AVALANCHE WEAK LAYER TRACING AND DETECTION IN SNOW PENETROMETER PROFILES

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1 AVALANCHE WEAK LAYER TRACING AND DETECTION IN SNOW PENETROMETER PROFILES Jmes Floer Deprtment of Geoscience Universit of Clgr, Clgr, Albert, Cnd, Bruce Jmieson Deprtment of Civil Engineering; Deprtment of Geoscience Universit of Clgr, Clgr, Albert, Cnd RÉSUMÉ L'identifiction de l couche frgile est un spect importnt de l prévision des vlnches. Les détils du profil de profondeur de l neige, tel que l résistnce à l pénétrtion, mesuré pr un pénétromètre numérique à hute résolution, peut fciliter l'identifiction rpide de l couche frgile. À présent, l'identifiction de l couche frgile se fit en personne pr un spéciliste; ce processus peut être lent si plusieurs profiles doivent être mesurés. Cet rticle présente une méthode pour trcer une couche frgile qui été identifiée dns un profil d un trnsect ou dns une grille de profils, permettnt un certin degré de chngement dns l profondeur ou l forme de l couche trcée. En utilisnt cette méthode, l technique de spiking déconvolution de Wiener sert identifier les coordonnées le plus probbles de l couche du profil en question, à l'intérieur du domine spécifié reltivement u profil originl. De plus, nous présentons un pln pour ugmenter cette méthode pour identifier les couches frgiles possibles dns un signl non-interprété. Nous proposons que le signl soit compré à une bse de donnés de signux de couches frgiles possibles, en utilisnt l'output de l méthode de déconvolution pour mesurer les chnces qu'une couche frgile soit présente dns le signl. Un sstème expert est prévu qui combinerit cette probbilité vec les connissnces expertes des probbilités sur l profondeur de l couche frgile, de s dureté, insi que l probbilité que l couche existe. ABSTRACT Wek ler identifiction is n importnt prt of vlnche forecsting. Digitl, high-resolution snow penetrometers cn id wek ler identifiction b giving rpid nd detiled depth profile for certin snow properties, such s force-resistnce. Presentl, wek ler identifiction is done b skilled humn interpreter; this process is slow if mn profiles need to be interpreted. This pper presents method for trcing wek ler tht hs been identified in one profile cross trnsect or grid of profiles, llowing for certin degree of chnge in the depth or the shpe of the ler being trced. In this method, the technique of Wiener spiking deconvolution is used to isolte the most likel loction of the ler in the profile being nlsed within user-specified rnge of depths reltive to the originl profile. In ddition, we present frmework for extending this method to identif potentil wek lers in n un-interpreted signl. We suggest tht the signl to be interpreted could be tested ginst dtbse of potentil wek ler signls, using the output from the deconvolution method to indicte the likelihood of ech wek ler being present in the signl. An expert sstem is envisged tht combines this likelihood with - priori (expert) knowledge of the wek ler s probble buril depth, hrdness nd probbilit of existence. 1. INTRODUCTION Avlnches pose significnt hzrd to winter bckcountr recretionlists, lpine trnsporttion corridors nd in some prts of the world, mountin villges. High resolution, digitl penetrometers (Dowd nd Brown 1986; Sihvol nd Tiuri 1986; Louge et l. 1998; Schneebeli nd Johnson 1998; Abe et l. 1999; Mckenzie nd Pten 22) re being developed for use in vlnche forecsting. These instruments llow rpid ssessment of snow strtigrph tht pertins to vlnche formtion, such s the depth to wek ler nd the thickness nd hrdness of n overling slb. Using digitl penetrometer, lrge number of strtigrphic profiles cn be collected over the course of field investigtion. In our own experience, we hve found it possible to collect nd surve between 6 nd 8 profiles per d using modified (Floer 26) SABRE probe (Mckenzie nd Pten 22) with two-person field crew. Other groups report higher numbers using other instruments (e.g. Birkelnd et l. 24). As equipment becomes more