mate scattering param-eters from observationsof α and T

Grenfell (1983) 16 350–2750 1 DOM-numerical I(θ), Fd, Fu, α, T Detailed angular resolution,optical and physical pro-perties are related

Trodahl et al. (1987) 500, 700 multiple Monte Carlo I (θ,x) Isotropic and anisotropicscattering, treats beamspread

Perovich (1990, 1993) 2 250–1000 multiple Analytic Fd, Fu, α, T Ultraviolet and visible wave-lengths, computationallysimple, easy ice charac-terization, isotropic scat-tering

Arrigo et al. (1991) 1 400–700 multiple Exponential Fd, T Detailed treatment of im-pact of biogenic materialon light transmission

Grenfell (1992) 4 350–2750 multiple DOM-analytic I(θ), Fd, Fu, α, T Tied closely to ice physicalproperties, treats verticalvariability in ice

Jin et al. (1994) select 250–4000 multiple DOM-numerical I(θ), Fd, Fu, α, T Coupled atmosphere–ice–ocean radiative transferabsorption model, deter-mines solar absorption ineach component

*Discrete ordinates method (Chandrasekhar 1960)

upwelling (Fu) and downwelling (Fd) irradiancesare

F z A z B z

F z C z B z

d

u

, sinh cosh

, sinh cosh

λ κ κ

λ κ κ

λ λ

λ λ

( ) = ( ) + ( )( ) = ( ) + ( )

where A, B, C and D are determined from theboundary conditions. For an optically thick me-dium (z → ∞), this solution converges to the ex-ponential decay law (eq 5). The major deficiencyof the two-stream model is its treatment of scat-tering, in particular, the simplifying assumptionof isotropic scattering. An important advantageof this formulation is that it directly utilizes theobservations of light extinction in sea ice madeby Grenfell and Maykut (1977) and Perovich andGrenfell (1981). Because of this, only a qualitativedescription of the ice is needed; blue or white,melting or cold, snow-covered or bare. Grenfell

(1979) used this model to investigate the depen-dence of albedo, transmittance, and i0 on thick-ness and ice type. He then used the results toderive simple parameterized formulae for αt andi0 suitable for use in sea ice thermodynamicmodels.

This two-stream formulation was expandedinto an n-layer model (Perovich 1990) and ex-tended into the ultraviolet (Perovich 1993). Thefocus of these studies was on the spatial and tem-poral variability of reflection, absorption, andtransmission of solar radiation by sea ice. To il-lustrate the utility of such models let us examinea particular problem of interest: the transmissionof visible and ultraviolet light through sea ice inthe Weddell Sea during spring. Spring is the pe-riod when ozone depletion is the greatest, as isthe consequent increase in incident ultraviolet ir-radiance and potential biological hazard. Physi-

16

cal properties data from Lange and Eicken (1991)were used to define the type and thickness of theice and snow cover (Fig. 17a) along a 100-mtransect in the Weddell Sea. Ice thicknesses in thisarea varied from 0.2 to 1.2 m, while the snowdepth ranged from 0.0 to 0.2 m. With these inputparameters, the model calculated estimates oftransmittance for the biologically harmful UV-Birradiance (280 to 320 nm) and the beneficial pho-tosynthetically active radiation (400 to 700 nm)(Fig. 17b). There is tremendous spatial variabilityin the UV-B transmittance over the 100-m transect,with values ranging over nearly two orders ofmagnitude from 0.0015 to 0.09. The primary in-fluence on transmittance is the snow depth, fol-lowed by the ice thickness. Maximum transmit-tances are associated with minimum snow depths.It is evident that the presence of an ice covercauses a marked reduction in transmitted lightlevels. This reduction is greater for the harmfulUV-B than for the beneficial visible, implying thatsea ice may moderate the biological impact ofenhanced incident ultraviolet irradiance on biotaliving in and under the ice.

Models based on the discrete ordinates method(DOM) of Chandrasekhar (1960) have been usedto treat scattering in more detail and examine theangular distribution of radiance. In the DOM, thephase function is approximated by a series ofLegendre polynomials (Liou 1973, 1974, Mobley1994). The discrete ordinates refer to particularangles at which the radiance is computed. Theseangles are not arbitrary, but are determined from

the roots of the Legendre polynomial. In this for-mulation, it is no longer necessary to assume thatthe radiance field is diffuse and that the phasefunction is isotropic. However, these models, par-ticularly for larger numbers of streams, are sig-nificantly more complex computationally.

