IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. GE-25, NO. 6, NOVEMBER 1987 751

Snow Property Measurements Correlative toMicrowave Emission at 35 GHz

ROBERT E. DAVIS, JEFF DOZIER, MEMBER, IEEE, AND ALFRED T. C. CHANG, MEMBER, IEEE

Abstract-Snow microstructure, measured by plane section analy- serve new snow in February, variable layered snow insis, and snow wetness, measured by the dilution method, are used to March, and melting snow in April.calculate input parameters for a microwave emission model that uses

the radiative transfer method. The scattering and absorbing properties The radiometer used to make the 35-GHz brightness-are calculated by Mie theory. The effects of different equivalent sphere temperature measurements is a periodically calibrated ac-

conversions, adjustments for near-field interference, and different snow coupled total power type. The radiometer was hand-heldwetness characterizations are compared for various snow conditions. about 1 m above the snow. The brightness-temperature

Index Terms-Snow, microwave, microstructure, wetness, radiative observations consisted of views at zenith angles rangingtransfer. from 00 to 700 in 100 increments for both horizontal and

vertical polarizations. The observations compared with themodel for each data are averages of two or more scans.

I. INTRODUCTION In the radiative transfer equation [3] radiance terms canT HE GOALS of this study are: 1) to develop and eval- be replaced by brightness temperature at microwave fre-

uate field techniques to obtain the ice and liquid phase quencies. The brightness temperature of a snow pack candata suitable for input to microwave emission models, and be found by solving the radiative transfer equation.2) to illustrate their utility to drive a discrete scatterer dTB I,)model of microwave emission at 35 GHz for a seasonal = -TB(TV, tt) + J(V, ii). (1)alpine snow pack with semi-infinite optical depth. dTvThe snow pack is characterized in the radiative transfer TB ( TV, ) is the monochromatic brightness temperature at

problem as one or two layers of uniform spheres that have optical depth T, in direction cos-1 It J,(rv, tu) is thebeen obtained by averaging snow property measurements. source function, which accounts for scattering of diffuseThe background medium is considered to be a mixture of radiation from other directions and for emitted radiation.air, ice, and liquid water. The model results are compared (to apparent brightness-temperature measurements at hor- WV X T P0(r0; ., p/) dp/izontal and vertical polarizations for a variety of view an- 2 -gles. We compare different equivalent sphere conver- 1sions, adjust the refractive index to compensate for close + [ - (T0)] T(TV) (2)proximity of the ice grains, and evaluate two geometric wv and Pv are the single-scattering albedo and phase func-configurations of liquid water in snow. tion; these are generally piecewise continuous functions

of depth for a nonuniform medium. The optical thicknessII. EXPERIMENTAL DESIGN of a layer is

Snow property measurements were carried out coinci- OiZQextdent with observations of microwave brightness temper- Irv = Nzext = 4 (3)ature during three periods in the 1984-1985 snow season 4rat a study plot on Mammoth Mountain in the eastern Sierra N is the number density of scatterers of radius r, z is theNevada, California. The facilities at the plot include elec- layer thickness, orext is the extinction cross section at fre-trical power, shelter, energy balance instrumentation, and quency v, 0i is the volume fraction of ice, and Qext is thearrays of thermistors in the snow pack [1], [2]. The pe- extinction efficiency at frequency v. The parameters usedriods of radiometric measurements were scheduled to ob- in the Mie calculations are the radius of the equivalent

sphere r for the layer and the relative index of refractionManuscript received September 30, 1986; revised July 10, 1986. of the spheres, as compared to the background medium.R. E. Davis is with the Sierra Nevada Aquatic Research Laboratory,

Mammoth Lakes, CA 93546.J. Dozier is with the Center for Remote Sensing and Environmental Op- III. MICROSTRUCTURE MEASUREMENTS

tics, University of California, Santa Barbara, CA 93106 and the Jet Pro-pulsion Laboratory, California Institute of Technology, Pasadena, CA Snow samples were obtained from snow pits at the same91109. time conventional snow properties were observed. Wet

A. T. C. Chang is with the Laboratory for Terrestrial Physics, NASAGoddard Space Flight Center, Greenbelt, MD 20771. snow samples were quick frozen using dry ice and a

