Multiple-Layer Adaptation of HUT Snow Emission Model: Comparison With Experimental Data

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 7, JULY 2010 2781

Multiple-Layer Adaptation of HUT Snow EmissionModel: Comparison With Experimental Data

Juha Lemmetyinen, Jouni Pulliainen, Senior Member, IEEE, Andrew Rees,Anna Kontu, Yubao Qiu, and Chris Derksen

Abstract—Modeling of snow emission at microwave frequenciesis necessary in order to understand the complex relations betweenthe emitted brightness temperature and snowpack characteris-tics such as density, grain size, moisture content, and verticalstructure. Several empirical, semiempirical, and purely theoreticalmodels for the prediction of snow emission properties have beendeveloped in recent years. In this paper, we investigate the capabil-ity of one such model to simulate snow emission during the peaksnow season—a new multilayer version of the Helsinki Universityof Technology (HUT) snow model. Developed with a single layer,the original HUT model was easily applied over large geographicareas for the estimation of snow cover characteristics by modelinversion. A single homogenous layer, however, may not accuratelyallow the simulation of vertically structured natural snowpacks.The new modification to the model allows the simulation of emis-sion from a snowpack with several snow or ice layers, with theindividual component layers treated as in the original HUT model.The results of modeled snowpack emission, using both the originalmodel and the new multilayer modification, are compared withreference measurements made using ground-based radiometersdeployed in Finland and Canada. Detailed in situ measurementsof the snowpack are used to set the model inputs. We show that, inmost cases, use of the multiple-layer model improves estimates forthe higher frequencies tested, with up to 38% improvement in rmserror. In some cases, however, the use of the multiple-layer modelweakens model performance particularly at lower frequencies.

Index Terms—Radiometry, snow cover.

I. INTRODUCTION

THE RETRIEVAL of snow cover parameters, such as snowdepth and snow water equivalent (SWE), from passive

microwave measurements dated from the earliest satellite-basedmeasurements with multifrequency radiometers [1]–[3]. Afterpromising initial results using the measured brightness tem-perature difference of two frequencies, several fundamentalproblems have been identified. The methods employ a low-frequency signal (K- or Ku-band) that penetrates a typical

Manuscript received May 26, 2009; revised September 13, 2009 andNovember 11, 2009. Date of publication March 22, 2010; date of currentversion June 23, 2010. This work was supported by the Department of RadioScience and Engineering, Helsinki University of Technology.

J. Lemmetyinen, J. Pulliainen, and A. Kontu are with the Arctic ResearchCenter, Finnish Meteorological Institute, 99600 Sodankylä, Finland (e-mail:[email protected]).

A. Rees is with the Department of Geography and EnvironmentalStudies, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada (e-mail:[email protected]).

Y. Qiu is with the Center for Earth Observation and Digital Earth, ChineseAcademy of Sciences, Beijing 100080, China (e-mail: [email protected]).

C. Derksen is with the Climate Research Division, Science and TechnologyBranch, Environment Canada, Toronto, ON M3H 5T4, Canada (e-mail: [email protected]).

Digital Object Identifier 10.1109/TGRS.2010.2041357

(dry) snowpack with relatively small scatter, providing a signallargely originating from the background brightness temperatureof the underlying surface beneath the snow. This is comparedto a higher frequency signal (typically Ka-band), which is moreinfluenced by scattering inside the snowpack; comparison ofthe two frequencies allows, to some extent, the formulation ofa linear relation between snow depth or water equivalent andthe signal difference. Comparison of the two frequencies alsolargely negates the effect of physical temperature of the snow-pack to the measured brightness temperature. However, scatterin the snowpack and, thus, the resulting channel difference reactalso to the structure, wetness, density, and the size of scatteringparticles (snow grains) [4]. Furthermore, observable scatteringat the higher frequencies saturates for thick snowpacks after acertain threshold [5]. Studies place this threshold value of SWEbetween 120 and 180 mm (see [6] and [7]). A possible wayto address the saturation effect for deep snow at Ka-band isthrough the use of two different K-band frequencies (e.g., 10and 19 GHz) [8].

However, the natural formation of snow layers with differingelectromagnetic properties further complicates the issue bycreating interlayer scattering effects and multiple reflectionsbetween layers. This results in a difficulty in determiningtemporally consistent parameters for empirical equations usingthe brightness temperature difference. Inconsistent results withmeasurements from multiple years have been pointed out whenusing the traditional algorithms based on channel difference,although this too may be addressed by the use of lower fre-quencies [8].

An approach to investigate the fundamental reasons behindthese phenomena and an alternative to empirical formulasare theoretical or semiempirical models which attempt to de-scribe the emission properties of a snowpack. Most models arebased on radiative transfer analysis, treating the snowpack asa scattering medium with varying degrees of complexity. Themicrowave emission model for layered snowpacks (MEMLS) isa well-documented example of a semiempirical model [9], [10],while a purely theoretical approach is the dense media radiativetransfer (DMRT) theory [11]. A two-layer modification (wetand dry snow layers), based on DMRT, is presented in [12],and a comprehensive multiple-layer adaptation is presentedin [13].

The radiative transfer model investigated in this paper isthe semiempirical Helsinki University of Technology (HUT)snow emission model [14]. The model describes the snowpackas a homogenous layer, using effective values for parametersinfluencing scatter such as density and grain size. Ancillary

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2782 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 7, JULY 2010

information makes possible the inversion of snowpack param-eters from microwave observations using the model, evenat regional or hemispheric scales [15]. When applied to apractical satellite data inversion analysis, soil, vegetation, andatmospheric effects can be addressed with separate simulationmodules as required.