Perovich and Grenfell (1982) developed a two-layer, four-stream model (radiances at two up-ward and two downward angles) and applied itto investigate the effects of ice thickness, and theinfluence of direct vs. diffuse incident solar ra-diation, on spectral albedo and transmittance.Using experimentally determined phase functionsthey found that single scattering albedos (ϖ0) foryoung ice were high: from 0.95 for warm meltingyoung ice to 0.9997 for young ice below the eu-tectic point.

Grenfell (1983, 1991) developed a single-layer,16-stream model and a multilayer, four-streammodel to explore relationships between ice physi-cal properties and ice optical properties. The four-stream (Grenfell 1991) model significantly ex-tended the work of Perovich and Grenfell (1982)by including vertically varying ice properties. Thesingle-layer, 16-stream model (Grenfell 1983) gen-erated a more detailed angular description of ra-diance, better represented the phase function, andimproved the treatment of refraction at the air-iceinterface for a homogeneous ice cover. This modelwas used to directly link the physical propertiesof the ice, such as the inclusion size distributionsof air bubbles and brine pockets, to radiative trans-fer in the ice. The absorption and scattering coef-

Figure 17. Theoretical estimates of ultra-violet and visible light transmissionthrough sea ice in the Weddell Sea. Icethickness, snow depth and physical prop-erties data are from Lange and Eicken(1991). Transmitted UV-B and visibleirradiance were computed using a two-stream model (Perovich 1990, 1993)

0.4

0

– 0.4

– 0.8

– 1.2

Thi

ckne

ss (

m)

Snow

Ice

Water

A

0.15

0.10

0.05

0 20 40 60 80 100Position (m)

Tra

nsm

ittan

ce Integrated VisibleIntegrated

UV-B

B

17

ficients depended explicitly on the amount andsize distribution of air bubbles and brine pockets.These values in turn depended on the ice growthconditions, thermal history, temperature, salinityand density. With this formulation, it was pos-sible to theoretically explore the impact of growthconditions and thermal history on spectral albe-dos and extinction coefficients. For example, Fig-ure 18 shows calculated estimates of spectral al-bedo for different ice densities and ice growthrates. The ice was 3 m thick in these cases. Thelarge impact of air bubbles on scattering and iceoptical properties is demonstrated in Figure 18a.There is an increase in albedo as the ice densitydecreases and the number of air bubbles increases.This increase is most pronounced at 470 nm, whereabsorption is smallest. The albedo at 470 nm wasabout 0.57 for bubble-free ice (ρ = 0.94) and in-creased to 0.84 for bubbly ice with an air volumeof 8% (ρ = 0.86). Calculations also indicated thatfaster growth rates result in larger albedos (Fig.18b). For these calculations the air volume wasassumed to be zero, so changes in albedo resultedfrom changes in the platelet spacing and the num-ber of brine inclusions. Faster grown ice has

smaller platelets, higher salinity, and morebrine inclusions (Weeks and Ackley 1982).This is consistent with our premise thatmore inclusions means more scatteringand higher albedos.

The Monte Carlo method is anotherapproach to radiative transfer modeling.As the name implies, Monte Carlo modelstake a statistical approach to solving theequation of radiative transfer (eq 2). Inshort, the absorption coefficient, the scat-tering coefficient and the phase functionare transformed into the probability thatover a given distance a photon is absorbedor scattered, and if scattered, in what di-rection. With these probabilities known,enormous numbers of photons are numeri-cally “shot” into the medium. The fate ofeach photon is decided by the roll of thedice, or more precisely, the whim of therandom number generator. Radiativetransfer in the medium is described bythe cumulative result of all the photons.Because of the large number of photonsneeded, Monte Carlo models are very in-efficient computationally. They are, how-ever, simple conceptually, simple to pro-gram, and widely applicable (Mobley1994). This method is particularly well

suited for complex geometries or boundary con-ditions, where other solutions to the equation ofradiative transfer are difficult or impossible.Trodahl et al. (1987) and Trodahl and Buckley(1989) effectively used Monte Carlo solutions inbeam spread studies, both to model observationsand infer information on the scattering proper-ties of sea ice. They found that scattering in thesurface layer of the ice was greater than in theinterior and that the scattering was anisotropic.