IEEE Log Number 8716805. cooler. In addition to the field description, micrographs

0196-2892/87/0600-0751$01.00 ©) 1987 IEEE

752 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. GE-25, NO. 6, NOVEMBER 1987

of selected snow samples were used with reference grids IV. MEASUREMENT OF LIQUID WATER CONTENTto obtain estimates of the particle average diameter. Measurements of snow wetness were obtained by theEach sample of snow was subdivided into specimens Of dilution technique because tests show that cold calo-

about 3 x 3 x 5 cm, carefully avoiding the edges of the rimetry is inconsistent and requires too much time, andblocks. Sections were prepared from the specimens ac- because dielectric techniques require sophisticated instru-cording to recently reported procedures [4]-[6]. For each mentation that was unavailable. Refinements and testingspecimen at least three sections were prepared, two that of the dilution method for measuring snow liquid fractionwere parallel and perpendicular to the structure of the have been reported [8] in which the tests show an accu-snow, and one with random orientation. Micrographs then racy of 1.5 percent and an acquisition rate of about 3 towere taken of the sections with a Nikon HFX photomi- 5 mm per sample.croscope using Kodak Ektachrome 400 35-mm slide The dilution method relies on the dilution of an aqueoustransparency film. A fiberoptic ring illuminator was used solution when it is mixed with wet snow. The concentra-to provide a cool light source, almost coaxial to the main tion change forms the basis for measurement. A stock so-optic tube of the photomicroscope. The lighting arrange- lution of mass S and impurity concentration Cs, is mixedment produces bright reflection from the pore filler and thoroughly into a wet snow sample of mass M, with un-maximum light penetration into the exposed ice grains, known water mass W. The solution is at 0°C and mixingwhich appear darker. is in an insulated container, so that melt or refreezing isThe micrographs were digitized with 8-bit brightness minimized. The impurity concentration in the stock so-

levels as 512 x 512 pixels using a frame-grabber video lution is small enough so that freezing point depression isdigitizer, part of a Model 70F image computer from In- negligible, but large enough to be well above the impurityternational Imaging Systems. The classification procedure concentration C,, in the liquid water in the snow sample.starts by calculating the snow density corresponding to The mixture of stock solution and snow liquid water hasmost values of the brightness level threshold. By compar- impurity concentration Cming the calculated densities to those measured indepen-dently for the snow specimen, this relationship guides the C SCs + WCw (6)user in determining a threshold brightness value. Next a S + Wvisual threshold is determined, which best replicates the This can be solved for W and divided by the snow massmicrograph appearance with a real-time density slicing M to give the liquid water mass fraction xw. Typically, xwoperation while the image is displayed on the monitor. x 100 is in the range 0 to 30 percentThe classified images are processed with a parallel-line

sampling technique that results in three measurement pa- Cmrameters and their distributions: W S CS

1) Point density PP, the number of pixels falling on ice W M MCm CW(profiles divided by the total number of pixels. CS C5

2) Intercept number density NL, the number of ice-pore The absolute concentrations Cs, Cm, and C, are notand pore-ice transitions.and pore-icetransitions.

needed, only their ratios. The volume fraction of liquid3) Ice intercept lengths L, the distances between pore- water onycan be obtainedice and ice-pore transitions.

All of these are ratio estimates of statistical parameters W= A,,,-. (8)and are subject to the standard estimates of error, which Pibecome smaller with increasing numbers of sample esti- If mixing of the stock solution is complete, errors in themates [7]. Volume density is equal to the point density, dilution method result from errors in the measurements ofi.e., the ice volume fraction 0i of the frozen specimen S, M, Cm / Cs, and Cw/ Cs.

Pi0, = VV = PP = - (4) V. APPROXIMATION OF RADIATIVE PARAMETERS

A. Equivalent SpheresPi is the number of pixels falling on ice, and PT iS the It has been shown that the optical properties of irregulartotal number of pixels. The snow density is pS = Pp, particles of ice can be approximated by equivalent sphereswhere Pi = 917 kg - m-3is the density ofice.''in the microwave part of the spectrum [9] and in theoret-The surface density or surface area per containing vol-

ume, IS ~~~~N. scattening it generally has been assumed that the equiva-SV= 2NL = 2 -i (5) lent sphere has the same diameter as the snow particles

LT disaggregated from the pack. The best conversion towhere NL is the intercept density of the grain boundaries, mimic the actual snow grains has not been determined ad-Ni is the number of profile boundary intersections, and LT equately. In addition, the effects of the dominant orien-is the length of the line scan. tation of microstructure features are not well understood.