portble nd esier to use, the number of profiles tht cn be collected is likel to increse. A consequence of the lrge mount of informtion tht cn be gthered using digitl penetrometers is tht lrge mount of dt must be quickl processed if it is to be used in timel mnner for the purposes of vlnche forecsting. We present two dt processing methods for nlzing digitl penetrometer signls: 1. Ler trcing this method will utomticll trce ler of interest (e.g. wek ler) tht hs been identified in one profile cross other profiles in trnsect or grid, even though the depth of the ler m chnge nd its exct shpe m vr. This method fetures Wiener spiking deconvolution where the user specifies the ler or interfce to serch for s wvelet. This lgorithm is well developed nd hs been successfull pplied to rel penetrometer dt processing tsks. 2. Wek ler detection this method nlses penetrometer signl for the presence of potentil wek ler. The proposed method is to scn the In : J. Loct, D. Perret, D. Turmel, D. Demers et S. Leroueil, (28). Comptes rendus de l 4e Conférence cndienne sur les géorisques: des cuses à l gestion. Proceedings of the 4th Cndin Conference on Geohzrds : From Cuses to Mngement. Presse de l Université Lvl, Québec, 594 p.

2 J. Floer et B. Jmieson penetrometer signl using dtbse contining rnge of known wek ler profile segments. If good mtch is found, the portion of the signl being nlsed is flgged s possible wek ler. This method is presented s frmework nd hs not et been implemented into n opertionl model. 1.1 Previous work Wiener spiking deconvolution ws developed during WW b Norbert Wiener to seprte rdr signls from noise (Leinbch 1995). This technique is commonl used for processing seismic reflection dt but hs generl pplictions for seprting desired component of signl of constnt smpling intervl from unwnted components within tht signl. Exmples of pplictions relevnt to nturl hzrds include processing seismic signls from erthqukes, nd monitoring volcnism from infrred remote sensing imges. Floer (23) suggested tht this technique might be useful for forecsting vlnches from hourl remote meteorologicl dt. It is generll ccepted tht dr slb vlnches initite in thin wek ler which lies beneth thicker, cohesive slb (McClung nd Scherer 26). Recognizing the presence of wek lers in mnul snow profiles s well s the overling slb properties is therefore fundmentl to slb vlnche forecsting. In the bsence of direct observtions of vlnche occurrences, it is the next most pertinent tpe of informtion for ssessing the stbilit of the snowpck (Schweizer et l. 23). McClung (1995) devised rulebsed model to help forecsters ssess the stbilit of snow profile. Contributions from ech of vriet of snow profile ttributes including, mong others, ler hrdness, ler thickness, crstl size nd crstl form, were combined using rules devised through series of interviews with expert forecsters. Schweizer nd Jmieson (23) found tht differences between the hrdness s well s grin size of the wek ler nd djcent lers were significntl lrger for unstble profiles compred with stble profiles. Schweizer nd Jmieson (27) included these vribles long with the bsolute vlues for hnd hrdness nd grin size (see Colbeck et l. 199) s well s the Rutschblock score (see McClung nd Scherer 26) in model for predicting whether given snow profile should be considered stble or unstble. The reported prediction levels of 65-77% if the depth to potentil filure plne ws known. If the principle wekness ws unknown, prediction levels were lower t 53-62%. Pielmeier nd Schweizer (27) clssified potentil filure lers in penetrometer signls collected with SnowMicroPen (SMP) (Schneebeli nd Johnson 1998). The found significnt differences between certin micromechnicl chrcteristics of the penetrometer signl, the most significnt of which ws the structurl length of the filure ler (Johnson nd Schneebeli 1999). Potentil filure lers were pre-identified using humn interprettion nd there ws no report on the performnce of the clssifiction if the potentil filure lers were not preidentified. Birkelnd