In a recent investigation [16], the HUT model was able tosimulate microwave emission from accurately characterizedsnowpacks with relatively good accuracy, with a maximumpercentage error of approximately 10%. However, due to uncer-tainties related to the averaging of model input parameters, theauthors nevertheless recommend the influence of snow layeringto be included in future snow models. The HUT model hasalso recently been applied in a data assimilation scheme [17];uncertainties related to determination of average snowpackscattering variables are addressed by calculating an effectivegrain size for each given area, based on weather station obser-vations and measured microwave emission of the same area.However, coupling radiative transfer models with land surfaceor hydrological models may also make possible the inclusionof snow layering in data assimilation in the future [18], [19].A preliminary attempt at assimilating pointwise microwaveradiance with a land surface model is presented in [20]. In orderto address these issues, we present in this paper a HUT modelmodified to include the simulation of an unlimited number ofvertically stacked snow (or ice) layers, each with scattering andemission properties computed using the original model. Theemployed method is similar to how a layered structure is treatedin MEMLS, albeit simplified by the omission of coherentcomponents in layer interactions. The relative simplicity of theoriginal HUT model in estimating the scattering and emissionproperties of individual layers based on observed snow grainsize is retained. The modification also makes the simulation ofemission possible from snow-covered lake or sea ice, althoughthis is not emphasized in this paper. This paper presents themodifications made and analyzes the effect of including snowlayering in comparison to the original one-layer HUT model.Initial results pointing out differences in model performancewhen compared with reference observations are presented.

Section II describes the modifications made to the HUT snowemission model to include multiple layers and demonstratesdifferences between the performance of the original and multi-layered models through a theoretical approach. Section IIIdescribes the data sets used as reference. Results of modelcapabilities in estimating the snowpack emission against thereference data are presented in Section IV, with the resultssummarized and discussed in Section V.

II. DESCRIPTION OF MODIFIED HUTSNOW EMISSION MODEL

A. Original HUT Snow Emission Model

The semiempirical HUT snow emission model calculates theemission from a single homogenous snowpack using a two-fluxapproximation. Input parameters of the model include snow-pack depth, density, effective grain size, and temperature. Snowmoisture content and snow (or ice) salinity can be included bymodifying the dielectric constant through empirical equations.

The model applies the delta-Eddington approximation to theradiative transfer equation. The emission of a medium withthickness d0 can then be obtained from [14]

TSNOW =T0κa

κe−qκs

(1− 1

L

)

=Tphysκa

κe−qκs(1−exp ((−κe+qκs) · d0 · sec θ))

(1)

where Tphys is the physical temperature, 1/L is the attenuation,κa is the absorption coefficient, κs is the scattering coefficient,κe is the extinction coefficient, θ is the incidence angle fromnadir, and q is an empirical constant defining the total forwardscattered incoherent intensity in the snowpack.

An empirical equation is used to relate the snow extinctioncoefficient to frequency and snow grain size [21], so that, forfrequencies 1–60 GHz

κe = 0.0018f2.8D2obs (2)

where f is the frequency in gigahertz and Dobs is the observedscattering particle (snow grain) diameter in millimeters.

The empirical parameter q in (1) has been defined for snowby fitting the HUT model to experimental snow slab emissiondata [14]. The emission data, presented in [9] and [22], rep-resent several snow types and span a frequency range from11 to 94 GHz. A common value of q = 0.96 was found to beapplicable for all frequencies in this range.

It should be noted that parameter q includes effects frommultiple scattering in the snowpack and is, as such, relativelyhigh compared to a case of singular scattering following, forexample, the Mie theory. As pointed out in [21], in snow, thelosses due to scattering are approximately equal to generationof incoherent intensity by scattering. This is supported alsoby recent theoretical studies of multiple scattering in snow,which predict, on microwave frequencies, the largest part oftotal volume scattering to be in the forward direction [23], [13].An analogous parameterization to the HUT model of volumescattering of a snow model has also been proposed in [24].

The absorption coefficient κa is determined from thecomplex dielectric constant of dry snow [14], applying thePolder–van Santen mixing model for the imaginary part.The calculation of the real part of the dielectric constant for drysnow is presented in [25]. Reflection and transmission coeffi-cients and the refraction angle at layer interfaces are calculatedfollowing the Fresnel equations. Emission from the snow layer(1) is considered as both up- and downwelling emissions. Theseare, in turn, reflected from interfaces between layers (air–snowand snow–ground). The transmission and multiple reflectionsbetween layer interfaces are calculated using the incoherentpower transfer approach presented in [26].

Emission from the ground is estimated using separate model,taking into account dielectric properties of the ground andcovering layers, frequency, polarization, and variations in sur-face roughness [27]. When simulating sceneries observed bysatellite instruments, effects of vegetation and atmosphere areapplied as in [28] and [29], respectively.

LEMMETYINEN et al.: MULTIPLE-LAYER ADAPTATION OF HUT SNOW EMISSION MODEL 2783

For emission from a layer consisting of pure ice, it is assumedthat q = 1 and thus κa = κe − qκs, corresponding to a nonscat-tering absorbing layer, simplifying (1) to

TICE = Tphys (1 − exp ((−κa) · d0 · sec θ)) . (3)

The determination of grain size from observations has tradition-ally been proven problematic; an empirical formula to relate theobserved grain size to an effective grain size suitable for theHUT snow emission model has been proposed by Kontu andPulliainen [30]. The formula reduces the effect of variationsand large values in the observed grain size. According to thestudy, the effective grain size Deff , i.e., the grain size value thatcorresponds to the total scattering effects from the snowpack,can be related to observations by

Deff = 1.5 · (1 − exp(−1.5 · Dobs)) . (4)

Here, Dobs is the average of maximum diameters of observedsnow grains in each layer, as weighed by the respective layerthickness and divided by the total thickness of the snowpack.When applying the original HUT model in this study, theparameters measured for layered snow are used likewise, so thatthe bulk value Z for parameter ζobs is obtained by

Zobs =

(N∑1

ζobs,n · dn

) /N∑1

dn (5)

where dn is the thickness of layer n.

B. Multiple-Layer Modification

The treatment of multiple layers is based on a two-fluxapproximation of each layer [31]. Layers are considered infinitein the horizontal direction. Only incoherent power transfer isconsidered. Layer interfaces between consecutive snow layers,and the topmost air–snow interface, are considered Lambertian.The upwelling emission flux Tn,↑ of layer n of a system, asshown in Fig. 1, can be determined as

Tn,↑ = Sn

(TSNOW,n + Tn+1,↓

tn · rn−1

l2n

+ Tn−1,↑tn−1

ln+ TSNOW,n

rn−1

ln

)(6)

where tn, rn, and ln are the Fresnel transmission and reflectioncoefficients and the loss factor of layer n, respectively. The lossfactor is derived as in (1). Sn is the geometric sum of multiplereflections in layer n, so that

Sn =1

1 − rnrn−1/l2n. (7)

In (6), the first term inside the parenthesis is the internal up-welling emission; the second term, the downwelling emissionfrom layer n + 1, reflected from layer n − 1; the third term, theupwelling emission from layer n − 1, reduced to interface n;and the last term, the internal downwelling emission, reflectedfrom rn−1 and reduced to rn.