DAVIS et al.: SNOW PROPERTY MEASUREMENTS 753

The conversion procedures for equivalent spheres tested To estimate the sizes of the ice spheres and water in-are: 1) the sphere of mean chord length equal to the mean clusions from rT, Oi, and O, we assume that melt occursintercept of the ice phase, 2) the sphere of equal volume- uniformly around the equivalent spheres. The radius ofto-surface ratio, 3) the sphere of equal mean diameter to the ice cores ri for different water contents isparticles in micrographs, and 4) the sphere of equal mean 1/3diameter to snow pit estimates. The section data were lim- - K( oi (15)ited to conversions (1) and (2) in this study and the par- ri- rT\10910w +

1

ticle parameter measurements to conversions (3) and (4).For the conversion (1) we assume that the mean inter- The central ice spheres decrease in radius and number

cept length of all the ice profiles, convex and concave, is density as the snow liquid water content increases.equal to the mean intercept lengths of circles that wouldform the profiles of the equivalent spheres. The relation-ship between the average radius of random circles cuttingspheres of equal size and the true radius of the spheres is We consider two configurations of the ice and liquid[7] water in approximating the average radiative properties.

The first characterization treats the equivalent spheres asRL = - -r (9) ice covered by a thin layer of water [11], [12]. While this

treatment is questionable for low water contents because

RL is the sperrdisndshaergeraiuo equilibrium thermodynamics constrains the liquid to oc-

circular section profile. Similarly, it can be shown that the cur as menisci between grains, and it is inconsistent withaverage radius and mean intercept length of the circles are mixing formulae comparisons to dielectric measurements,related by it is used to illustrate the effect of different ice-water ge-

ometry. The problem of scattering from concentric spheres2 - (10) was solved by Aden and Kerker [13] and is not repeatedL here.

The second characterization treats the ice and waterwhere L is the mean intercept length. Thus separately. The size of the ice spheres as melt progresses

8 is calculated using (15), and the water is assumed to occur

RL = -L = 0.81 L. (11) as small menisci approximated by spherical shapes areheld between two ice spheres. This is a more realistic

The surface density Sv and the volume density Vv are used treatment since the liquid water in snow nestles betweento calculate the radius of the sphere of equal volume-to- the grains, but it assumes complex shapes. The ratio ofsurface ratio the number of water spheres to the number of ice spheres

/Vv\ is arbitrarily selected based on Colbeck's [11] suggestionRV = 3 S (12) that wet seasonal snow may be dominated by two-grain

bonds. Thus, the radius of the water sphere rw can be cal-

The diameter-equivalent sphere can be obtained from the culated from the number density of ice spheres N and the

particle' information by using the mean diameters from the liquid water volume fraction 0,,particle observations from the microscope and field. 3OW 1/3

__ = (~~~~~~~~~~~~~3W) (16)RDM = (13) \2NW/

Once the radius of the water spheres is determined, theand relative refractive index of the spheres is calculated and

D the combined scattering and absorption properties of the

RDF = F (14) layer are estimated according to Dozier and Warren [14].2

_ SQ ice ~ waterSice ext + SiwaterQextwhere DM is the mean estimated grain diameter from the Q-(17)micrographs of disaggregated particles, and DF is the ice + 5watermean estimated grain diameter from the field observa- QS ice ± 5 watertions. RDM and RDF are the radii of the equivalent spheres. Qsca - iceQsca waterQsca (18)

For the wet snow cases, the samples returned from the ice + 5waterfield were frozen so that the section and disaggregate pa- 6o= Qsca/Qext (19)rameters represent the combined dimensions of the ice andwater. Further, the field measurements of particle dimen- where 5ice and 5water are the geometric cross sections ofsions also incorporate the liquid inclusions. Therefore, the ice and water, respectively. Equation (3) is used to cal-equivalent-spheres, which are part ice and part water, can culate the optical depth by adding the contributions of icebe described by a total radius rT. and water.

