FMCW radars for snow...

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nology 52 (2008) 118–131www.elsevier.com/locate/coldregions

Cold Regions Science and Tech

FMCW radars for snow research

Hans-Peter Marshall a,b,⁎, Gary Koh a

a Cold Regions Research and Engineering Laboratory, Hanover, NH, United Statesb Institute of Arctic and Alpine Research, University of Colorado at Boulder, 1560 30th St., Campus Box 450, Boulder, CO 80309, USA

Received 3 November 2006; accepted 16 April 2007

Abstract

Frequency Modulated Continuous Wave (FMCW) radars have been used by snow scientists for the past 30 years. This radartechnology provides a promising alternative to point measurements, as properties such as snow depth can be measured quickly and non-destructively. Recent advances in microwave FMCWradar technology have resulted in lightweight, portable instrumentation. This is incontrast to the early FMCWradar systemswhichwere often too heavy to cover large distances efficiently. These advanced FMCWradarsprovide snow scientists and hydrologists with the ability to map snow pack properties, such as depth, snow water equivalent (SWE) andstratigraphy, rapidly over large distances, at high resolution. We discuss the development of FMCW radar over the past 30 years andreview the diverse applications of these radars by snow scientists.© 2007 Elsevier B.V. All rights reserved.

Keywords: Snow depth; Snow stratigraphy; Instrumentation; Radar; Snow hydrology; Remote sensing; Snow water equivalent; Spatial variability

1. Introduction

Snow pit characterization is a fundamental procedurefor investigating snow cover properties and processes(e.g. Pielmeier and Schneebeli, 2003). However, snowpits are time consuming and represent only pointcharacterizations of snow properties. Extrapolating fromthese measurements is difficult, due to the large degree oftemporal and spatial variability that most snow coversexhibit (e.g. Sturm and Benson, 2004). The potential ofground-based radar technology for monitoring the spatialand temporal variability of snow cover properties has longbeen recognized by the snow science community, since

⁎ Corresponding author. Institute of Arctic and Alpine Research,University of Colorado at Boulder, 1560 30th St., Campus Box 450,Boulder, CO 80309, USA. Tel.: +1 303 859 3106; fax: +1 303 492 6388.

E-mail address: [email protected] (H.-P. Marshall).

0165-232X/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.coldregions.2007.04.008

these kinds of measurements are non-destructive, and canbe taken automatically and very quickly. Over the past30 years, numerous studies on radar-snow cover interac-tions have been conducted. Due to the contributions ofthese investigations, snow pit measurements supplemen-ted by ground-based radar technology is now recognizedas an important technique in snow cover research.

Various radar waveforms (impulse, step-frequency,FMCW) have been used to investigate snow packproperties. For example, commercially-available impulseradars are currently used operationally in Scandinavia'sdeep snow packs (e.g. Sand and Bruland, 1998; Lundberget al., 2000) and snow pack studies have been performedon glaciers (e.g. Harper and Bradford, 2003). Radarvertical resolution is inversely proportional to bandwidth(see Appendix). Pulsed radars, with a maximum band-width of approximately 2 GHz, have a vertical resolution(N6–8 cm) which makes it difficult to accurately

mailto:[email protected]://dx.doi.org/10.1016/j.coldregions.2007.04.008

119H.-P. Marshall, G. Koh / Cold Regions Science and Technology 52 (2008) 118–131

measure shallow snow depths or detailed sub-seasonalstratigraphy. One advantage of the FMCW radarwaveform is the wide bandwidth (4–10 GHz) that canbe achieved at a moderate cost, resulting in a verticalresolution of 1–3 cm.

This paper reviews the history of FMCW radarresearch by the snow science community. We firstpresent the theory of FMCW radar operation, and thenpresent a historical review of important studies leadingto the current status of FMCW radars for snow research.These studies, along with recent advances in microwaveFMCW radar technology, have resulted in lightweight,portable instrumentation with high vertical resolution.These characteristics are essential for investigating snowcover properties such as depth, stratigraphy and snowwater equivalent, rapidly and over large distances.

An example of an FMCW radar profile from theauthors' lightweight portable system is shown in Fig. 1,illustrating the large spatial variability in snow depth andlayer thickness that can occur over short distances.Accurate characterization of this kind of snow packvariability requires measurements that can be takenrapidly, such as those that can be made with radar andother automated instruments.

2. Theory of FMCW radar

A Frequency Modulated Continuous Wave (FMCW)radar transmits a periodic signal whose frequency FT(t)varies linearly with time

FTðtÞ ¼ Flow þ BwPL t ð1Þ

where Bw is the bandwidth, Flow is the low frequency,and PL is the pulse length of the transmitted signal. Thepulse length PL is chosen such that the signal contains

many cycles (PL≫1

FTðtÞ). In addition, this pulse length ismuch larger than the two-way travel time T to the mostdistant reflector (PL≫Tmax).