An exciting new modeling development hasbeen the inclusion of biological effects in sea iceoptical models. Sea ice is the habitat of a richmicrobial community (Palmisano and Sullivan1983, Garrison et al. 1986). Ice biota both affectand are affected by the spectral irradiance withinthe ice. Arrigo et al. (1991) developed a bio-opti-cal model to investigate the interdependence be-tween biology and transmitted light. They used asimple exponential decay law to model irradi-ance within the ice, but they coupled this with asophisticated treatment of the extinction coeffi-cients (κ). They formulated polynomial relation-ships defining spectral extinction coefficients fordry snow, wet snow, congelation ice, platelet ice,

Figure 18. Calculated estimates of spectral albedo as a function ofice density and growth rate (from Grenfell 1983). The ice was 3m thick. The air volume was zero for the growth rate simulation.Figure 18a shows albedo as a function of ice density (ρ): a) ρ =0.86 g cm–3, b) ρ=0.88 g cm–3, c) ρ = 0.90 g cm–3, d) ρ = 0.91 gcm–3 and e) ρ = 0.94 g cm–3. Figure 18 shows albedo as a func-tion of growth rate (f) for a) f = 8 × 10–5 cm s–1, b) f = 4 × 10–5

cm s–1, c) f = 2 × 10–5 cm s–1 and d) f = 8 × 10–6 cm s–1 .

1.0

0.8

0.6

0.4

0.2

0400 600 800 1000 1200 1400

Wavelength (nm)

Alb

edo

400 600 800 1000 1200 1400

a

b

c

d

e

a

bc

d

A B

18

ice cooler than the eutectic point, and as a func-tion of brine volume. Most importantly, they alsoderived relationships for the extinction contribu-tions from absorption due to microalgae and de-tritus. With this model it is possible to examinethe impact of biogenic material on transmittedspectral irradiance and to investigate temporalchanges.

Combining field observations with model cal-culations, Arrigo et al. (1991) were able to com-pute a time series of transmitted spectral irradi-ances (Fig. 19). The calculations were done forbare ice in McMurdo Sound, Antarctica, roughly1.7–1.8 m thick, between 7 October and 5 Decem-ber. During this period there was a constant in-crease in the amount of microalgae and detritus.On 7 October, levels of microalgae were low andthere was no detritus present, so light losses wereprimarily due to extinction by the sea ice. By 13November the spring bloom had produced sig-nificant amounts of algae and detritus. The pres-ence of this biogenic material resulted in an over-all reduction, and a change in the spectral shape,of the transmitted irradiance. The distinct spec-

tral shape of the transmitted irradiance is charac-teristic of ice with biogenic material. Algae anddetritus levels continued to increase through 5December, causing a further reduction in trans-mittance.

A model was recently developed to examineradiative transfer in a coupled atmosphere–ice–ocean system (Jin et al. 1994). The model is amultilayer and multistream formulation based onthe discrete ordinates method. Radiative transferwithin the entire atmosphere–ice–ocean system isdetermined based on a description of physicalproperties of the atmosphere, ice and ocean fromwhich the optical properties are derived. Themodel computes the distribution and absorptionof solar radiation in the atmosphere, ice and ocean.Results indicate that sea ice has a strong influ-ence on the distribution of solar radiation in thesystem (Jin et al. 1994). Such models provide apromising tool for investigating atmosphere–ice–ocean radiative feedbacks.

SUMMARY AND CURRENTAREAS OF INTEREST

By now the reader is no doubt aware that theoptical properties of sea ice are variable and com-plex. The reader is also aware that much of thiscomplexity is comprehensible. While many of thedetails still need to be determined, we do have aqualitative understanding of sea ice optical prop-erties and their variability. This understanding isbased on a few fundamental principles. Changesin such optical properties as the albedo, reflec-tance, transmittance, and extinction coefficient aredirectly tied to changes in the state and structureof the ice. Physical changes in the ice which en-hance scattering, such as the formation of airbubbles due to brine drainage, result in largeralbedos and extinction coefficients. Radiativetransfer in sea ice is a combination of absorptionand scattering. Differences in the magnitude ofthese optical properties are due primarily to dif-ferences in scattering. Spectral variations aremainly a result of absorption.

In addition to these general principles, thereare also several specific comments that can bemade regarding the sea ice optical properties.Spectral absorption coefficients for ice are wellknown, however, representative values for brineare less certain. Absorption by algae and particu-lates is also important and needs further investi-gation. More work, both experimental and theo-

500 600 700

Wavelength (nm)

400

10– 1

10– 2

10– 3

10– 4

a

b

c

Tra

nsm

itted

Irra

dian

ce (

µEin

m

s

nm

)

– 2

– 1

– 1

Figure 19. Seasonal changes in underice spectral irra-diance calculated using a bio-optical model (Arrigo etal. 1991). Curves are predicted spectral transmittedirradiance at noon on a) 7 October 1984, b) 13 Novem-ber 1984 and c) 5 December 1984.