Fig. 1. Schematic overview of the new multiple-layer HUT snow emissionmodel, with N -layers of snow or ice, each with brightness temperatureTSNOW,n, reflection rn, and attenuation ln. Air and ground layers (layersN + 1 and “0,” respectively) contribute their respective up- and downwellingbrightness temperatures TSKY and TGND to the system.

Similarly, the downwelling emission is

Tn,↓ = Sn

(TSNOW,n + Tn+1,↓

tnln

+ Tn−1,↑tn−1 · rn

l2n+ TSNOW,n

rn

ln

). (8)

Describing the up- and downwelling fluxes of each layer thenmakes possible the solving of the upwelling emission TN,↑beneath the topmost layer, which gives the observed emissionfrom above the snowpack when multiplied by tN = (1 − rN ).The complete equations used by the modified HUT modelare provided in the Appendix. For a one-layered system, theupwelling emission is calculated directly using (6), reducingthe solution to the original model. The multiple-layer adap-tation can also be directly employed in the simulation of awater–ice–snow system, such as snow-covered lake ice.

C. Emissivity Approximation

The emissivity of an isothermal system can be determinedas e = TB/Tphys, which is the ratio of emitted brightnesstemperature and physical temperature. Since a snowpack istypically not isothermal, the HUT model uses an approximationfor the effective temperature of the layered system Tphys,eff .Use of the empirical forward scattering parameter q in (1)prevents the calculation of emissivity through comparison oftwo brightness temperature estimates with two differing valuesof downwelling radiation. Rather, the effective temperature isobtained by considering the layered snow–ground structureas a system with n attenuators (snow layers), each with theattenuation Ln and physical temperature Tphys,n. The groundis considered an attenuator with infinite loss. The effectivetemperature is approximated by reducing it to the snow sur-face using the Friis formula, analogous to reducing the noisetemperature of a system of attenuators to the output.

When applied for SWE inversion, an approximation ofTphys,eff = Tphys,GND (ground temperature) has been used


Fig. 2. Difference of brightness temperature estimation given by one- and multiple-layer models (N layers) for idealized snowpacks. Snowpack with(top row) SWE = 150 mm and (bottom row) SWE = 300 mm. Grain size variation: (left) 1, . . . , 2 mm from top to bottom and (right) 1, . . . , 4 mm.Vertical polarizations depicted.

with the original model [17]. This is an accurate enough ap-proximation for practical applications considering the minimaleffect of typical physical temperature variations. However, forhigher frequencies and deep snowpacks, the approximation de-teriorates somewhat as an increasing portion of the microwaveemission originates not from the ground but the snowpack itself.This holds true also for the present approximation, e.g., theeffects of layer reflections are not included.

D. Multilayer Versus One-Layer Model Analysis

The performance of the multiple-layer adaptation versus theoriginal model is analyzed here using an idealized situation,whereby a snow layer of certain depth was divided first intoequally sized N = 2 layers, then N = 3 layers, and so forth.Grain size was set to increase linearly toward the lower snowlayers. Snow density also has an appreciable effect on the modelsimulation at higher frequencies; however, in order to simplifythe modeling situation, density was kept constant at 0.3 g/cm3

throughout the snowpack. SWE was therefore equal betweenall layers. Temperature was kept constant for all layers, and thelayer interfaces, as well as the underlying surface, were consid-ered ideally flat. Model simulations were then performed usingthe layered structure as an input to the new model, and using theweighed average values of grain size and the total SWEin the original model, demonstrating the fashion in which thetwo versions of the model would be used. The resulting differ-

ence in vertically polarized brightness temperature estimates isshown in Fig. 2, with two example snow thicknesses used (0.5and 1 m). Grain size for both is set to increase first from 1 mmin the topmost layer to 2 mm in the lowest one, and then from1 to 4 mm, respectively. The difference between estimates isvery small in all of these cases for frequencies below 10 GHz,with the greatest differences occurring at the highest frequency.Doubling the SWE value has a small effect compared to that ofincreasing the grain size gradient, which causes an increasingdifference at frequencies above 20 GHz.

Due to the demonstration setup, the greatest difference isapparent in the first division of the snowpack from N = 1(TB,N − TB,1 = 0 in Fig. 2) to N = 2 layers. Further divisionscause the resulting estimate to approach the one layer modelas N approaches infinity, as differences between consecutivelayers are diminished. Large differences between consecutivelayers thus cause a larger departure from the one-layered modelthan if the same contrast (in grain size) is distributed over morelayer divisions.

While natural snowpacks are more complex than the ide-alized ones used earlier, Fig. 2 demonstrates that includingsnow layering in the model has the largest effect on highfrequencies particularly regarding grain size. In (2), the effect ofgrain size is determined through the scattering coefficient witha frequency-dependent ratio of f2.8 [21], which emphasizeshigher frequencies. Including density variations complicatesthe situation somewhat, as also lower frequencies are more


affected through the absorption coefficient in (1). The effect ofdensity on the simulated difference between the models is onthe order of 20%, when restricting density to values conceivablein realistic snowpack structures.

III. REFERENCE DATA

In order to test the modified HUT snow emission model,two data sets consisting of in situ snowpack observationsand reference radiometer measurements were used. The firstreference data set was acquired by Environment Canada (EC)within a five-day period in April 2007. Ground-based mi-crowave radiometers were used to measure snowpack bright-ness temperatures at ten sites within a 3-km2 area nearDaring Lake in the Canadian Northwest Territories (NWT). Thesites included seven tundra and three lake ice sites. Snowpitmeasurements were performed at each radiometer measurementsite. A fortuitous rainfall event, followed by refreezing, formeda distinct thin ice layer on top of the snowpack in the study areabefore the initiation of measurements. A test where the surfaceice lens was manually removed, and the resulting change inbrightness temperature measured, was performed at all sites.The effect of this ice lens on the radiometer measurementsis described in detail by Rees et al. [32]. Weather conditionsduring the campaign remained otherwise stable except forone small snowfall event. Together with the unique verticalsnowpack conditions and detailed snowpack measurements, theEC data form an ideal means to investigate multilayer modelperformance.