et l. (24) suggested tht chnge in the mximum penetrtion resistnce within wek ler m indicte n increse in bond strength within tht ler. 2. LAYER TRACING Profiles were collected using SABRE penetrometer tht mesures force-resistnce using piezo-electric sensor connected to 12 mm dimeter rounded tip. The profiles were interpolted to regulr depth spcing of.5 cm. For our purposes, we refer to ler s being smll section of penetrometer profile tht contins definble signl tht we re interested in. This section of the signl m represent wht we would consider to be n ctul snowpck ler, such s wek ler or crust, or it m represent n interfce between two djcent snowpck lers. 2.1 Method The bsic steps in the ler trcing method comprise of: 1. Expert identifiction of the ler (or interfce) of interest in the originl penetrometer signl. 2. Pre-processing of the penetrometer signls. 3. Wiener spiking deconvolution. 4. Post-processing of the deconvolved output to determine most likel loction of the ler of interest in the profile being nlsed Expert identifiction of ler of interest A short, contiguous section of the originl penetrometer profile (figure 1) is defined s the region of interest nd this forms the mster wvelet, defined s: W = where w _ mx G w _ min d G ( ), [1] is the originl force depth signl nd w _ w _ min nd min define the upper nd lower boundries respectivel of the ler of interest identified b n expert Pre-processing Pre-processing is done on both the originl penetrometer signl, nd the penetrometer signl being nlsed G G ( ) () i g,. We dopt the nottion to describe processing steps tht re pplied to both the originl signl nd the signl being nlsed (subscripts,). The superscript i denotes, in romn numerls, the order in which these steps re performed. The ssocition with the depth () s the independent vrible is ssumed from here on nd dropped from the nottion.

3 Avlnche wek ler trcing nd detection in snow penetrometer profiles A condition of Wiener deconvolution is tht there is n identifible component contined within signl tht is otherwise comprised of rndom noise. Rndom noise is chrcterised b Gussin distribution with men of zero. In order to pproximte this condition, we first remove the brod trend nd then ppl high pss filter, which retins the informtion pertinent for thin-ler or lerinterfce identifiction. in our cse, smll portion of the mster signl G. We must lso specif the desired output e, which we set s spike mrking the strt of the ler of interest. The brod trend ws removed from b fitting lestsqures, 4 th order polnomil to the signls nd retining the residuls. =, I g, G, f, [2] f = where, 1 4 nd the coefficients to 4 re found b minimizing the sum of squres between G, f,. nd A high pss filter ws subsequentl pplied to the trendremoved dt. This ws pplied in the frequenc domin using fst Fourier trnsform (FFT) nd inverse FFT methods (e.g. Ifechor nd Jervis 1993, p. 53) to convert to the dt into frequenc domin nd bck to the sptil domin respectivel. 4 I g ω) = (1 H ) g ( ),, ( H, ω [3] w here (ω) is used to denote tht the filter is pplied in the frequenc domin nd H H is Hnn window (e.g. Tlor 1994, p. 436) defined s: 1 1+ cos π < τ H H = 2 τ otherwise. [4] τ is the frequenc cut-off prmeter used to control which wvelengths re ccepted b the filter. We set τ reltive to the totl depth of the penetrometer signl, d. In prctice, for 2 cm push smpled t n intervl of.5 cm, setting τ = d 2.5 gve cut-off wvelength of pproximtel 8 cm, which worked well. Figure 1 shows how tpicl processed signl compres to the unfiltered signl Wiener spiking deconvolution The method of Wiener spiking deconvolution reduces signl component contined within signl G to desired output e b ppling n inverse filter. We find b defining wvelet w s the portion of the signl we re tring to find, F igure 1. ) Tpicl unfiltered penetrometer profile. A wek ler is interpreted from this signl t depth of 6 cm nd this is ssigned to be the mster wvelet. b) Filtered signl from ) with trend removed nd high pss filter pplied. Once we