19

retical, needs to be done investigating scatteringin sea ice. The albedo is quite sensitive to thesurface state. If the ice has an appreciable snowcover, visible wavelength albedos are above 90%and little light is transmitted to the ocean. In verycold ice (T<–24°C), hydrohalite precipitates, caus-ing a sharp increase in albedo and extinction co-efficient to values comparable to snow. There is aless pronounced, but still potentially significant,effect at temperatures below –8°C where mirabiliteprecipitates. The presence of liquid water on thesurface causes a decrease in albedo, which is morepronounced at longer wavelengths. If the surfacedrains, the brine pockets become air bubbles, re-sulting in more scattering and an increase in al-bedo and extinction coefficient. Ice that is grownfaster has more platelets and more brine inclu-sions, and consequently, large albedos and ex-tinction coefficients. The optical properties de-pend not only on the volume of brine or air, buton how that brine or air is distributed.

Sea ice optical properties is currently a researcharea of considerable interest and activity. Eventhough much has been learned about the opticalproperties of sea ice, there are still numerous im-portant and intriguing problems extant. A majorgoal is quantifying relationships between thephysical and the optical properties. Achieving thisgoal entails not only a better understanding ofthe optical properties, but a better understandingof the physical properties. Because of the poten-tial climatological impact of ice–albedo feedback,one area of particular concern is determining howthe changes in the physical state of the ice duringthe summer melt season affect the albedo of theice cover.

An improved understanding of scattering insea ice is needed. This can be addressed throughlaboratory studies of the scattering properties ofsmall sea ice samples (Miller et al. 1994) andthrough field studies investigating the spread ofa collimated beam of light in ice (Longacre andLandry 1994). Another approach to estimating thescattering properties of sea ice is to use Mie theory(Bohren and Huffman 1983). A statistical descrip-tion of the ice microstructure is needed for thisapproach, including detailed information on theinclusion size distributions for the air bubblesand brine pockets (Perovich and Gow 1991). Littleis known regarding these size distributions andhow they vary with ice physical properties suchas brine volume, density and growth rate.

In the past there has been an abundance ofalbedo measurements, but few observations of

transmitted light. This deficiency has impededradiative transfer modeling efforts, ice heat bal-ance studies, and bio-optical investigations. Thisis beginning to change as advancing technologyleads to improved instrumentation and innova-tive new approaches to measuring light in andunder the ice are developed. New sensors makeit possible to measure detailed spectral transmit-tances even under thick snow-covered ice. Fiberoptic probes can be frozen in the ice to measurethe radiance distribution within the ice. Powerfultechniques are being applied to measure in-situprofiles of transmitted irradiance, beam spread,and diffuse attenuation coefficient.*

Many pressing issues concerning sea ice opti-cal properties can only be addressed through in-terdisciplinary studies. A combined effort isneeded to examine such issues as assessing ice–albedo feedback, ascertaining the impact of en-hanced incident levels of ultraviolet irradianceon biota living in or under the ice, and usingsatellite-measured microwave signatures as aproxy for large-scale ice albedo. Recent experi-mental programs have recognized this and haveemphasized acquiring a comprehensive data set,including information on the ice state and struc-ture, biota, particulates and microwave signatures,as well as complete optical measurements.

Another approach to these problems is throughmodeling, in particular through the integrationof models. As the previous section demonstrated,there are several good radiative transfer modelsfor sea ice that include information on the physi-cal properties of the ice (Grenfell 1983, 1991, Jin etal. 1994). There are also models that treat thephysical properties of sea ice during the first yearof growth (Cox and Weeks 1988, Wade and Weeksin press). Thermodynamic sea ice models include,typically in a parameterized fashion, the reflec-tion, absorption and transmission of solar radia-tion. The effects of biogenic material on transmit-ted irradiance can be considered (Arrigo et al.1991), and there has been progress towards de-veloping a true bio-optical model where the intri-cate interplay between the light levels in and un-der the ice and the amount of biological activitycan be fully explored (Arrigo et al. 1993).

General, comprehensive, interdisciplinarymodels are needed models that couple the ice

* Personal communication with S. Pegau, College ofOceanic and Atmospheric Sciences, Oregon State Uni-versity.