For the simple case of only one reflector a distance zfrom the radar, the received signal also has a frequencyFR(t) which varies linearly with time

FRðtÞ ¼ Flow þ BwPL ðt þ TÞ

¼ Flow þ BwPL t þz2v

� �ð2Þ

where T is the two-way travel time to the reflector, z isthe distance to the reflector, and v is the velocity of thesignal. Fig. 2 shows the frequency of both thetransmitted and received waves as a function of time.

Note that the two-way travel time T is linearly related tothe frequency difference ΔF between the two signals,which is constant over the pulse length PL. AwindowedFast-Fourier Transform (FFT) is used to transform thesignal into the frequency domain, where the frequencydifference can be used to measure the two-way traveltime and the electrical distance to a given reflector.Details are given in the Appendix, and the formulation isextended to multiple reflectors. The range resolution andantenna footprint of an FMCW radar are also discussed.

3. Historical review of FMCW radar measurementsin snow

The first use of FMCW radars for snow research wasreported in a series of papers by Ellerbruch et al. (1977),Boyne and Ellerbruch (1979) and Ellerbruch and Boyne(1980). They used an X-band (8–12 GHz) FMCW radarto investigate the relationship between the electromag-netic and physical properties of snow packs. Theyconducted multiple experiments over several snowseasons using a downward-looking FMCW radarmounted on various platforms and an upward-lookingradar buried in the ground. Fig. 3 illustrates an early use ofFMCW radar over a snow pack. These radar backscattermeasurements as a function of snow pack depth werecorrelated with snow properties such as density, hardness,stratigraphy, and moisture content. They were the first todemonstrate that an FMCW radar could be used tomeasure the snow water equivalent (SWE) of a dry snowpack, provided that an independent measurement of snowdepth, ds, was available. Below we briefly review theSWE measurement procedure using FMCW radar asoutlined by Ellerbruch and Boyne (1980).

FMCW radar measures the transit time of themicrowave signal in the snow pack. This transit time isproportional to the electrical depth of snow, ds

ffiffiffiffies

p. In

other words, it is possible to measure εs using FMCWradar if an independent measurement of ds is available.For a dry snow pack, a two-component model can be usedto express snow depth, ds=di+da, where di and da are thedepth of solid ice and air, respectively. The electrical depthof snow can be expressed as ds

ffiffiffiffies

p ¼ di ffiffiffieip þ da ffiffiffiffieap ,where εi=3.17 and εa=1 are the dielectric constant of iceand air, respectively. This is equivalent to the well-knowncomplex refractive indexmethod (CRIM), which assumesthat the complex refractive index of a mixture is equal tothe volumetric sum of the complex refractive indices of allthe components (e.g. Wharton et al., 1980; Shen et al.,1985).

The expression for the snow electrical depth(obtained using FMCW radar) can be easily solved for

Fig. 1. Example profile from a portable FMCW radar. Red represents a strong reflection, blue represents no reflection. On the left side of the image,the snow surface can be seen at a depth of 70 cm, and the ground at 170 cm. The snow depth varied from more than 1 m to less than 30 cm in adistance of less than 30 m. The two obvious surface indentations between 10 and 20 m are ski tracks perpendicular to the profile. (For interpretation ofthe references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2. Frequency vs time for a typical FMCW transmitted (solid line) andreceived (dashed line) waveform. Note that the frequency differenceΔF isconstant over the entire pulse lengthPL, and is proportional to the two-waytravel time to the reflector T.

120 H.-P. Marshall, G. Koh / Cold Regions Science and Technology 52 (2008) 118–131

di. SWE can then be determined by converting the depthof solid ice to depth of water equivalent. Conversely, itcan also be shown that FMCW radar can be used tomeasure ds provided that an estimate of mean snowdensity, ρs is available to estimate the snow dielectricconstant, εs.

Ellerburch and Boyne also conducted studies toinvestigate temporal changes in snow pack properties.They demonstrated that FMCW radar could be used tomonitor the freeze/thaw process in a snow pack, due tothe large contrast in dielectric properties of water and iceat microwave frequencies. They made continuous, static(stationary platform) radar backscatter measurementsover snow during a day when the temperature rose abovefreezing. From the changes in the surface reflection, theycalculated the change in the dielectric constant of thesurface snow as it experienced melt and an increase inliquid water content throughout the day. An example oftime series FMCW radar data illustrating the effect ofsurface melt–freeze on the radar measurement is shownin Fig. 4. They also made an attempt to infer snowproperties using FMCW radars. For example, they notedthat depth-hoar layers produce a noticeably stronger radarreflection that other layers in the snow pack. Many of theobservations reported by Ellerbruch and Boyne in theseearly studies have since been reproduced and refined bysubsequent FMCW radar investigators.