hve clculted our inverse filter, we cn use it to serch through nother signl G. If we encounter section of G tht is similr to the wvelet w, then the signl t this point will be trnsformed to spike tht represents the loction of this similr ler. If our condition tht the rest of the signl comprises of rndom noise is met (which is not the cse, nd is discussed in section 2.1.4), then the rest of the signl, which bers no resemblnce to w is reduced to. We define the filter such tht: e ˆ = w, [5] where represents the convolution opertor (e.g. Ifechor nd Jervis, 1993, p. 6). ê is our estimtion of the desired output e, which is n n-length vector comprising of unit spike t e with vlues t ll other points being zero: e = (1,,...,). [6]

4 J. Floer et B. Jmieson The wvelet w is defined over the sme intervl s the mster wvelet in eqution [1] but is tken from the prefiltered signl g : cse of mixed del wvelet, we itertivel clculte the error from eqution [1] for rnge of different positions for the spike in e from to n-1. The position m tht minimises ε is then used to clculte the optimum inverse filter. If e is vried from its originl form in this w, then the finl deconvolved output must be offset b m if the spikes re to mtch up with the strt of the ler of interest. w = w _ mx g w _ min d [7] The finl step is to use the inverse filter to deconvolve the signl being nlsed. The finl deconvolved output is clculted b: From Robinson nd Treitel (198), the generl form of the mtrix eqution for n optimum filter is: R = C, [8] where R is the utocorreltion mtrix of the wvelet w nd C is the crosscorreltion vector between w nd e. In expnded form, this cn be written s: r r1 K rn 1 c r r K r c 1 n = M M O M M M rn rn L r n cn R C, [9] where subscripts within R nd represent utocorreltion nd crosscorreltion lgs respectivel. The inverse filter is optiml in the sense tht it lestsqures minimises the error between the ctul nd desired outputs. This error is given b the sclr ε, summed over the n elements in e: C Γ = g Post-processing, [11] If our penetrometer profiles chnged in hrdness smoothl over the whole rnge of depths except t the ler of interest, then the pre-processing lgorithms in section would indeed reduce our signl to the ler of interest + rndom noise pproximtion. However, the penetrometer profiles tht were collected in the Columbi Mountins of British Columbi frequentl contin lers of similr wvelength to tht of the ler of interest, but tht do not represent the ler we wish to identif. Additionll, it is common in our profiles for the mgnitude of the vritions to increse with depth. When ler of the sme shpe s the mster wvelet is encountered but is twice the mplitude, then the resulting spike t this loction will be twice s high s the spike generted when the wvelet is deconvolved with itself (termed the wvelet spike from here on). In order to get round this problem, we must further filter the deconvolved dt. In similr mnner to the pre-processing filters, we define i post-processing steps γ, tht gin must be performed in the order described b the romn numerl i. To reduce the effect of high mgnitude, short wvelength lers such s crusts tht tend to generte spurious detection spikes, we tke the difference between the deconvolved output nd the wvelet spike nd normlize it to unit wvelet spike. n 1 i= 2 ε = ( e i eˆ i ). [1] eˆ = (ˆ e Γ ) 2 I γ [12] eˆ For good detection, we must mtch the energ build-up chrcteristics of e to the energ build-up chrcteristics of w. w is sid to be minimum-del wvelet if ll its energ is concentrted towrds the front of the wvelet. In this cse, we set e = (1,,...,), with the spike t the beginning s in equt ion [6]. w is sid to be mximum-del wvelet if ll its energ is concentrted towrds its end nd in this cse we modif the desired output to be e = (,,...,1), with the spike t the end of the vector. In the more generl Note: if the signl + rndom noise condition is not closel pproximted then we will get better results b replcing ê in eqution [12] with Γ = ). ( w _ min Since we expect some correltion between the depth of the ler of interest in the originl profile nd the profile being nlsed, we filter the results bsed on the depth. Our filter comprises of tpered window, in which we specif vlue