The second set of observations was made at the ArcticResearch Center of the Finnish Meteorological Institute (FMI-ARC) in Sodankylä, Finland, between the 5th and 13th ofMarch 2008. The Helsinki University of Technology Radiome-ter (HUTRAD) system was mounted on a tower and used tomeasure the brightness temperature of the underlying snow-pack. The FMI-ARC satellite data calibration and validationsite in Sodankylä offers extensive facilities for acquisitionof different atmospheric, snow, air, and ground temperaturemeasurements, as well as comprehensive in situ snowpackobservations throughout the winter season. Additional in situmeasurements of the snowpack were made in the test areaduring the campaign. Weather and snow conditions at the testsite remained stable for a period of five days, after which a sig-nificant rise in temperature caused the beginning of snowmelt.At the end of the campaign, falling temperatures caused theformation of a dense refrozen layer on top of the snowpack.Although similar to the Canadian case, the refrozen layer wasnot as distinct. Furthermore, some moisture was observed inseveral layers of the snowpack even after surface refreezing.

A. Radiometer Observations

Canadian radiometer observations consist of dual-polarization measurements at 6.9, 19, 37, and 89 GHz. Theradiometers were mounted on a portable sled at the height ofapproximately 1.5 m from the snow surface which resulted in(−6 dB) footprint dimensions of approximately 1.5 by 1.5 m.Radiometers were calibrated with a two-point calibration

TABLE ISUMMARY OF REFERENCE RADIOMETER CHARACTERISTICS

technique using microwave-absorbing material (warm point)liquid nitrogen (cold point) before and after the campaign.Calibration drift was estimated to be approximately ±8 K at6.9 GHz, ±2 K at 19 GHz, < 1 K at 37 GHz, and ±4 K at89 GHz, which, given the limited opportunities for calibrationdue to the logistical complications of deployment in theCanadian sub-Arctic, are considered acceptable uncertaintyvalues for the EC measurements.

The radiometer data from Sodankylä are dual-polarizationobservations at 18.7-, 36.5-, and 94-GHz channels of theHUTRAD system. The radiometer was mounted on an ∼8-mtower, with antennas pointing to the chosen study area ofapproximately 5 × 5 m at an incidence angle of 55◦. TheHUTRAD system was calibrated twice per day with a techniquesimilar to the EC radiometers. Calibrations were timed tocoincide with AMSR-E/Aqua (Advanced Microwave ScanningRadiometer) overpasses of the test area, in order to enablelater comparison with satellite data. A total of 14 calibratedobservations were made. Although the HUTRAD system wasset to measure a continuous time series, the observations usedin this study represent averaged values within ±10 min fromcalibrations in order to ensure data quality. A summary ofcharacteristics of reference radiometer instrumentation is pre-sented in Table I. Sensitivity and accuracy values representvalues within the indicated integration time and directly aftercalibration.

B. Ground Reference

Snowpit observations at the Canadian sites consist of a bulkdepth and density measurement of the snowpack, density profilemeasurements, and snowpack stratigraphy observations. Den-sity values were measured using a wedge-shaped density cutter,with the density profile measured in 10-cm increments. Snowlayering was determined visually, with grain size estimatesmade for each layer by examining grains on a visual referencegrid. Temperatures were recorded at ground level, in the centerof the snowpack, and at ∼2 m above the ground level. An


Fig. 3. Observed snowpack layering, grain size, and density profiles at NWT sites. Sites 4, 5, and 6 are tundra lake sites; remaining sites are tundra. Locationsof ice lens are indicated with thickened horizontal lines. Numbers to the right of each layer correspond to grain size (in millimeters), density (in grams per cubiccentimeter), and temperature (in degree Celsius).

ice lens was observed at all sites, with some sites having ashallow layer of new snow on top of the lens. The snowpitmeasurements are summarized in Fig. 3.

The number of observed snow layers varied between two andfour, not including the ice lens. Observed grain sizes averagedfrom typically 0.5 mm in the top layers to 5 mm in the bottomlayers. The density values shown in Fig. 3 for each layer rep-resent averages of the density profile results applicable to eachlayer. Snow density typically increased from 0.3–0.34 g/cm3

in the top layers to 0.35–0.48 g/cm3 in the layers above depthhoar, with the hoar layer density values typically lower thanthis. These relatively high density values are typical of sub-Arctic tundra snow due to the prevalence of wind slabs withinthe snowpack.

The test area at the Sodankylä site is typical of the borealforest/tundra transitional zone, dominated by open canopyconiferous forests. Although no vegetation is present in theactual test area or the radiometer footprint, the surroundingvegetation is likely to have influenced the formation of thesnowpack so that it is representative of a typical snowpack ina sparse boreal forest (no wind slabs) rather than a open area(e.g., the Canadian tundra sites), where wind strongly affectsthe snowpack formation. Conditions during the measurementswere characterized by low temperatures and clear weather untilMarch 10th, after which air temperatures rose quickly to justbelow or even above zero during daytime. By the end of thecampaign, temperatures dropped again to a few degrees belowfreezing point.

Ancillary snowpack measurements were made in the im-mediate vicinity of the test area, consisting of snow depth,SWE, vertical structure, temperature profile, snow grain sizeprofile, and density profile measurements. A measurement trackof approximately 20 m, situated 5–10 m from the test area,was designated. A 1–2-m section of snow from the track wasremoved each time before establishing a new measurementpoint (snowpit). A total of 18 snow pit measurements weremade, all during daytime.

Snow depth was determined using a simple manual measure-ment tool. Ground-level variation in the test area was fairlysmall (±10 cm, determined during summer), so snow depthmeasurements are considered representative of the test areato this degree of accuracy, barring variations in the snowpackitself. The test area snow depth was also measured from thesnowpack directly in the radiometer footprint at the end ofthe campaign from several points, when the test involvingremoval of snow layers was performed. Snowpack SWE wasestimated by taking a snow core volume weighed using a stan-dard snow scale. The snowpack density profile was measuredin 10-cm increments using the snow fork measurement tool[33]. Comparing density values between the average snow scalemeasurement and those measured with the snow fork indicatesthat scale values exceed the average value measured by thesnow fork. The bias of error between the density measured withthe snow scale and the weighed average density is 0.04 g/cm3.This bias is possibly due to a calibration bias in the snowfork instrument. When used as model inputs, the value of0.04 g/cm3 is added to all density profile values to compensatefor the bias.