In the early 1980s Gubler and Hiller (1984) beganexperiments in alpine snow with an X-band FMCWradar and introduced the use of buried radars as a tool foravalanche research. By burying the radars just beneaththe soil in avalanche chutes and looking upward, theywere able to monitor the flow of avalanches as theypassed above the radars. This technique is still being

Fig. 4. Example FMCW radar traces from several different timesduring continuous static measurements, covering a 48 day period.Photo: Hal Boyne.

Fig. 3. Early FMCW radar system, Berthoud Pass, Colorado. Photo: Hal Boyne.


used today to investigate avalanche dynamics such assnow cover erosion, snow layer entrainment and flowheight. They also observed changes in reflectivity of thenear-surface layers during a day when temperatures roseabove 0 °C. They made continuous static measurementsat two sites for 1 full winter, and also performed spatialmeasurements from an over-snow vehicle. They notedthat horizontal microwave measurements in a snow pithad much greater range since the layers behaved aswaveguides, and suggested that this technique could beused to register fracturing and collapse within layers inan avalanche starting zone. Schmidt et al. (1984) usedFMCW radar to profile snowdrifts, as part of a blowingsnow study. Gubler and Weilenmann (1986) made staticmeasurements while removing layers sequentially fromthe surface, and also qualitatively compared FMCWradar measurements with ram and morphological pro-files. Gubler and Rychetnik (1991) presented FMCWprofiles that indicated significantly less snow layering inforest stands than in open fields.

Gubler and Hiller (1984) also began preliminaryanalysis of FMCW radar data acquisition and signalprocessing procedures to optimize the radar performance.They used an X-Band FMCW system (8–12.4 GHz), andused a pulse length of 0.0132 s but only sampled over0.0124 s, to avoid problems of linearity at the ends of theramp. They used 3 filters in the hardware: a high-passfilter to reduce 1/f noise, a low-pass filter to normalizesignal amplitudes from different distances, and anotherlow-pass filter (b25 kHz) to reduce noise from above themeasurement range. Processing FMCW data requiresperforming a Fourier transform, and therefore the win-dow chosen for this is important. They chose to use arectangular window to achieve maximum resolution(although they also tried Hanning and Flattop windows),

at the expense of spectral leakage (magnitude informationmay not be accurate).

They attempted to quantify the FMCW radarbackscatter from a static snow pack using varioussemi-empirical models of radar transmission andbackscatter from snow cover. They modeled the snowpack as layered material of varying densities and showedthat the power reflection coefficient R2 and powertransmission coefficient T2 =1−R2 are strongly depen-dent on the ratio of layer thickness d1 to wavelength λ.From a theoretical simulation, they find that ice layers(large dielectric contrast to snow) of 0.5 mm thicknessand buried surface hoar a few mm thick can be resolved.They discuss various dielectric mixing models, and findthat with a simple linear mixing model like that usedabove, for ρsb500 [kg/m

3] they can estimate meandensity Pqs to within ±5%. They state that if the non-

Fig. 6. Ice crust which formed on windy day, detected by FMCWradar.

Fig. 5. C Band FMCW radar built at National Hydrology ResearchInstitute in Canada. For scale, the blue electronics housing is23 cm×28 cm×33 cm. White focusing lenses, attached to bottom ofblue horn antennas, establish far-field geometry at closer than nominalfor the standard gain horns (Narda 3.95–5.85 GHz shown). Photo: M.Demuth. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)


linearities in the more complicated mixing equationswere important over the density range of interest, thenthe radar estimate of SWE would depend on the layeringof the snow pack.

The results of Gubler's work were incorporated bythe National Hydrology Research Institute in Canada todevelop a portable C/X-band FMCW radar for glacio-logical and snow accumulation studies (Demuth et al.,1993; Pomeroy and Gray, 1995). The radar featuredseveral innovations that improved system performanceand extended its utility in both static and traversingapplications (Fig. 5). System components, including theYIG oscillator, were assembled into an insulated andtemperature controlled housing, which, along with bat-teries and a collapsible boom was fitted to a back-packframe or a lightweight carbon-fiber sledge assembly.Focusing lenses, designed by Gubler, were included onthe ends of the horn antennas.