5 Avlnche wek ler trcing nd detection in snow penetrometer profiles of 1 for the depth rnge where the ler is most likel to be found. The vlue tpers linerl to zero t both ends of the window over second rnge of depths. Both depth rnges tht define the window cn be customised b the user bsed on the expected vribilit between the profiles. The window is pplied in the sptil domin nd: γ = H γ, T I [13] where H T is the tpered window described bove. The finl step is to rnk the spikes in the filtered, deconvolved output γ. A full utomted implementtion of this scheme might simpl select the highest rnked spike s the ler of interest, wheres n expert sstem could present the user with selection of smll number of likel loctions for the ler of interest. Figure 2 shows the originl interpreted ler nd the trced ler for two different exmples; the top 1 rnked spikes re shown in ech cse. In our implementtion of this model, we used the Interctive Dt Lnguge (IDL) v6.2. Routines for finding the utocorreltion mtrix, nd the crosscorreltion mtrix nd for generting the filter windows were coded from scrtch. IDL s built in CONVOL routine ws used for performing the convolution opertions nd the FFT routine ws used for performing the fst Fourier trnsforms. The length of the wvelet hs the gretest influence on performnce time. On 1.7 GHz computer running Microsoft Windows XP, processing time for running the ler detection routine on single profile ws pproximtel.25 s for 3 cm wvelet contining 6 dt points nd 5 s for n 8 cm wvelet contining 16 dt points. Wvelets greter thn the wvelength cut-off (8 cm in our cse) should not be used. 2.2 Testing the method The ler trcing lgorithm ws tested b trcing severl lers of interest cross two different trnsects of penetrometer profiles tht were collected using our modified SABRE penetrometer. The trnsects were collected in the winter of 27 from the Columbi Mountins in British Columbi nd ech trnsect comprised of 11 individul profiles. Trnsect 1 ws collected on 21-Feb 27 on slope tht vried grdull in spect from NW to NE. Profile spcing for this trnsect ws pproximtel 2 m. Trnsect 2 ws collected on 15-Mr 27 on wind-ffected slope with significnt vribilit in snow cover depth. Profile spcing for this trnsect ws pproximtel.5 m. The lers of interest were grouped into four ctegories: Crusts (or thin, high resistnce lers); wek lers; interfces (rpid increses in force-resistnce); nd other ler tpes tht did not fit into the other three ctegories. Figure 2. Trcing ler from the interpreted signl (left signl in ech frme) to n un-interpreted signl (right signl in ech frme) for: ) wek ler nd; b) pek representing reltivel hrd ler. The spikes represent the 1 most likel positions for the loction of the trced ler. Note tht in ) there re severl possible positions for the trced ler nd the one chosen ctull hs the third highest spike vlue. In b) there in onl one vible position nd the spike vlue t this point is much greter thn the other spikes. The testing method comprised of identifing ler of interest in the first profile nd then trcing it cross subsequent profiles in the trnsect. Ech time ler of interest ws trced to new profile, the ler tht hd just been identified becme the new reference ler nd ws ssigned s the new mster wvelet. In this w, identifiction of ler in new profile ws performed using ler informtion from the closest profile, rther thn from the first profile in the trnsect. If the ler ws judged to hve been correctl identified (bsed on mnul expert comprison between the two signls) b one of the top 1 rnked deconvolution spikes, then this ws recorded long with the rnk of the spike tht best represented the position of the identified ler. If the correct position of the ler ws not represented b n of the top 1 rnked deconvolution spikes, then the ler ws considered not to hve been identified.