20

physical properties, optical properties, biologicalproperties and thermodynamics, and that link theice to the atmosphere and ocean. Models wherechanges in ice temperature cause changes in thephysical properties of the ice, which in turn im-pact the ice optical properties and thereby thephysical properties and the biological activitywithin the ice. Models where changes in the iceare coupled to energy exchange with the atmo-sphere and ocean. Developing such models is adaunting task, but a task with substantial rewards.

LITERATURE CITED

Allison, I., R.E. Brandt and S.G. Warren (1993)East Antarctic sea ice: Albedo, thickness distribu-tion and snow cover. Journal of Geophysical Re-search, 98(C7): 12417–12429.Andreas, E.L. and S.F. Ackley (1981) On the dif-ferences in ablation seasons of the Arctic and Ant-arctic sea ice. Journal of Atmospheric Science, 39:440–447.Arrigo, K.R., J.N. Kremer, and C.W. Sullivan(1993) A simulated Antarctic fast ice ecosystem.Journal of Geophysical Research, 98(C4): 6929–6946.Arrigo, K.R., C.W. Sullivan and J. N. Kremer(1991) A bio-optical model of Antarctic sea ice.Journal of Geophysical Research, 96: 10581–10592.Bohren, C.F. and B.R. Barkstrom (1974) Theoryof the optical properties of snow. Journal of Geo-physical Research, 79(30): 4527–4535.Bohren, C.F. and D.R. Huffman (1983) Absorp-tion and Scattering of Light by Small Particles. NewYork: Wiley.Born, M. and E. Wolfe (1965) Principles of Optics.New York: Pergamon.Buckley, R.G. and H.J. Trodahl (1987) Thermallydriven changes in the optical properties of seaice. Cold Regions Science and Technology, 14: 201–204.Burt, W.V. (1954) Albedo over wind roughenedwater. Journal of Meteorology, 11: 283–290.Chandrasekhar, S.C. (1960) Radiative Transfer. NewYork: Dover.Chernigovskiy, N.T. (1963) Radiational proper-ties of the central Arctic ice cover. Trudy Arktiches-kogo I Antarkticheskogo Nauchno-Issledovatel’skogoInstituta, Tom 253: 249–260.Cota, G.F. and E.P.W. Horne (1989) Physical con-trol of Arctic ice algal production. Mar. Ecol. Prog.Ser., 52: 111–121.Cox, G.F.N. and W.F. Weeks (1988) Numericalsimulations of the profile properties of unde-

formed first-year sea ice during the growth sea-son. Journal of Geophysical Research, 93: 12,449–12461.Dunkle, R.V. and J.T. Bevans (1957) An approxi-mate analysis of the solar reflectance and trans-mittance of a snow cover. Journal of Meteorology,13: 212–216.Ebert, E.E. and J.A. Curry (1993) An intermediateone-dimensional thermodynamic sea ice modelfor investigating ice-atmosphere interactions. Jour-nal of Geophysical Research, 98: 10085–10019.Frederick, J.E. and D. Lubin (1988) The budgetof biologically active ultraviolet radiation in theearth-atmosphere system. Journal of GeophysicalResearch, 93: 3825–3832.Garrison, D.L., C.W. Sullivan and S.F. Ackley(1986) Sea ice microbial communities in Antarc-tica. BioScience, 36: 243–250.Gilbert, G.D. and R.R. Buntzen (1986) In-situmeasurements of the optical properties of Arcticsea ice. In Proceedings of SPIE Ocean Optics VIII,637: 252–263.Gilbert, G.D. and J. Schoonmaker (1990) Mea-surements of beam spread in new ice. In Proceed-ings of SPIE Ocean Optics VIII, 1302: 545–555.Gow, A.J. and W.B. Tucker, III (1990) Sea ice inthe polar regions. In Polar Oceanography, Part A:Physical Science (Walker O. Smith, Ed.), p. 47–122.San Diego: Academic Press.Grenfell, T.C. (1979) The effects of ice thicknesson the exchange of solar radiation over the polaroceans. Journal of Glaciology, 22: 305–320.Grenfell, T.C. (1983) A theoretical model of theoptical properties of sea ice in the visible andnear infrared. Journal of Geophysical Research, 88:9723–9735.Grenfell, T.C. (1991) Radiative transfer model forsea ice with vertical structure variations. Journalof Geophysical Research, 96: 16991–17001.Grenfell, T.C. and D. Hedrick (1983) Scatteringof visible and near infrared radiation by NaCl iceand glacier ice. Cold Regions Science and Technol-ogy, 8: 119–127.Grenfell, T.C. and G.A. Maykut (1977) The opti-cal properties of ice and snow in the Arctic Basin.Journal of Glaciology, 18: 445–463.Grenfell, T.C. and D.K. Perovich (1981) Radia-tion absorption coefficients of polycrystalline icefrom 400–1400 nm. Journal of Geophysical Research,86: 7447–7450.Grenfell, T.C. and D.K. Perovich (1984) Spectralalbedos of sea ice and incident solar irradiance inthe southern Beaufort Sea. Journal of GeophysicalResearch, 89: 3573–3580.