754 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. GE-25, NO. 6, NOVEMBER 1987

C. Optical Properties of Ice and Water e = e + ie" = (n + ik)2. (23)The~~~~~~~~~~~~~~~~~~~~ rerctv ineiE

ice at ikqunc 3523)(\The refractive index of ice at frequency 35 GHz (X = For dry snow we sum the refractive indices of air and ice8.57 mm) is interpolated from the data compiled by War- weighted by volume fraction, and square the result to ob-ren [15]. While the real part of the refractive index of ice tam the real and imaginary parts of the dielectric function.is independent of temperature, and is 1.78 v = 35 GHz,the imaginary part is temperature dependent, varying from Ed5 = (Gini + nafair + io kice)2 (24)3.5 x 10-3 at -1°C to 1.4 x 10-3 at -20°0C. This af- ai

ice a where Oa is the volume fraction of air, and nair = 1. Thisfects ext and, therefore, the single scattering albedo W. is a convenient formula because it gives the real andThe refractive index of water is interpolated from the dataof Lane and Saxton: [16] Nwal = 3.95 + i2.44. imaginary parts with one calculation and shows good

agreement with empirical formulae. For wet snow we useD. Effects of Grain Contact the empirical relationships of Tiuri et al. [18] in which

the dielectric effect of liquid water is superposed on theIn some of the model runs we attempt to compensate deeti rpriso r nwfor the effects of close particle spacing usLng the methodproposed by Gate [17]. The real part of the relative re- Ac' = Ew - Ed (25)fractive index of the Mie spheres is divided by the effec-tive refractive index of the surrounding medium. For dry AW = (0.100w + 0.80Gw) ew (26)snow e= (0. 100, + 0.80G2 )cE (27)

nmed = Goflice + Ganair (20) where E,' and E- are the real and imaginary parts of the

and for wet snow dielectric function of water. These are given by the Debyenmed - (E' )1/2. (21)

relaxation spectran =(Ews (21)

The estimation of the dielectric function of wet snow E' E(V) = c-, + ES- E . (28)is discussed in a following section. Here we only adjust 1 + t)0the real part of the index of refraction of the equivalent Substitutingspheres and assume that there is no effect on the imagi- 82.8nary part. Since the wavelength is large, the medium im- E' = 4.9 + 2 (29)mediately surrounding the spheres is assumed to have the 1 + (v/vo)same constituent mix as the bulk. and

E. Averaging for Snow Stratigraphy ,, 82.8 (v/vo)Some of the snow pit observations show many layers W +

(30)1 + (v/vo)2with quite different properties. Rather than increase the

model complexity to accommodate several layers, we av- where 82.8 is the difference between the high-frequencyerage the parameters into two layers. The averaging limit and the static dielectric function of water, v is thescheme is based on the optical thickness of the layer and frequency under consideration (35 GHz), and vo = 8.8its optical depth GHz is the relaxation frequency. These values agree well

with interpolated experimental data from Lane and Saxton'ri +I Ti ~ ~~~~~~[16].

Xi ( 2 ) exp [-(ri+l + r0)/2]X n ((22) VI. RESULTS

j (i+I- T1i exp [-(Ti+1 + r0)/2] A. Snow Property Measurements\2 The primary stereologic measurements based on the real

where x is the parameter being averaged. We average the dimensions of the sections are influenced by the micro-temperature of the snow pack and the single scattering scopic resolution. In general, mean intercept lengths de-albedos for all model calculations. crease and surface densities increase with increased mag-

nification. This is because the ice-grain profiles appearF. Dielectric Properties of the Medium more convoluted, partly a result of the preparation tech-We use formulae that fit the empirical data to estimate nique. We use low magnification to maximize the number

the dielectric properties of the medium. Considering the of profiles included, but at very low magnification, un-data available,4 we will avoid considerations requiring de- even illumination is more of a problem.tailed information about the shape of the constituents, The dilution method for measuring snow wetness isthough it is recognized that no physical insight can be convenient as a field technique and measurements showobtained from empirical formulae. good correlation to brightness-temperature data in the caseThe complex dielectric function e of a medium is re- of a thin (0-3 cm) actively melting snow layer at the sur-

lated to the complex refractive index n face (Fig. 1).