In the 1980s, Japanese researchers also began aprogram to develop an FMCW system for use in alpinesnow (Fujino et al., 1985a,b). They found the technique tobe fairly effective at non-destructively measuring andmonitoring stratigraphic features within the snow pack,but stated that there were many ambiguous points ininterpretation of the data. They used two different fre-quency ranges, L/C-Band (2–8 GHz) and X-Band (6–12 GHz), a pulse length of 10–100 ms, a single antenna(different from other experiments), and a transmittingpower of 40mW. They performed laboratory experimentswith glass beads and polystyrene foam, and chose thebandwidth, pulse length, and filter ranges to give the mostaccurate distance measurements with the highest resolu-tion. Theywere the first to discuss instrumentation-relatedsignals.

They performed an experiment in which they placedsome liquid water between two pieces of filter paper,and then increased the amount of liquid water whileobserving changes in the signal. The surface intensityincreased up to some saturation value, and the near-surface water masked the signal from the lower layersdue to strong attenuation within the liquid water. Thisgroup was also the first to place metal reflectors withinthe snow pack to identify surface, ground and internalinterfaces. They made static measurements at onelocation for 2 entire winters, and noted correlatingreflections with layer interfaces was difficult, so theyinserted metal mesh plates at layer boundaries. From thechange in location of the surface reflection, theycalculate the settlement of the snow pack, and fromthe change in location of the ground reflection, they cancalculate the change in mean dielectric constant. In thisway they can monitor SWE throughout the seasonwithout any manual measurements, however they didn'tmeasure appreciable change in SWE, only densification.


When the snow pack became wet, the change in liquidwater content (LWC) caused a change in the complex partof the dielectric constant, drastically increasing attenua-tion and therefore the ground reflection was no longerdetectable. Theywere the first to plot frequency differencefrom metal reflectors vs actual depth to see the velocityprofile, but did not use this tomake any calculations. Theypresented results of changes in reflection intensity every30 min for one day, and noted an increase in reflectivitywith an increase in LWC, which was confirmed with thecalorimetricmethod. They found that the snowpack depthcould be found with reasonable accuracy using justan average dielectric constant Pes , and noted that thechanges in signal intensity were not effected when thesystem parameters were changed. Their suggestedimprovements were to develop the relationship betweenphysical properties and the response of the system, as afunction of frequency, to develop theoretical models as afunction of simplified snow parameters, to adopt typicalvalues of the dielectric constant for wet and dry snowpacks (εws,εds), and to use a ram penetrometer instead ofmanual snow pits to make ground truth measurementseasier.

The most recent publication by the Japanese group(Sasaki et al., 1993) described the development of the firstportable lightweight FMCW system. It had a frequencyrange of 8–18 GHz, they used a saw-tooth wavegenerator, and a variable sweep period of 1–100 ms.Their system had an active high-pass filter, a program-mable gain amplifier, an amplitude limiter, and an anti-aliasing programmable low-pass filter. The powerrequired was 48 W, and they could run the unit for morethan 2 h. The total weight of the systemwas 11.0 kg. Theystated that the unit was used to ground truth satellite data,however no quantitative results were presented.

In January of 1990, Forster et al. (1991) mademeasurements of snow stratigraphy in the upper 6 m of asite at the Upstream B camp in West Antarctica with anX-Band FMCW radar. The strongest reflections werefrom the upper 3 m, from which reflections from pairs ofdepth-hoar/wind crust layers were identified. Theselayers were interpreted as the autumn/winter of one year,and therefore accumulation rates could be calculated.They also made measurements with one antenna rotated90° to observe cross-polarization returns, in which thelayer interfaces were all located at the same depth, butthe amplitudes were significantly smaller.

The next innovative use of FCMW radar for snowresearch was reported by Koh (1992) and Koh and Jordan(1995). They used high frequency millimeter waveFMCW radar (26.5–40 GHz) mounted on a gantryapproximately 6.0 m above the snow pack to investigate

near-surface processes during snowmelt. Air temperatureand incoming solar radiation are obvious indicators ofsnow wetness, however their FMCW studies revealednon-intuitive processes governing snowmelt. Koh (1992)measured radar backscatter at normal incident angle overa wet snow cover and observed an inverse relationshipbetween radar backscatter and wind speed on a warm day,and the radar backscatter amplitude surprisingly de-creased in the afternoon although temperatures wereabove 0 °C. The decrease in radar backscatter occurred asthe wind speed increased. He interpreted this result aswind affecting the heat transport, causing a decrease inLWC at the surface. The evaporative cooling of wet snowdue to wind has since been observed visually. Fig. 6shows a thin layer of ice that formed on the surface of thewet snow during a high wind event, while temperatureswere above 0 °C.