21

Ingram, W.J., C.A. Wilson and J.F.B. Mitchell(1989) Modeling climate changes: An assessmentof sea ice and surface albedo feedbacks. Journal ofGeophysical Research, 94(D6): 8609–8622.Jin, Z., K. Stamnes, and W.F. Weeks (1994) Theeffect of sea ice on the solar energy budget in theatmosphere-sea ice-ocean system: A model study.Journal of Geophysical Research, 99(C12), 25281–25294.Lange, M.A. and H. Eicken (1991) The sea icethickness distribution in the northwestern WeddellSea. Journal of Geophysical Research, 96: 4821–4837.Langleben, M.P. (1971) Albedo of melting sea icein the southern Beaufort Sea. Journal of Glaciology,10: 101–104.Light, B. (1995) A structural-optical model of coldsea ice. M.S. Thesis, University of Washington,Seattle (unpublished).Liou, K.N. (1973) A numerical experiment onChandrasekhar’s discrete ordinates method forradiative transfer: Applications to cloudy andhazy atmospheres. Journal of Atmospheric Sciences,30: 1303–1326.Liou, K.N. (1974) Analytic two-stream and four-stream solutions for radiative transfer. Journal ofAtmospheric Sciences, 31: 1473–1475.Lofgren, G. and W.F. Weeks (1969) Effects ofgrowth parameters on substructure spacing inNaCl ice crystals. Journal of Glaciology, 8: 153–164.Longacre, J.R. and M.A. Landry (1994) In-situmeasurements of optical scattering from the wa-ter-ice interface of sea ice. In Proceedings of SPIEOcean Optics XII, 2258: 944–954.Lubin, D., J.E. Frederick and A.J. Krueger (1989)The ultraviolet radiation environment of Antarc-tica: McMurdo Station during September–Octo-ber 1987. Journal of Geophysical Research, 94: 8491–8496.Maykut, G.A. (1982) Large-scale heat exchangeand ice production in the central Arctic. Journal ofGeophysical Research, 87: 7971–7985.Maykut, G. A. and T. C. Grenfell (1975) Thespectral distribution of light beneath first-year seaice in the Arctic Ocean. Limnology and Oceanogra-phy, 20: 554–563.Maykut, G.A. and B. Light (1995) Refractive in-dex measurements in freezing sea ice and sodiumchloride brines. Applied Optics, 34: 950–961.Maykut, G.A. and D.K. Perovich (1987) On therole of shortwave radiation in the summer decayof a sea ice cover. Journal of Geophysical Research,92(C7): 7032–7044.Maykut, G.A. and N. Untersteiner (1971) Someresults from a time dependent, thermodynamic