6 J. Floer et B. Jmieson 2.3 Results Tble 1 shows the number profiles tht were correctl identified for ech ler tht ws trced cross the trnsect. Most of the lers were identified quite well, with ll but two of the lers showing correct identifiction for 9-1 out of the possible 1 trcings. (Note: since there were 11 profiles in ech trnsect, there re 1 possible trcings, since the ler ws mnull identified in the first profile.) We cn compre how well ech ler ws trced b looking t the men rnk of the deconvolution spike for the identified lers. It is cler tht crusts, or spikes representing thin high-resistnce Tble 1. Results from the ler-trcing method test. lers perform best using this ler-trcing lgorithm. The crust lers tested hd men rnk vlues between 1.1 nd 2.. Interfces between lers of different resistnces performed the next best, with those showing shrp increse in force-resistnce performing better thn those showing more grdul increse. The sitution for the wek lers ws more vrible. The low densit shllow ler, which ws in the reltivel quiet, upper prt of the signl, performed prticulrl well, with men rnk vlue of 1.2. The wek ler buried 4-Feb 27 ( surfce hor ler tht ws recorded with thickness of 1 mm in mnul profile close to, nd on the sme d s trnsect 1) hd Number of Men rnk of spike Ler Description Trnsect Number of profiles identified profiles not identified used for the identifiction Crusts High densit pek ~ 6 cm Lower crust ~ 13cm Thin ner-surfce sun crust Double-peked ner-surfce crust Lower crust ~ 11cm Wek lers Wek ler (buried 4-Feb 27) Thick (8cm) low densit zone Low densit shllower ler Wek Ler (buried 4-Feb 27) Interfces Shrp, high mgnitude resistnce increse Shrp, low mgnitude resistnce chnge Uneven resistnce chnge Other Flt portion within ler smll depression close to crusts 2 1 N/A brod low densit ler close to crust men rnk vlue of 2.7 when trced cross trnsect 1. We hd less confidence in identifing this ler in trnsect 2 but we mnged to trce ler which shred chrcteristics of this ler cross trnsect 2 in ll but one profile, with men rnk vlue of 3.1. In both cses, this wek ler l beneth reltivel hrd ler tht gve pronounced spike in the signl. It is likel tht the proximit of this spike to the wek ler dversel ffected the bilit to detect this ler. Overll, lers in the Other ctegor, which represented firl nondescript lers, performed the lest well compred to the other ler tpes. Lers tht were not identified well re of interest s the provide insight to the limittions of the method. The thick low densit zone ws quite prominent low-resistnce ler, lthough it ws chrcterized b firl grdul hrdness trnsitions. Since the thickness of this ler ws the sme s the cut-off wvelength of the high-pss filter (8 cm), it is likel tht there ws ver little residul signl remining fter filtering to llow for unique identifiction. The other ler tht performed poorl ws the brod, low densit ler ner crust. Agin, its brod nture probbl ment tht some of its unique chrcteristics were filtered out nd the proximit to the crust ws likel responsible for drowning the signl t this point with mn spurious spikes ssocited with rpid signl trnsitions ner the crust. 3. WEAK LAYER DETECTION In the ler-trcing method described bove, we ssume tht given ler is present in signl being nlsed nd we tr to find the optimum loction for tht ler bsed on vlues from the deconvolved output. In our ler-detection method, we remove the ssumption tht given ler is present nd we use the deconvolved output vlues to indicte the likelihood of finding prticulr ler within this signl. We cn repet this tsk mn times using different potentil lers tht re ssigned s the mster wvelet.