Snow layering was determined visually. Values for mini-mum, maximum, and “typical” grain size in each layer weredefined using a visual reference grid. Digital photographs ofthe snow grains were used for verification, quality control,and reanalysis of the measurements. Measured snow layering,observed average grain size, and density are shown in Fig. 4.

In the Sodankylä data, the total amount of observed distinctlayers in the snowpack varies between four and nine. Snowpitmeasurements occurred very close to each other (less than 2 m),and it is difficult to determine whether the large variation inlayering was due to interpretation errors or true variations in thesnowpack. Some common features can be observed, however,at least for the period of dry snow. First, a bottom layer of20–40 cm, consisting of large coarse grains, is identified in allthe observed snowpits. This layer was clearly discernible, andthe results can be used as an indication of the local variability in


Fig. 4. Observed snowpack layering, grain size, density, and temperature profiles in Sodankylä, Finland, from 5th to 9th of March 2008 (dry snow period).Numbers to the right of each layer correspond to grain size (in millimeters), density (in grams per cubic centimeter), and temperature (in degree Celsius).

depth of the lowest layer. Similarly, all observations agree witha surface layer with small average grain sizes (0.2–1 mm), albeitwith varying depth. The amount and structure of intermediatelayers vary the most; this may then be due to both variations inthe snowpack itself and observation uncertainties.

A final snowpit measurement was made in the radiometer’sfield of view on March 13th. This would have been the idealmeasurement to determine snowpack structure during the cam-paign; however, the period of wet snow lasting several days,with refreezing occurring at night, is thought to have affectedthe snowpack structure so that the results are not representativeof the dry snow period before March 10th.

IV. MODEL ANALYSIS

A. Canadian Observations

The Canadian (NWT) sites represent highly variable snowand terrain conditions, with SWE values ranging from 70 mmat wind-scoured sites to almost 300 mm in depositional areas.Sites 4, 5, and 6 are lake ice sites. Here, the one layer model isapplied as in [34], thus simulating actually a two-layer situationwith ice covered by a homogenous snowpack. The remainingsites are tundra, with varying underlying ground vegetation.The model simulations are focused on the situation where theice lens covering the snowpack was manually removed. One-layered results particularly at H-pol deteriorate significantlydue to the effect of the ice lens that can obviously not be cap-tured with a single-layer model, so comparisons of simulationswith the lens removed capture more typical snow conditions.Moreover, the observed lens thickness was of comparable sizeto the wavelength at 6.9 and 19 GHz. Due to this, it is prob-able that coherent effects in layer interactions influenced theobservations, undetected by the incoherent approach used bythe HUT model. Comparisons to simulations at some of thesites using a coherent model seem to support this [32]. Resultsfor model errors, compared to observed values, are summarizedin Table II.

The simulation results presented in Table II represent thesites as arranged by their measured SWE values, from smallestto largest. Fig. 5 shows the model errors at each site andfrequency for both one- and multiple-layer models. The modelimprovement is also presented in terms of change in the esti-mate bias at each site, when using the two versions of the HUTmodel.

From Fig. 5, the multiple-layer adaptation can be seen toparticularly reduce the higher frequency errors for tundra siteswith large SWE values (sites 7–10). The errors of individualsites at 89 GHz are improved by 11–25 K (representing animprovement of 30%–55% to the one-layer model error) forboth H and V polarizations. The results at 37 GHz improvesimilarly by 1–25 K (or by 27%–96% of the one-layer modelerror), with the exception of V-pol at site 7. The results forthe lower frequencies deteriorate, albeit very slightly, in almostall of these cases. Because the snowpack becomes increasinglytransparent at these frequencies, a minimal effect of addingsnow layers was expected. Results for tundra sites with shallowsnow (sites 1–3) are less conclusive; only the 89-GHz channelat site 3 is significantly improved at both polarizations. Thefirst site, with the least snow, shows deterioration in model-ing accuracy on all channels above 6.9 GHz when using themultiple-layer adaptation; this may be an indication that thelayering effects are overemphasized by the model for shallowsnowpacks. For deep snow, effects of interlayer reflections aredampened by the generally larger attenuation.

It should be noted that, for the lake ice sites (4, 5, and 6),model errors are fairly large using both versions of the model.This may indicate that the ice layer is not properly simulatedby the simplification in (3). The applied equation is intendedto be valid for pure (“black”) ice, whereas in natural lakes,a large part of the ice can be a surface layer of “white” iceformed partly by slushing events at the base of the snowpackon top of the ice. Should the dielectric constant of the whiteice layer be determined reliably, however, it can be included inthe simulation. Notably, the lowest 6.9-GHz frequency shows


TABLE IISIMULATION ERRORS USING MULTIPLE-LAYER HUT SNOW EMISSION MODEL AT CANADIAN SITES 1–10, AFTER REMOVAL OF SURFACE ICE LENS.

BIAS, RMS, AND UNBIASED RMS ERRORS OF ALL SITES, USING MULTIPLE- AND SINGLE-LAYER MODELS

Fig. 5. Bias errors ΔTB of all frequencies for ten sites in the Canadian NWT. (Above) One-layer model errors and (middle) errors of multiple-layer adaptation.(Below) Modeling absolute bias error improvement in kelvins. Positive values represent a decrease, and negative values represent an increase of absolute biaserror. (Left) Vertically polarized channels and (right) horizontally polarized channels.

large errors on both polarizations for the completely frozenlake sites 5 and 6. These errors may also be related to thesimulation of emission from the ground layer [27]; the input

values for ground surface roughness and the complex dielec-tricity of frozen ground are determined as 3 mm and 6 − 1 ∗ j,respectively. These are empirical constants traditionally used


TABLE IIIBIAS, RMS, AND UNBIASED RMS ERRORS OF ALL CANADIAN NWT SITES USING MULTIPLE- AND

SINGLE-LAYER MODELS, INCLUDING SURFACE-LAYER ICE LENS

Fig. 6. Change of absolute value of bias error in kelvins, when simulating a situation with ice lens on top of the snowpack. Difference between one- andmultiple-layer models. Positive values represent a decrease of error, and negative values represent an increase.

with the HUT model if an in situ measurement is unavailable[14], [15], [17]. These may cause increasing errors particularlyat lower frequencies which are more influenced by the groundsurface than the snowpack.