Following this study, Koh and Jordan (1995) used themillimeter wave FMCW radar to detect the onset of sub-surface melting in a seasonal snow cover. They demon-strated the ability of solar radiation to penetrate into asnow cover, which can lead to sub-surface temperaturemaximum. The onset of the sub-surface melting wasaccurately predicted using a mass- and energy-balancemodel for snow (SNTHERM) developed by Jordan(1991). This study was the first attempt to link mass-and energy-balance models of snow such as SNTHERMto predict the response of FMCW radar signatures. Theyconcluded that on calm, clear days when the airtemperature is near freezing, sub-surface meltingis likely to occur in low-density snow. Conditions thatlead to an increase or decrease of snow wetness are ofconsiderable interest to snow remote-sensing and ava-lanche formation.

Koh et al. (1996) made measurements at 3 differentfrequency ranges (C-, X-, and Ka-Bands) and showedthat a multiband approach is required for FMCWmeasurements in a wide range of snow pack conditions.This type of FMCW system was ideal for profilingstratigraphy, depth, SWE, and for monitoring LWC,however the interpretation of the signal still remainedchallenging. In dry snow, the two-way travel time T tothe ground interface could be used to determine depth ormean density if the other was known, using any of thefrequency ranges they investigated. Koh et al. (1996)observed a melt–freeze cycle with continuous staticmeasurements, and found that if a snow pack hadundergone several melt–freeze cycles, lower frequency(2–6 GHz) measurements were necessary for identifyinglocations of ice/crust layers.

Holmgren et al. (1998) used an X-Band FMCWsystem, similar to that used by Koh et al. (1996), to

Fig. 7. FMCW radar mounted on over-snow vehicle (see boom to right) in Alaska. Directional antennas prevent multiple reflections from vehicle.


investigate the accuracy of making snow depth measure-ments with radar. The system was mounted on an over-snow vehicle (see Fig. 7), 19,000 measurements of depthweremade, and the systemwas ground-truthed bymaking3800 manual measurements of depth (hand probe). Theydeveloped an automated iterative algorithm for pickingthe surface and ground reflections, however this had to belocally calibrated with the manual depth measurements.All of the measurements were made in Alaska, where theground is usually frozen in the winter, causing a smaller

Fig. 8. FMCWradar used along snow pit wall to measure melt-water channelsfor maximum sensitivity to vertical structures.

dielectric contrast than with unfrozen ground. Theyshowed examples where in some cases the groundreflection was very obvious, but in other cases it wasimpossible to locate. They attributed this difficulty to avariable frozen ground surface, and the orientation of theantennas relative to the ground surface being differentfrom normal. They were able to remove some randomnoise from the radar signal by using an Optimal (Wiener)filter. In general, the radar depths were accurate, howeverif manual measured depths had not been made to locally

. Radar was moved horizontally along track, and antennas were oriented

Fig. 9. Stationary FMCW radar used during CLPX measurements in Colorado, in 2002 (A) and 2003 (B). Horn antennas were attached to boom,which was moved along ∼2 meter arc during measurements. Signal generator and amplifier are shown on top of tripod, and data was recorded onlaptop computer. This set-up allowed measurements of a wide range of radar parameters (e.g. incidence angle, frequency, bandwidth) to be made atthe same location.


calibrate the radar signal, large errors would haveoccurred. Their recommendations mainly focused ondeveloping a better system formounting the antennas suchthat they would remain normal to the ground surface, butthey also suggested using lower frequency (2–6 GHz),using 2 antennas instead of a single horn, using a high-passfilter to remove DC coupling before A–D conversion, andusing an adjustable amplifier to maximize resolution andincrease the magnitude of the ground reflection.

Sturm et al. (2002) used this system to map snowdepths and study temporal and lateral spatial variability ofsnow cover on sea ice as part of the Surface HEat Budgetof the Arctic (SHEBA) project. They used snow depthsfrom FMCW radar profiles to calculate semi-variograms,and found a consistent range of 13–30m, with an averageof 20 m. The sill of the variogram in different locationsvaried with the roughness of the underlying sea ice, whichthey classified into 4 categories: smooth thin ice, refrozenmelt ponds, hummocky ice, and deformed ice.

Another novel use of FMCW radar for snow researchwas reported by Albert et al. (1999), who investigatedmelt pathways in a snow pack. Their experimental set-upis illustrated in Fig. 8. The figure shows a 2–6 GHzFMCW radar mounted on a platform and pulled along a

track by a motorized pulley system. A fresh snow trenchwas excavated and the antennas were oriented tomaximize sensitivity to vertical features in the snow.They were able to detect old refrozen fingers and new wetfingers up to about a meter into the seasonal snow pack.