7 Avlnche wek ler trcing nd detection in snow penetrometer profiles The steps required for implementing this model re shown schemticll in figure 3. We focus on the detection of wek lers since these lers re of prticulr interest to vlnche forecsters. However, it would be lso possible to use this technique to look for crusts or other fetures within the penetrometer signl. We strt b building dtbse of wek lers from expert interprettion of penetrometer signls combined with knowledge of the previling snow stbilit. Ech wek ler wvelet includes the trnsition from the slb, through the wek ler itself nd into the underling snow. Informtion bout locl vlnche conditions, stbilit test results nd other informtion helpful to vlnche forecsters should be retrievble ginst the wek ler wvelets. Next we perform the deconvolution technique outlined in section 2 for ll wek lers in the dtbse. In the most generl cse, we cn set the depth filter to be unit for ll depth vlues, mking no ssumptions bout the likel depth of the wek ler. In prctice, however, we expect to get better results if we llow detection within specified rnge of depths, s ±15 cm compred to the input wek ler depth. With this ssumption, we ccept tht the shpe of wek ler tht cuses vlnches t, s, depth of 4 cm is likel to be different from one tht cuses vlnches t 1 cm. Figure 3. Schemtic of the steps involved in the proposed wek ler detection model. Preliminr testing suggests tht detection of similr looking lers from one profile to nother profile collected t different time nd plce but with similr snowpck chrcteristics is quite good. We hve, however, found tht the length of the wvelength hs significnt impct on the mgnitude of the deconvolved output. It will likel be necessr to fix the number of dt points for ech wvelet to uniform vlue. In n opertionl model, the deconvolved output could be used in two possible ws. First, it could be used in nerest neighbours pproch to estblish the closest mtch between the penetrometer signl nd the dtbse of potentil wek lers. The informtion bout vlnche conditions ssocited with the highest rnked mtch could be used b the forecster to help mke judgment regrding current conditions. Second, the deconvolved output could be ssigned s metric to indicte the likelihood of tht point representing wek ler. The probbilit densit function describing the probbilit of given output vlue representing wek ler could be generted from testing set of known wek lers. This frmework shres mn similrities with n vlnche forecsting scheme presented b McClung nd Tweed (1994), lthough our initil focus is on forecsting the presence of wek lers rther thn direct forecsting of vlnche occurrences. As with McClung nd Tweed s model, the posterior probbilit for group membership (in our cse into wek ler/non-wek ler ctegories) could be modified using prior expert knowledge. Such knowledge could tke the form of n expert opinion of how likel wek ler ws to be found in given snowpck, likel depth of buril or likel hrdness chrcteristics of the wek ler nd slb. 4. DISCUSSION Mn reserchers (Schneebeli et l. 1999; Pielmeier nd Schneebeli 23; Kronholm et l. 24) hve rgued tht verticl resolution in the order of few micrometres is necessr for relible wek ler detection from forceresistnce penetrometer signls. Although we do not directl dispute this, we rgue tht significnt informtion cn lso be glened from the brod shpe of the wek ler. Anlsing the brod shpe of the penetrometer signl does not necessitte such high resolution mesurements. Aside from computer performnce, which could be significntl enhnced with code optimiztion, there is no reson wh our methods could not be pplied to higher resolution penetrometer dt, such s tht from the SMP. Also, micromechnicl informtion could be combined with n nlsis of the shpe of the ler. For ler trcing, this could tke the form of helping to determine the correct ler in cse where the deconvolved output indictes two or more possible positions of roughl equl likelihood. This could be done b weighting the position which most closel mtches the micromechnicl chrcteristics of the ler being trced. For wek ler detection, the posterior probbilit of ler being wek ler could be ltered bsed on probbilit densit function linking the micromechnicl informtion to the probbilit of being wek ler. 5. CONCLUSION We hve presented method for trcing wek lers cross trnsect of penetrometer signls nd frmework for