Modeling improvement in the presence of the ice lens atthe NWT sites is also presented in Table III and Fig. 6. Theeffect of the ice lens is also discussed in [32]. The effect ofthe ice lens on horizontally polarized simulations is clearlydiscernible. As the one-layer model does not simulate the icelens in any fashion, resulting errors at H-pol are significantlylarger than those presented in Table II. Vertically polarizedchannels exhibit similar improvement as is the case withoutthe lens. Use of the multiple-layer model reduces these errorsin almost all cases, as shown in Fig. 6 (with the exception of6.9 GHz), but the absolute rms errors for H-pol are still largerthan that for the situation without the lens at all frequencies.

Scatterplots of the NWT site simulations for snowpackswhere the ice lens has been removed are shown in Fig. 7. Theseplots demonstrate the significant improvement in the brightnesstemperature simulations at certain sites, particularly at 37 and89 GHz. Lower frequencies are less affected, but the deteriora-tion of the simulation seen at some sites is small in the contextof the measured brightness temperature values (also in Fig. 5).

Fig. 8 shows the same scatterplot image but for the undis-turbed snowpack, i.e., the situation where the ice lens wasnot yet removed. Results with V-polarizations, less affectedby the lens, are comparable to those in Fig. 7. The effect ofthe lens on one-layer simulations is, however, clear at H-pol;simulated values using the one-layer model overestimatebrightness temperature in several cases as the effect of thelens cannot be captured by the single-layer simulation. By

using the multiple-layer model, results are visibly less scattered.However, the model still does not capture the dynamic rangeof observations particularly at 6.9 GHz. This was also seen inFig. 6 as increased error at 6.9-GHz H-pol at six out of tensites. Some of this error may be attributed to the omission ofcoherence effects by the HUT model or to the uncertaintiesrelated to simulation of ground surface emission, as discussedpreviously. There was also a large uncertainty in the 6.9-GHzradiometric observations, due to the observed calibration driftof 8 K. However, observations comparing the undisturbedsnowpack to the situation where the ice lens has been removedshow that the lens has a consistent effect also on 6.9 GHz atalmost all sites, with the lens causing a drop of up to 20 K inobserved brightness temperature for H-pol.

B. Time Series Observations

The time series of HUTRAD observations from theSodankylä site is shown in Fig. 9. The start of snowmelt is clear-ly seen as a rise in brightness temperature after March 10th.Also shown are the HUT model estimations, using the multiple-layer adaptation. Model estimates are from the precise time ofthe ground observations, which do not always coincide exactlywith radiometer measurements. Note that no ground measure-ments were made during the night-time AMSR-E overpass,although the radiometers were calibrated. Wet snow was sim-ulated by applying a snow moisture value of 0.5% to any layerwith a physical temperature above −1 ◦C. While this is a highlysimplistic approach, it bears no further consideration here asthe analysis is focused on dry snow conditions. Fig. 9 shows ageneral overestimation at the lowest measured frequency, i.e.,


Fig. 7. Scatterplot images of measured versus simulated brightness temperatures at all NWT sites. (Top row) One-layer and (bottom row) multiple-layer models.

Fig. 8. Scatterplot images of measured versus simulated brightness temperatures at all NWT sites. Same as in Fig. 7, but including the effect of ice lens.

18.7 GHz, throughout the dry snow period. This is partly due tothe setting of ground surface roughness (3 mm), which shouldbe considered an empirical parameter and does not relate toany actual observation. More importantly, the model is unableto simulate the clear rise in brightness temperature betweenMarch 5th and March 10th at 18.7-GHz H-pol. The observedincrease is on the order of 20 K. Some increase in simulationscould be expected due to the general rise in physical tempera-ture, but this is not obvious from the results. Clearly, some otherphenomena not captured by the in situ measurements, and thusignored in the simulations, affected the observations.

The highest frequency (94 GHz), in turn, is generally under-estimated. It should be noted that atmospheric effects affect theresults at 94 GHz significantly. In this study, the principal com-ponent atmospheric model described in [35] is applied, withconditions set to simulate a 20% opaque atmosphere. This isalso largely an empirical setting and greatly affects the absoluteerror at 94 GHz (and also 89 GHz in the case of the NWT sites).For intercomparison of the two model versions, however, it is oflittle effect since both versions of the HUT model use the samemethod for simulating atmospheric effects, with the exceptionof reflectivity calculation described in Section II-C.


Fig. 9. Time series of modeled and observed brightness temperatures from 5th to 12th of March 2008 at FMI-ARC Sodankylä site. Model values calculatedusing the multiple-layer adaptation. Dry snow conditions before March 10th. Night-time observations (calibrations) on March 8 and 12 were not considered dueto technical reasons. Two 36.5-GHz H-pol observations between March 10 and 11 are likewise lacking due to a technical failure.

TABLE IVBIAS, RMS, AND UNBIASED RMS ERRORS USING MULTIPLE- AND SINGLE-LAYER MODELS. SODANKYLÄ TIME SERIES (DRY SNOW PERIOD)

Snowpack conditions during the dry snow period betweenMarch 5th and 10th can be considered to have remained stable,in the sense that no significant snow accumulation occurred,and uncertainties related to determining snowpack stratigraphyand grain size remained the same. Considering this, the five-dayperiod of measurements can be used as an indication of modelperformance and applicability in the prevailing conditions as awhole. The deviation of all simulation values (not including wetsnow) compared to observations is summarized in Table IV, aswell as the bias error, rms error, and unbiased rms error valuesof the comparisons using both the original and the modifiedmodel. Each radiometer observation is compared to the modelsimulation of the temporally closest snow pit measurement.Snow layer and ground temperatures are set according to auto-mated weather station observations at the time of the referenceobservation; the simulated values used in Table IV thus deviateslightly from those simulated directly from snowpit measure-ments (Fig. 9). Other snowpack parameters are assumed to haveremained stable.

In Fig. 10, the performances of the original one-layer modeland the multiple-layer adaptation are compared. Model im-provement is defined here as the difference of the errors ofthe two models, expressed as a percentage of the originalmodel error. Negative values thus represent a decrease in modelaccuracy, and positive values represent an increase. Both the

bias and rms errors increase on the 18.7-GHz channels, whileimprovement is seen at 94 GHz and the vertically polarized36.5-GHz channel. Unbiased rms values, however, improvealso for 18.7 GHz.