DAVIS et al.: SNOW PROPERTY MEASUREMENTS 755

280

270 45 HORIZONTAL POLARIZATION 0 3 0 0 0 03O3 D _270

260 0 0.10

250 00 260 0 e -

1000 11C 0 1200 1N0014C0 TB 250 _ OTB 240I 0.06e

2rees30elvin as the snow surac lye metswih ncrasngliui0 0 0wa04 240 \

grw2o30c hcns s wapoce0.6 0.04 =5l000

0 ~~~~~~~~~~~~~~~~~~230-0 _

2206 0 0.02

2101000 1100 1200 1300 1400 T 210B

TM 0

Fig. 1. Increase in brightness temperature TB (left axis), expressed in de-grees Kelvin as the snow surface layer melts with increasing liquid watercontent 35, (right axis). The snow was initially frozen and the wet layergrew to 3 cm thickness as O, approached 0.06. s=1 Fe. ll,0198

180T21

w=0.45

170

B. Modeling and MeasurementsurementsSpheres with equal volume-to-surface ratio and equal 0_

mean chord lengths underestimate the volume scattering1ONin snow at 35 GH-z as shown in Figs. 2 and 3 for a new I I Isnow condition and an old shnow condition, respectively. 10 20 30 40 5 60 70 60Equal-diameter spheres overestimate the scattering at 35 Fig. 2. Results for Feb. 11, 1985. Symbols represent measurements, andGHz (Figs. 2 and 3), a result shown in other studies, un- lines represent results from a single-layer model. Units of TB are degreesless the calculations are adjusted for near-field intei-fer- Kelvin and the view angle is expressed in degrees from vertical.

ence, which improves the correspondence between modelresults and radiometric measurements.

280The adjustment to the relative refractive index- to ac-

count for the close spacing and contact of the ice grains 270causes a reduction in the amount of scattering. Therefore, d Tonly the model parameters using the larger equivalentspheres from the particle measurements have been modi- \

0fled. Figs. 4 and 5 show the results for new snow and old 240 \snow conditions. The coffections improve the correspon- 0

dence between the model and the radiometric measure- 230 0 wments considerably, although the model shows poor-efacivindeoagreement with the horizontally polarized data. The hor-izontal-polarization data show a much larger dynamic TB 210

range, and so larger differences between theory and ex- 200periment could be expected. However, the effects ofstrong dielectric contrasts within the pack also may ac- 10Ecount for the larger differences in bfrightness temperature. T269K

180 -e=1.58+0.0032i

Altenatively, the data probably could be matched by w=re.finding equivalent sphere sizes somewhere between those 170n[3 VERTICAL POLARIZATItested, rather than by adjusting the refractive index of the f HORIZONTAL POLARIATIONspheres. Thus, what constitutes the best equivalent sphere 160

conversion is unresolved. Also, the possible dependence 150of the appropriate equivalent sphere size on frequency re-I I I I I Imains unaddressed, as well as the effects of orientation of 10 20 30 40 50 60 70 80

microstructure features. More accurate microwave mea- VWNk

yields thigeprtesher eemissivitiesiandbettermoe results.thanrmrnsuigmaurmnsfo peiu as

Whereas the model calculations for the March wet snow then adding a wet snow layer to the top, the model cal-

756 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. GE-25, NO. 6, NOVEMBER 1987

290 _ 280

270 270

260 260 -

23400 - 013 240>°-X \0

230 -230-0 ~~~~~~~~~~~~~~~~~0

220 -O0220

0 0

2100 \ TB 210 - °0 B

0190 SINGLE LAYER ADJUSTED 190 DUAL LAYER Bw =0.016

e=1 .51+O.0019i UPPER CURVES: CONCENTRIC180 T=261K T=271.9180~ ~~~~~~~~~~~~~~~~~~~~~~~~~8

w=0.45 w=0.0021 (TOP LAYER)