4. Recent FMCW radar-snow studies

A major focus of the recent FMCW radar studies wasfor ground truth of remote-sensing measurements. Theprimary goal of these remote-sensing studies was toevaluate and improve satellite radar retrieval algorithmsfor snow depth, SWE, density and wetness. The NASACold Land Processes Experiment (CLPX) is an exampleof such studies (e.g. Cline, 2000). Microwave FMCWradars operating at 2–6, 8–12 and 14–18 GHz band-widths measured the electromagnetic discontinuities in awide range of snow pack conditions in Colorado duringthe 2002 and 2003 CLPX campaigns. These measure-ments were made with the radars mounted at the end of aboom (cf Fig. 9A and B) attached to tripods. Marshallet al. (2004a) document FMCW radar measurements inboth wet and dry snow conditions, with snow depthsranging from 40–350 cm. They also looked at the effect

Fig. 10. (A) Portable FMCW radar mounted on sled, Devon Ice Cap, Nunavut, Canada. Small white box at end of boom (left) contains radar, and bluebox contains laptop computer for data acquisition. Measurements were made down to temperatures below −30 °C. (B) 200 m 8–18 GHz profile.Strong layer reflections occurred down to∼2 m, and the thickness of layers could be used to infer annual accumulation rates. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version of this article.)


of radar incidence angles (0–45°) on the radarsignatures. They found that layering was still visible at15° incidence, but that at 45° the radar signal wasdominated by the ground reflection. This is because asthe incidence angle increases, the surface scatteringfrom layer boundaries decreases, along with the verticalresolution. Marshall et al. (2004b) found that a highcenter frequency (Ku-band, 14–18 GHz) provided themost information in a dry snow pack, whereas C-bandfrequencies (2–6 GHz) were optimal for deep, wet snowpacks. Marshall et al. (2005) located the depths of majorreflections with metal reflectors, which agreed with

layer boundaries observed in an adjacent snow pit, andfound that the location of reflections occurred at largechanges in dielectric properties that were measured withan in-situ dielectric sensor. This study found that spatialvariability in the radar signal occurred on length scalesless than 1 m, and that the measurement of this spatialvariability was repeatable. They were able to measuresnow water equivalent and snow depth to within 10%.

Recently, ground-based FMCW measurements (8–18GHz) were used in conjunction with two aircraft/satelliteoverflights, as part of calibration/validation campaigns.The first measurements were taken coincident with

Fig. 11. FMCWradar measurements from heated sled built by Jon Holmgren, Barrow, AK. High gain horn antennas are attached to the boom on the rightside of the sled, and an instrument which measures the distance to the ice–water interface (EM-31) is in the black box behind the sled. These twoinstruments, when used together can estimate both snow depth and sea ice thickness simultaneously. Photo: Matthew Sturm.


ASIRAS overflights onDevon Ice Cap, Nunavut, Canadain 2005 and 2006 (Demuth et al., 2006) and illustratedgreat spatial variability in the percolation and wet-snowfacies of this polar firn (see Fig. 10A,B). The figures showthe radar set-up and the 8–18 GHz profile over a 200 mtraverse. The profile shows numerous continuous layers,

Fig. 12. Comparison of FMCWradar and SnowMicroPenetrometer (SMP) methe locations of radar reflections near the SMP measurement, and the right phighlight peaks in the radar pdf which are greater than 0.02, showing good

the thickness of which can be used to estimate spatialvariations in annual accumulation rates. The effect ofmelt-water percolation in the polar firn is also evident.This was one of three sites measured as part of thecalibration/validation campaign for the European SpaceAgency CryoSat project (Wingham et al., 2006).

asurements (fromMarshall et al., 2007). The left panel shows the pdf ofanel shows the hardness measurements from the SMP. The gray bandsagreement between the two instruments.


In March 2006, FMCW radar measurements weremade as part of the AMSR-Ice06 field calibration/validation project, where over 150,000 snow depthswere measured on sea ice near Barrow, AK (see Fig. 11;Marshall et al., 2006b). These measurements are com-pared with coincident measurements with an automateddepth probe, at a coarser resolution. Marshall et al.(2006a) document large differences in the magnitude ofspatial variability of snowpack properties covering awiderange of snow pack types (alpine, sea ice, polar firn),using an 8–18GHz FMCWradar, and compare the resultswith measurements using several other high resolutionsnow science instruments.

Gogineni et al. (2003) designed and developed anairborne FMCW radar for measurements of snowthickness over sea ice. This radar has a 2–8 GHzbandwidth, and was recently flown to support AMSR-Ice06 validation studies. The use of airborne radar systemsis ideal for supporting remote-sensing applications.Kanagaratnam et al. (2001)measured internal snow layersin Greenland using a 170–2000MHz FMCW radar on anaircraft. Yankielun et al. (2004) successfully measuredsnow depth from an aerial tramway up to 70 m above theground with an L-Band FMCW radar (1.12–1.76 GHz).They concluded that deep snow packs could be accuratelysurveyed by helicopter-borne FMCW radar systems.