In terms of SWE, the prevailing snow conditions inSodankylä were similar to those at NWT sites 2 and 3. Again,similar behavior of the modeling results can be seen, withsome improvement observed at higher frequencies and alsoindeterminate or deteriorating values at lower frequencies whenapplying the multiple-layer model. This is a further indicationthat the use of the multiple-layer adaptation may not properlysimulate interlayer effects at low frequencies, at least with thetype of in situ data available here.

V. CONCLUSION

This paper has presented a new modification to the HUTsnow emission model, which enables the model to deal withmultiple layers of media, each with different scattering and ab-sorption characteristics. The modified model was tested againstin situ data and reference radiometer measurements collected atsites in Canada and Finland by two different research groups.The new multiple-layer model was compared to the originalone-layer model using data from both countries. The firstdata set was collected at several tundra sites in the CanadianNWT, including on frozen tundra lakes. Here, the use of the


Fig. 10. Change of modeling errors, comparing one- and multiple-layermodels with HUTRAD observations on 5th–10th of March 2008. (Above) Biaserror, (middle) rms error, and (below) unbiased rms error. Errors expressedas error change in percentage from the one-layer model (negative value =decreased accuracy, positive value = increased accuracy).

multiple-layer model was seen to decrease the modeling rmserrors by 6%–38% on horizontally polarized channels and1%–38% on vertically polarized channels, depending on fre-quency. Generally, higher frequencies and sites with the largestSWE values showed the highest level of improvement. Thedecrease in error is under 5% of the observed value in allcases, but this, at some sites, represents an improvement ofover 10 K, which already has a significant impact on modelinversion of SWE from observations. For some sites withshallow snowpacks, modeling accuracy was decreased whenmultiple layers were considered. The highest increase in errordetected was 6 K. These values represented a situation where anice lens, formed on top of the snowpack by a rainfall event, hadbeen manually removed. Model improvement in the presenceof the ice lens was more pronounced for H-pol, and of similarmagnitude for V-pol. However, performance of the HUT modelwas generally weaker than that in the case without the lens,also when using the multiple-layer model. Some of this maybe attributed to the omission of coherence effects in the model,particularly on the lower frequencies. A comparison study witha coherent model supports this assumption [32].

A second data set was collected at one site at the FMI-ARC satellite calibration/validation site in Sodankylä, Finland.Measurements were made over eight days, with radiometercalibrations occurring twice a day. Of the time series, five dayswere in dry snow conditions. The bulk snow conditions at

Sodankylä were comparable to the NWT sites with intermediatelevels of SWE (100–150 mm), although the vertical propertieswere different as the NWT data represent tundra snow (stronglywind influenced) and the Sodankylä data represent boreal snow.For the Sodankylä data, the use of the multiple-layer modelinduced a significant increase in rms error at the lowest fre-quency of 18.7 GHz. However, the higher frequencies showedan improvement with the exception of one channel (36.5-GHzH-pol). The rate of improvement and the differences betweenthe traditional one-layer model and the new multiple-layeradaptation were comparable to those observed in the NWT siteswith similar snow conditions.

The results of this study show that the simulation of multiplelayers of snow can be used to improve estimations of snowpackbrightness temperature of the HUT snow emission model, par-ticularly for deep snowpacks where the accuracy of the originalmodel deteriorates. If applied to a practical inversion scheme(e.g., the assimilation method described in [17]), together witha thermodynamic model predicting snow states, the new modelcould be applied to potentially further improve retrieval of snowproperties from satellite-based passive microwave data. Onefurther potential application is the inclusion of simulation ofsnow-covered lake ice, which significantly decreases estimationaccuracy for lake-rich areas. Future studies will focus on theseissues; further performance comparisons with other multiple-layer snow models such as MEMLS will also be carried out.

APPENDIX A

The flux of up- and downwelling emissions for each layerof a system of snow layers is solved. The wanted result is theupwelling emission from the topmost layer N .

By adopting the following notations for layers from top tobottom

x1 = TN,↑x2 = TN,↓. . .

x2N−1 = T1,↑x2N = T1,↓ (9)

(6) and (8) for N layers can be expressed with a linear systemof equations so that

a11x1 + a12x2 + · · · + a1,2Nx2N = b1

a21x1 + a22x2 + · · · + a2,2Nx2N = b2

. . .

a2N1x1 + a2N2x2 + · · · + a2N,2Nx2N = b2N . (10)

In order to solve xn, the terms ajk and bj in (10) are expressedusing a 2N ∗ 2N matrix A and vector b of length 2N , so that

A =

⎡⎢⎣

a11 a12 . . . a1,2N

a21 a22 . . . a2,2N

. . . . . . . . . . . .a2N1 a2N1 . . . a2N,2N

⎤⎥⎦ b =

⎡⎢⎣

b1

b2

. . .b2N

⎤⎥⎦ . (11)

Then, solving the determinants of A according to Cramer’s rule,we get

xn =det(An)det(A)

(12)


where An is obtained by replacing the nth column of A with b.By using (6) and (8) and inserting the downwelling sky

brightness temperature Tsky,↓ and the upwelling ground bright-ness temperature TGND,↑ to (11), we get

A=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

1 0 SNtN−1lN

0 . . . . . . . . . 00 1 SN

tN−1·rN

l2N

0 . . . . . . . . . 0. . . . . . 1 . . . . . . . . . . . . . . .0 . . . Sn

tn·rn−1l2n

1 0 Sntn−1ln

. . . 0

0 . . . Sntn

ln0 1 Sn

tn−1·rn

l2n. . . 0

. . . . . . . . . . . . . . . 1 . . . . . .0 . . . . . . . . . 0 S1

t1·rGNDl21

1 0

0 . . . . . . . . . . 0 S1t1l1

0 1

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(13)

where tn, rn, ln, and Sn are the Fresnel transmission andreflection coefficients, the loss factor, and the geometric sumof multiple reflections of layer n, respectively. Similarly

b =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

SN

(TSNOW,N

(1 + rN−1

lN

)+ TSKY

tN ·rN−1

l2N

)SN

(TSNOW,N

(1 + rN

lN

)+ TSKY

tN

lN

). . .

Sn

(TSNOW,n

(1 + rn−1

ln

))Sn

(TSNOW,n

(1 + rn

ln

)). . .