170 170 -

LOWER CURVES: SEPARATE

T=269.7160 ri VERTICAL POLARiZATION 160 0 VERTICAL POLARIZATION

w=0.0027(TOP LAYER)

0 HORIZONTAL POLARIZATION 10| e=1.47+0.032i 0 HORIZONTAL POLARIZATION150 5 =47002

10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80MBNNANGLE

VEWANGLEFig. 4. Results for Feb. 11, 1985. The refractive index of the spheres hasbeen adjusted, densities near the surface have been used to calculate e. Fig. 6. Results from Mar. 20, 1985, showing difference in the geometry

of liquid water specified in the model. Upper curves are obtained byusing a concentric-sphere configuration and the lower curves by usingseparate spheres of ice and water. Measurements and calculations are forlow water content.

270

260_

250 [t 0: n. 0 230|\Z0 N ]-

090270 _ DL L_ 0240 [

260230 0 0

0

220 0 20

T 24~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~10-=7.

TB 21024

230-

2150)

200~~~~~~~~~~~~~~~~~~~~~~~~~2o DUALLAYER

T-269KT180 e=1.58+0.0032i TB 210

w=0.092

170 VERTICAL POLARiZATION ew=0.59 1

0 HORIZONTAL POLARV-ATION DU0ALLAYER fr = 0.058160 ~~~~~~~~~~~~~~~~~~~~~~~~~~UPPERCURVES: CCNCENTRr-

180 T-272.7150

w=0.0015(TOPLAYER)170

10 20 30 40 50 60 70 60 T=270.9

VIBNANG-kE ~~~~~~~~~~160w=0.002iITOPLYER)

culations for the wet spring snow in April use a single Blayer. Fig. 6 illustrates the results for a low liquid watercontent from the March data. It shows that the separate- Fig. 7. Results from Mar. 20, 1985, showing difference in liqiud geometry

in the model, at greater water content. The upper curves result fromsphere geometry of water and ice gives better model re- concentric-shell geometry and the lower curves result from separate-sults, but at O,w 2 0.05 the concentric-shell treatment of sphere geometry.

DAVIS et al.: SNOW PROPERTY MEASUREMENTS 757

liquid water gives better results, as shown in Fig. 7. The [18] M. Tiuri, A. H. Sihvola, E. G. Nyfors, and M. T. Hallikainen, "Thetemperatures shown on the figures are the result of the complex dielectric constant of snow at microwave frequencies," IEEE

J. Ocean. Eng., vol. OE-9, pp. 377-382, 1984.property averaging scheme described by (22). Neither [19] A. Denoth, "The pendular-funicular liquid transition in snow," J.characterization predicts the increase in brightness tem- Glaciology, vol. 25, no. 91, pp. 93-97, 1980.perature depicted in Fig. 1. This result may reflect the [20]-, "The pendular-funicular liquid transition and snow metamor-change in dielectric behavior observed at lower frequen- phism," J. Glaciology, vol. 28, no. 99, pp. 357-364, 1982.

cies [19], [20] when the snow undergoes a transition be- *tween the pendular and funicular saturation regimes or itmay be an artifact of the characterization of wet snow. | l Robert E. Davis received the BA. degree in ge-

ography in 1976 from the University of Califor-REFERENCES nia, Santa Barbara. He received the M.A. degree

in 1980, and the Ph.D. degree in 1986 from the[1] R. E. Davis and D. Marks, "Undisturbed measurement of the energy same institution.

and mass balance of a deep alpine snowcover," in Proc. Western He is currently working as an assistant re-Snow Conf., vol. 48, pp. 62-67, 1980. searcher in the Center for Remote Sensing and En-

[2] R. E. Davis, J. Dozier, and D. Marks, "Micrometeorological mea- vironmental Optics at The University of Califor-surements and instrumentation in support of remote sensing obser- nia, Santa Barbara. His research interests are snowvations of an alpine snow cover," in Proc. Western Snow Conf., vol. physics, snow property measurements, remote51, pp. 161-164, 1984. sensing of snow, and heat and mass transfer in

[3] S. Chandrasekhar, Radiative Transfer. New York: Dover, 1960. porous media. Currently he operates an experimental field station at the[4] R. Perla, "Preparation of section planes in snow specimens," J. Gla- Sierra Nevada Aquatic Research Laboratory, Mammoth Lakes, CA.

ciology, vol. 28, pp. 199-204, 1982.[5] R. Perla and J. Dozier, "Observations on snow structure," in Proc. *

6th Int. Snow Science Workshop, Mountain-Rescue (Aspen, CO), pp.182-187, 1984.