A recent FMCW radar study echoing the early ava-lanche applications of FMCW radar was conducted byMarshall et al. (2007). This study was a quantitative at-tempt to correlate the snowelectromagnetic propertieswithsnowmechanical properties. They used a small lightweightFMCW radar (similar to radar shown in Fig. 10A) toinvestigate layering in an alpine snow pack. They foundthat the locations of layer transitions measured with theradar agreed with those found in a snow micropenetrom-eter profile towithin 1.6 cm.Using ameasurementwith thehorn antennas pointed at the sky, they demonstrated that allinstrumentation-related noise could effectively be removedwith signal processing techniques. They used a newmethod of analyzing the radar data, which focuses onlocations of layer transitions rather than the magnitude ofthe reflection, since this was shown to be very sensitive tolayer thickness for thin layers with a thickness less than thewavelength (∼2 cm). The comparison of the FMCWradarmeasurements and the snow micropenetrometer measure-ments is shown in Fig. 12.

5. Conclusions

The FMCW radar technique has been used in snowresearch since the late 1970s. The great promise demon-strated by the early studies has encouraged snow scientists

to refine FCMW radar as a snow research tool. Thetechnique has the advantage of very high verticalresolution, directional antennas, low power, and band-width flexibility to operate at frequencies currently usedby the active microwave remote-sensing community.FMCW radars have now been used with success formonitoring avalanche flow, measuring stratigraphy, snowdepth, and SWE, as well as for ground truth of remotesensing. Recently lightweight portable versions have beenbuilt, allowing a large number of measurements to bemade rapidly and over large distances. FMCW radar hasbecome a very useful snow science tool, for making highresolution measurements of snow structure over largedistances, as well as continuous measurements through-out the winter. This kind of information, which previouslywas not practical to collect using traditional manualmethods, will help snow scientists better understand thespatial and temporal variability of snow structure and itseffect on remote-sensing measurements.

Acknowledgements

The authors would like to thank Hal Boyne, MichaelDemuth, and Matthew Sturm for supplying the photo-graphs. John Bradford and an anonymous reviewer pro-vided comments which greatly improved this manuscript.

Appendix A

Below we will use angular frequency ω=2πF tosimplify notation. We represent the transmitted signal atthe radar, with some amplitude A in complex notation asEx,T=Ae

−itωT and the received signal, with a differentamplitude R as Ex,R=Re

−itωR, where t is time, and ωTand ωR are the transmitted and received angularfrequencies, respectively. The amplitude of the reflectionR is affected by dispersion, volume scattering, and atten-uation. The hardware of the FMCW radar multiplies thereal part of these two signals together before digitallysampling, therefore the measured signal M is

M ¼ RealðAe�itxTÞRealðRe�itxRÞ¼ A RcosðxTtÞcosðxRtÞ ð3Þ

and using Euler's equation

M ¼ AR 12ðeitxT þ e�itxTÞ 1

2ðeitxR þ e�itxRÞ ð4Þ

and

M ¼ AR4

½eitðxTþxRÞ þ e�itðxTþxRÞ þ eitðxT�xRÞþ e�itðxT�xRÞ� ð5Þ


Therefore

M ¼ A2ðRcosð½xT þ xR�tÞ þ Rcosð½xT � xR�tÞÞ: ð6Þ

Note that there is a high frequency component,due to the first term in Eq. (6), which changes withtime. Note also there is a low frequency component

DF ¼ FT � FR ¼ 12k ðxT � xRÞ which is constant intime, due to the linear variation in frequency of thetransmitted and received waves. A low-pass filter isapplied, therefore the filtered signal Mf is now just thesecond term in the above equation, which contains thefrequency difference between the transmitted andreceived waves. Substituting Eqs. (1) and (2) into thesecond term of Eq. (6), we have

Mf ¼ AR2 cosð2ktDFÞ

¼ AR2

cos 2k tz Bw2 v PL

� �� : ð7Þ

Note that the frequency of this signalΔF is constant intime. A zero-padded, windowed Fast-Fourier Transform(FFT) is typically applied to the filtered signal Mf,resulting in one large peak in power spectral density atΔF. One great advantage of the FMCWradar technique isthat the filtered measured signal Mf contains frequenciesthat are orders of magnitude less than the frequencies ofthe transmitted and received waves FT, FR. For a typicalFMCW system for measuring snow, the frequencies ofinterest in the measured signal Mf are in the kHz range(103 Hz) while the radar operates in the microwave region(109 Hz). Therefore, the data acquisition hardware onlyneeds to record samples at the rate of several hundredkHz. Commercial impulse radar systems, in contrast,must record samples at a rate at least 4 times the centerfrequency to adequately sample the received signal. Thisfact has limited the high frequency range of these systems,as data acquisition hardware which samples in the GHzrange is prohibitively expensive.