model of sea ice. Journal of Geophysical Research,76: 1550–1575.Miller, D. M.S. Quinby-Hunt and A.J. Hunt (1994)Polarization-dependent measurements of lightscattering in sea ice. Proceedings of SPIE OceanOptics XII, 2258: 908–920.Mobley, C.D. (1994) Light and Water: RadiativeTransfer in Natural Waters. San Diego: AcademicPress.Nicodemus, F.E., J.C. Richmond, J.J. Hsia, I.W.Ginsberg and T. Limperis (1977) Geometrical con-siderations and nomenclature for reflectance. NBSMonograph 160, U.S.Palmisano, A.C. and C.W. Sullivan (1983) Seaice microbial communities (SIMCO): I. Distribu-tion, abundance and primary production of icemicroalgae in McMurdo Sound, Antarctica in 1980.Polar Biology, 2: 171.Perovich, D.K. (1979) The Optical Properties ofYoung Sea Ice. M.S. Thesis (unpublished), Geo-physics Program, University of Washington, Se-attle, Washington (Office of Naval Research Con-tract N00014-76-C-0234, Scientific Report No. l7,Department of Atmospheric Sciences, Universityof Washington, Seattle).Perovich, D.K. (1990) Theoretical estimates of lightreflection and transmission by spatially complexand temporally varying sea ice covers. Journal ofGeophysics, 95: 9557–9567.Perovich, D.K. (1991) Seasonal changes in sea iceoptical properties during fall freeze-up. Cold Re-gions Science and Technology, 19: 261–273.Perovich, D.K. (1993) A theoretical model of ul-traviolet light transmission through Antarctic seaice. Journal of Geophysical Research, 98: 22,579–22,587.Perovich, D.K. (1994) Light reflection from seaice during the onset of melt. Journal of GeophysicalResearch, 99: 3351–3359.Perovich, D.K. and J.W. Govoni (1991) Absorp-tion coefficients of ice from 250 to 400 nm. Geo-physical Research Letters, 18: 1233–1235.Perovich, D.K. and A.J. Gow (1991) A statisticaldescription of the microstructure of young seaice. Journal of Geophysical Research, 96: 16,943–16,953.Perovich, D.K. and T.C. Grenfell (1981) Labora-tory studies of the optical properties of young seaice. Journal of Glaciology, 27: 331–346.Perovich, D.K. and T.C. Grenfell (1982) A theo-retical model of radiative transfer in young seaice. Journal of Glaciology, 28: 34l–357.Perovich, D.K. and G.A. Maykut (1990) The treat-ment of shortwave radiation and open water in

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large-scale models of sea ice decay. Annals of Gla-ciology, 14: 242–246.Perovich, D.K., G.A. Maykut and T.C. Grenfell(1986) Optical properties of ice and snow in thepolar oceans: I. Observations. Proceedings of SPIEOcean Optics VIII, 637: 232–241.Perovich, D.K., G.F. Cota, G.A. Maykut and T.C.Grenfell (1993) Bio-optical observations of first-year Arctic sea ice. Geophysical Research Letters, 20:1059–1062.Roesler, C. and R. Iturriaga (1994) Absorptionproperties of marine-derived material in Arcticsea ice. Proceedings of SPIE Ocean Optics XII, 2258:933–944.Schlosser, E. (1988) Optical studies of Antarcticsea ice. Cold Regions Science and Technology, 15:289-293.Smith, R.C. (1989) Ozone, middle ultraviolet ra-diation and the aquatic environment. Photochem-istry and Photobiology, 50: 459–468.Smith, R.C. and K.S. Baker (1981) Optical prop-erties of the clearest natural waters (200–800 nm).Applied Optics, 20: 177–184.Smith, R.C., W . Zhengming and K.S. Baker(1992a) Ozone depletion in Antarctica: Modelingits effect on solar UV irradiance under clear-skyconditions. Journal of Geophysical Research, 97: 7383–7397.Smith, R.C., B.B. Prezelin, K.S. Baker, R.R. Bidi-gare, N.P. Boucher, T. Coley, D. Karentz, S. Mac-Intyre, H.A. Matlick, D. Menzies, M. Ondrusek,Z. Wan and K.J. Waters (1992b) Ozone depletion:Ultraviolet radiation and phytoplankton biologyin Antarctic waters. Science, 255: 952–959.SooHoo, T.B., A.C. Palmisano, S.T. Kottmeier,M.P. Lizotte, S.L. SooHoo and C.W. Sullivan(1987) Spectral light absorption and quantumyield of photosynthesis in sea ice microalgae anda bloom of Phaeocystis pouchettii from McMurdoSound, Antarctica. Marine Ecology, 33: 175–189.Thomas, C.W. (1963) On the transfer of visibleradiation through sea ice and snow. Journal ofGlaciology, 4: 481–484.Thorndike, A.S. (1992) A toy model linking at-mospheric thermal radiation and sea ice growth.Journal of Geophysical Research, 97(C6): 9401–9410.Trodahl, H.J. and R.G. Buckley (1989) Ultravio-let levels under sea ice during the Antarctic spring.Science, 245: 194–195.Trodahl, H.J. and R.G. Buckley (1990) Enhanced