[6] R. Perla, J. Dozier, and R. E. Davis, "Preparation of serial sections Jeff Dozier (M'86) received the B.A. degree inin dry snow specimens," J. Microscopy, vol. 142, no. 1, pp. 111-I geography in 1968 from California State Univer-114, 1986. sity, Hayward, and the M.Sc. and Ph.D. degrees

[7] E. R. Weibel, Stereological Methods, 1, Practical Methods for Bio- in 1969 and 1973, respectively, from the Univer-logical Morphometry. New York: Academic, 1979. sity of Michigan, Ann Arbor.

[8] R. E. Davis, J. Dozier, E. R. LaChapelle, and R. Perla, "Field and He has taught since 1974 at the University oflaboratory measurements of snow liquid water by dilution," Water California, Santa Barbara, where he is now Pro-Resources Research, vol. 21, no. 9, pp. 1415-1420, 1985. fessor of Geography and a researcher in the Cen-

[9] A. Mungai and W. J. Wiscombe, "Scattering of radiation by mod- ter for Remote Sensing and Environmental Op-erately nonspherical particles," J. Atmos. Sci., vol. 37, no. 6, pp. tics. Recently, he joined the Jet Propulsion1291-1307, 1980. Laboratory, California Institute of Technology,

[10] A. T. C. Chang, A. Rango, and J. C. Shiue, "Remote sensing of Pasadena, part-time, as a member of the technical staff in the Earth andsnow properties by passive microwave radiometry: GSFC truck ex- Space Sciences Division and as Project Scientist for the high-resolutionperiment," in Microwave Remote Sensing of Snowpack Properties, imaging spectrometer (HIRIS). His research interests are in remote sensingA. Rango, Ed. NASA Conf. Pub. 2153, NASA Goddard Space Flight of snow properties, energy balance modeling of snow processes in alpineCenter (Greenbelt, MD), pp. 169-186, 1980. terrain, and snow chemistry and runoff.

[11] S. C. Colbeck, "Grain clusters in wet snow," J. Colloid Interface Dr. Dozier serves on the Committee on Glaciology of the NationalSci., vol. 72, no. 3, pp. 371-384, 1979. Academy of Sciences.

[12] -, "Classification of seasonal snow cover crystals," Water Re-sources Research, vol. 22, no. 9, pp. 59S-70S, 1986. *

[13] A. L. Aden and M. Kerker, "Scattering of electromagnetic wavesfrom two concentric spheres," J. Appl. Phys., vol. 22, pp. 1242-1246, 1951. Alfred T. C. Chang (M'86) was born in Shang-

[14] J. Dozier and S. G. Warren, "Effect of viewing angle on the infrared hai, China, in 1942. He received the Ph.D. degreebrightness temperature of snow," Water Resources Research, vol. in physics from the University of Maryland, Col-18, no. 5, pp. 1424-1434, 1982. lege Park, in 1971.

[15] S. G. Warren, "Optical constants of ice from the ultraviolet to the Since 1974, he has been at the NASA Goddardmicrowave," Appl. Opt., vol. 23, no. 8, pp. 1206-1225, 1984. Space Flight Center, Greenbelt, MD, where he is

[16] J. A. Jane and J. A. Saxton, "Dielectric dispersion of pure polar a Research Physicist in the Laboratory for Terres-liquids at very high radio-frequencies," in Proc. Royal Society Lon- trial Physics. His areas of research include micro-don, vol. A-213, pp. 400-408, 1952. wave radiometry, radiative transfer calculations in

[17] L. F. Gate, "Light-scattering cross sections in dense colloidal sus- relation to remote-sensing applications, and de-pensions of spherical particles," J. Opt. Soc. 4mer., vol. 63, no. 3, velopment of techniques for determining the prop-pp. 312-317, 1973. erties of snow, soil, ice, and the atmosphere by remote sensing.