Since we know the bandwidth Bw, the pulse lengthPL, and presumably have an estimate for the velocity v,we can calculate the distance to the reflector z. Thepower at the frequency difference ΔF is related to thedielectric contrast between the medium and the reflector,as well as the losses due to volume scattering, atten-uation, and spreading effects.

Note that in wet snow, some dispersion will occurwhich will cause the low frequency component to varysomewhat with time. This results in a broader peak, re-ducing the resolution. Although snow depth and stratig-

raphy have beenmeasuredwith FMCWradar inwet snow(e.g. Marshall et al., 2004a,b), an attempt to use thebroadening of the FMCW peak to derive informationabout snow wetness has not been made. This would be avery worthwhile direction for future snow radar research.

Appendix B. A.1 Multiple reflectors

Since the effect of multiple reflectors are additive, wecan easily generalize Eq. (7) to the case of N reflectors:

Mf ¼ A2XNn¼1

Rncosð2ktDFnÞ

¼ A2

XNn¼1

Rncos 2ktznBw2v PL

� �� ð8Þ

where Rn is the amplitude of the nth reflected wave,ΔFn is the frequency difference between the transmittedsignal and the nth reflected wave, and zn is the distanceto the nth reflector. We will therefore have a peak in thefrequency spectrum of the filtered measured signal Mf,corresponding to each reflector. Note that the distance toeach major reflector zn can be calculated independent ofmany of the characteristics of the radar system, such asthe power transmitted and the gain of the antennas. Thisresult is therefore quite robust, as it also does not dependon unknown quantities such as the attenuation of thesignal within the medium and volume scattering losses.The magnitude of the power returned from a givenreflector, Rn is much more difficult to interpret.

Appendix C. A.2 Range resolution

The range resolution, or the minimum separation atwhich two reflectors can be resolved, of the processedsignal depends on several factors. Data is recorded for theentire duration of the pulse, therefore the number of datapoints collectedN= fsPL, where fs is the sample frequency,i.e. the rate at which the measured signal Mf is sampledduring data acquisition. The smallest frequency differencethat can be distinguished is approximately fs/N. Convert-ing this to two-way travel time, we have

dT ¼ fsNPLBw

¼ fsN

NFs

1Bw

¼ 1Bw

ð9Þ

and therefore range resolution is limited by the bandwidth.To get an estimate of the resolution in terms of snowdepth, we calculate

dz ¼ dT v2¼ v

2Bwð10Þ


and for a typical velocity of EM waves in snow ofv=2.4×1010 [cm/s], and a typical FMCW radar band-width Bw=6 GHz, we have δz=2 cm. Using measure-ments at several different bandwidths, Marshall et al.(2004a,b) showed that this theoretical resolution corre-sponded to the separation at which two reflectors, whichdiffered in magnitude by a factor of 20, could be distin-guished. If the two reflectors differed in magnitude byonly a factor of 2, the minimum separation was δz/2. Thisis another advantage of the FMCW technique: it is mucheasier to achieve a very wide bandwidth (and hence ahigher vertical resolution) than with the impulse radartechnique. Note that layers much thinner than 1 cm can bedetected by both impulse and FMCW radars. Their thick-ness, however, can not bemeasured, and the magnitude ofthe reflection is very sensitive to small changes in layerthickness due to constructive and destructive interferenceof the signal (e.g. Marshall et al., 2007).

Appendix D. A.3 Antenna footprint

Another major advantage of the FMCW radar tech-nique is that measurements in the microwave frequencyrange allow the use of reasonable-sized horn antennas.These antennas have a very directional antenna footprint,typically on the order of 50 cm×50 cm at a height of50 cm at −3 dB. This prevents multiple reflections fromthe sled and any nearby metallic objects from creatingnoise in the image. This directionality also allows mea-surements with the horn antennas pointed at the sky to beused to effectively remove instrumentation-related noise(e.g. Marshall et al., 2007).

Dipole antennas, which are typically used for im-pulse radar systems, transmit and receive in all direc-tions. This can cause reflections from nearby objectsin any direction to obscure snow pack reflections, andmakes removal of instrumentation-related noise muchmore difficult.

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FMCW radars for snow researchIntroductionTheory of FMCW radarHistorical review of FMCW radar measurements in snowRecent FMCW radar-snow studiesConclusionsAcknowledgementsapp1A.1 Multiple reflectorsA.2 Range resolutionA.3 Antenna footprintReferences

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