ultraviolet transmission of Antarctic sea ice dur-ing the austral spring. Geophysical Research Let-ters, 17: 2177–2179Trodahl, H.J., R.J. Buckley and S. Brown (1987)Diffusive transport of light in sea ice. Applied Op-tics, 26: 3005–3011.Tsay, S. and K. Stamnes (1992) Ultraviolet radia-tion in the Arctic: The impact of potential ozonedepletions and cloud effects. Journal of Geophysi-cal Research, 97: 7829–7840.Tyler, J.E., and R.C. Smith (1970) Measurements ofSpectral Radiance Underwater. New York: Gordonand Breach.Untersteiner, N. (1961) On the mass and heatbudget of Arctic sea ice. Arch. Meteorol. Geophys.Bioklim., Series A, 12: 151–182.van de Hulst, H.C. (1981) Light Scattering by SmallParticles. New York: Dover.Voss, K.J. and J.S. Schoonmaker (1992) Tempera-ture dependence of beam scattering in young seaice. Applied Optics, 31: 3388–3389.Voss, K.J. R.C. Honey, G.D. Gilbert and R.R.Buntzen (1992) Measuring the point spread func-tion of sea ice in situ. In Proceedings of SPIE OceanOptics XI, 1750: 517–522.Wade R.H. and W.F. Weeks (in press) Radar back-scatter estimates from a combined ice growth andsurface scattering model of first-year sea ice.EARSel.Warren, S.G. (1982) Optical properties of snow.Review of Geophysics and Space Physics, 20: 67–89.Weeks, W.F. and S.F. Ackley (1982) The growth,structure, and properties of sea ice. USA ColdRegions Research and Engineering Laboratory,Monograph 82-1.Weeks, W.F. and W.L. Hamilton (1962) Petro-graphic characteristics of young sea ice, Point Bar-row, Alaska. American Mineralogy, 47: 945–961.Weller, G. (1972) Radiation flux investigations.AIDJEX Bulletin, 14: 28–30.Weller, G. and P. Schwerdtfeger (1967) Radiationpenetration in antarctic plateau and sea ice. InPolar Meteorology, World Meteorological Organiza-tion Technical Note No. 87, p. 120–141.Wiscombe, W.J. and S.G. Warren (1980) A modelfor the spectral albedo of snow, 1, Pure snow.Journal of Atmospheric Science, 37(12): 2712–2733.Zaneveld, J.R.V. (1964) The transparency of seaice in the visible region. M.S. Thesis, Massachu-setts Institute of Technology (unpublished).

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APPENDIX A: LIST OF SYMBOLS

E0 radiance of the direct beam component of the incident radiation fieldf growth rateF irradianceFd downwelling irradianceFu upwelling irradianceI radiancei0 fraction of incident irradiance transmitted through the top 0.1 m of the iceIr reflected radiancekb absorption coefficient of brineki absorption coefficient of iceksi absorption coefficient of sea iceN real index of refractionp(µ, µ′, φ, φ′) phase functionR bidirectional reflectance distribution function (BRDF)R0 normalized reflected radiance at nadirS source functionT transmittancex horizontal positionz depth within the mediumα albedoαt wavelength-integrated, or total, albedoφ azimuth angleφ0 solar azimuth angleκ extinction coefficientκt wavelength-integrated, or total, extinction coefficientsλ wavelengthνs volume fraction of iceνb volume fraction of brineθ zenith angle (0 pointing downward, π pointing upward)θ0 solar zenith angleµ cosine of the zenith angle, θρ densityσ scattering coefficientτ nondimensional optical depthϖ0 single scattering albedo

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The Optical Properties of Sea Ice Office of Naval ResearchContractsN0001495MP30002N0001495MP30031

Donald K. Perovich

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33Albedo Optical properties Sea iceAbsorption Scattering

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Sea ice is a translucent material with an intricate structure and complex optical properties. Understanding thereflection, absorption, and transmission of shortwave radiation by sea ice is important to a diverse array ofscientific problems, including those in ice thermodynamics and polar climatology. Radiative transfer in sea iceis a combination of absorption and scattering. Differences in the magnitude of sea ice optical properties are dueprimarily to differences in scattering. Spectral variations are mainly a result of absorption. Changes in suchoptical properties as the albedo, reflectance, transmittance, and extinction coefficient are directly related tochanges in the state and structure of the ice. Physical changes that enhance scattering, such as the formation ofair bubbles due to brine drainage, result in larger albedos and extinction coefficients. The albedo is quitesensitive to the surface state. If the ice has a snow cover, albedos are large. In contrast, the presence of liquidwater on a bare ice surface causes a decrease in albedo, which is more pronounced at longer wavelengths. Sea-ice optical properties depend on the volume of brine and air and on how the brine and air are distributed.