S1

(TSNOW,1

(1 + rGND

l1

)+ TGND

tGNDl1

)S1

(TSNOW,1

(1 + r1

l1

)+ TGND

tGND·r1l21

)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

.

(14)

The upwelling emission x1 = TN,↑, reduced to above layer N ,is then

TB,UP = tNx1 = (1 − rN )det(A1)det(A)

. (15)

ACKNOWLEDGMENT

The authors would like to thank K. Asmus, W. Strapp,and A. Walker of Environment Canada for the support of theground-based radiometer measurement program and alsoA. Silis, P. Toose (Environment Canada), M. English (WilfridLaurier University), R. Kelly, and C. Duguay (University ofWaterloo) for providing field assistance. The authors would alsolike to thank B. Reid (Indian and Northern Affairs Canada) forproviding meteorological observations at Daring Lake and thestaff at FMI-ARC Sodankylä station for their assistance withfield measurements.

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[33] A. Sihvola and M. Tiuri, “Snow fork for field determination of the densityand wetness profiles of a snow pack,” IEEE Trans. Geosci. Remote Sens.,vol. GRS-24, no. 5, pp. 717–721, Sep. 1986.

[34] A. Kontu, S. Kemppainen, J. Lemmetyinen, and J. Pulliainen, “Deter-mination of snow water equivalent on lake ice from passive microwavemeasurements,” in Proc. IGARSS, Boston, MA, 2008.

[35] J. Pulliainen, J.-P. Kärnä, and M. T. Hallikainen, “Development of geo-physical retrieval algorithms for the MIMR,” IEEE Trans. Geosci. RemoteSens., vol. 31, no. 1, pp. 268–277, Jan. 1993.

Juha Lemmetyinen received the M.Sc. (Tech.) de-gree from the Helsinki University of Technology(TKK), Espoo, Finland, in 2004.

From 2004 to 2008, he was a Researcher with theTKK Laboratory of Space Technology and the De-partment of Radio Science and Engineering, TKK,specializing in radiometer calibration techniquesand remote sensing. He is currently a Scientist inArctic Research at the Finnish Meteorological In-stitute, Helsinki, Finland. His current research inter-ests include applications of microwave radiometers,

radiative transfer modeling, and remote sensing of snow.

Jouni Pulliainen (S’91–M’95–SM’03) received theM.Sc., Licentiate in Technology, and the Doctor ofScience in Technology degrees from the HelsinkiUniversity of Technology (TKK), Espoo, Finland,in 1988, 1991, and 1994, respectively.

From 1993 to 1994, he was the Acting Directorof the Laboratory of Space Technology, TKK. From2001 to 2006, he was a Professor of space technol-ogy with TKK, specializing in remote sensing. Heis currently a Research Professor with the FinnishMeteorological Institute, Sodankylä, Finland, where

he is the Head of the Arctic Research Center. His research interests includedirect and inverse modeling in remote sensing, and, additionally, remote sensingdata assimilation and application development, e.g., for the needs of climatechange investigations. Recently, his work has focused on the active and passiveremote sensing of boreal forests and snow cover applying both microwaveand optical data (including atmospheric correction). He has been a PrincipalInvestigator or Project Manger for several nationally funded and interna-tional research projects, including several European Space Agency (ESA) andEuropean Commission contracts. He has authored about 250 scientific papersand technical reports in the field of remote sensing.

Dr. Pulliainen was a member of the ESA Advisory Committee on Education(2001–2007). He is also a member of the ESA CoreH2O MAG.

Andrew Rees received the B.Sc. degree in geography and environmentalscience from Nipissing University, North Bay, ON, Canada, in 2000 and theM.Sc. degree in geography from the University of Calgary, Calgary, AB,Canada, in 2003. He is currently working toward the Ph.D. degree in geographyat Wilfrid Laurier University, Waterloo, ON.

He is also currently a Contract Faculty Member with the Department ofGeography, Nipissing University. His research activities are currently focusedon investigating Canadian tundra snow cover distribution and properties usingin situ snow measurements and multiscale remote sensing observations.

Anna Kontu was born in Espoo, Finland, in 1981.She received the M.Sc. (Tech.) degree from theHelsinki University of Technology (HUT), Espoo,in 2006, where she is currently working toward theD.Sc. (Tech.) degree.

From 2005 to 2006, she was a Research Assistantwith the Laboratory of Space Technology, HUT,where she worked on her Master’s thesis on thetesting of the Soil Moisture and Ocean Salinity satel-lite calibration system. Since 2006, she has been aResearch Scientist with the Arctic Research Center,

Finnish Meteorological Institute, Sodankylä, Finland. Her current researchinterests include remote sensing of snow and microwave radiometry.

Yubao Qiu received the M.S. degree in earth probingand information technology from the China Univer-sity of Geosciences, Wuhan, China, in 2003 and thePh.D. degree in cartography and geographic infor-mation systems from the Institute of Remote SensingApplication, Chinese Academy of Sciences (CAS),Beijing, China, in 2008.

From 2003 to 2006, he was an Assistant Lecturer/Researcher with the Institute of Mathematical Ge-ology and Remote Sensing, China University ofGeosciences, performing research and development

activities in the field of mathematical geology and remote sensing. From2007 to 2008, he was with the Laboratory of Space Technology, HelsinkiUniversity of Technology, Espoo, Finland. As a part of his work, he took part infield activities at the Arctic Research Center, Finnish Meteorological Institute,Sodankylä, Finland. He is currently an Assistant Researcher with the Centerfor Earth Observation and Digital Earth, CAS. His current research activitiesconcern microwave remote sensing and snow/ice work.

Chris Derksen received the B.E.S. degree in geography and the M.A. andPh.D. degrees from the University of Waterloo, Waterloo, ON, Canada, in 1997,1998, and 2001, respectively.

He is currently a Research Scientist with the Climate Research Division,Science and Technology Branch, Environment Canada, Toronto, ON, and holdsadjunct faculty positions with the Department of Geography and EnvironmentStudies, Wilfrid Laurier University, Waterloo, and the Department of Geog-raphy and Environmental Management, University of Waterloo. His researchactivities focus on remote sensing of terrestrial snow cover and the use ofsatellite-derived data sets to identify interactions between the climate systemand the cryosphere.

Multiple-Layer Adaptation of HUT Snow Emission Model: Comparison With Experimental Data

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Multiple-Layer Adaptation of HUT Snow Emission Model: Comparison With Experimental Data