8 J. Floer et B. Jmieson extending this method to the problem of generic detection of wek lers in penetrometer signls. For the ler-trcing lgorithm, we were successful in trcing lers cross the trnsect in 13 out of the 15 cses in our test. Lers tht trced well were crusts, interfces nd wek lers tht were not positioned ner to crust. Wek lers tht were found ner crust, s well s broder, less distinct fetures, performed less well in our tests. The next step will be to build nd test the wek ler detection model. This will require populting dtbse with severl known wek lers identified in rnge of different penetrometer profiles. The influence of wvelet length on the deconvolved signl output needs to be investigted further. It is lso probble tht improvements to the pre- nd post-filtering will enhnce model performnce. Although we designed these techniques with dt from force-resistnce penetrometer in mind, there is no reson wh the could not lso be pplied to high-resolution penetrometer signls from other snow properties, such s cpcitnce nd opticl reflectivit. 6. ACKNOWLEDGEMENTS For meticulous field work observtions we would like to thnk Dve Guthier, Lur Bkermns, Ctherine Brown nd Thoms Exner. For support we re grteful to the Nturl Sciences nd Engineering Reserch Council of Cnd, Helict Cnd, Cndin Avlnche Assocition, Mike Wiegele Helicopter Skiing, Cnd West Ski Are Assocition, nd Prks Cnd. We re grteful to Mrtin Schneebeli nd Krl Birkelnd for helpful reviews tht improved the qulit of this pper. 7. REFERENCES Abe, O., R. Decker, B. Senso, T. Ikrshi, D. Rem nd B. Tremper, Snow profille observtions for vlnche forecsts using the new genertion rmmsonde, Seppo no kenku (Reserches on snow nd ice), 61(5), Birkelnd, K. W., K. Kronholm, M. Schneebeli nd C. Pielmeier, 24. Chnges in the sher strength nd micropenetrtion hrdness of buried surfce-hor ler, Annls of Glciolog, 38, Colbeck, S., E. Akit, R. Armstrong, H. Gubler, Lfeuille J., K. Lied, D. McClung nd E. Morris, 199. Interntionl clssifiction for sesonl snow on the ground, CRREL Report MP 2794, Interntionl Assocition of Scientific Hdrolog. Dowd, T. nd R. L. Brown, A new instrument for determining strength profiles in snow cover, Journl of Glciolog, 32, Floer, J. A., 23. Sttisticl vlnche forecsting using meteorologicl dt from Ber Pss, British Columbi, Cnd, (Mster's thesis), Universit of British Columbi, BC, Cnd, 98 pges. Floer, J. A., 26. An updte on digitl penetrometer technolog, Avlnche.c - The Journl of the Cndin Avlnche Communit, winter 26, Ifechor, E. C. nd B. W. Jervis, Digitl Signl Processing, Addison-Wesle. Johnson, J. B. nd M. Schneebeli, Chrcterizing the microstructurl nd micromechnicl properties of snow, Cold Regions Science nd Technolog, 3(1-3), Kronholm, K., M. Schneebeli nd J. Schweizer, 24. Sptil vribilit of micropenetrtion resistnce in snow lers on smll slope, Annls of Glciolog, 38, Leinbch, J., Wiener spiking deconvolution nd minimum-phse wvelets; tutoril, The Leding Edge, 14(3), Louge, M. Y., R. L. Foster, N. Jensen nd R. Ptterson, A portble cpcitnce snow sounding instrument, Cold Regions Science nd Technolog, 28, M ckenzie, R. nd W. Pten, 22. A portble, vriblespeed, penetrometer for snow pit evlution, Proceedings of the Interntionl Snow Science Workshop (22: Penticton, BC), McClung, D. M. nd P. Scherer, 26. The Avlnche Hndbook, The Mountineers, third edition ed., 342 pges. McClung, D. M., Use of Knowledge in Avlnche Forecsting, Defence Science Journl, 45(2), McClung, D. M. nd J. Tweed, Numericl vlnche prediction: Kooten Pss, British Columbi, Cnd, Journl of Glciolog, 4(135), Pielmeier, C. nd M. Schneebeli, 23. Strtigrph nd chnges in hrdness of snow mesured b hnd, rmsonde nd snow micro penetrometer: comprison with plnr sections, Cold Regions Science nd Technolog, 37(3), Pielmeier, C. nd J. Schweizer, 27. Snowpck stbilit informtion derived from the SnowMicroPen signl, Cold Regions Science nd Technolog, 47(1-2), R obinson, E.A. nd S. Treitel, 198. Geophsicl signl nlsis, Prentice-Hll, Inc. Schneebeli, M. nd J. B. Johnson, A constnt-speed penetrometer for high-resolution snow strtigrph, Annls of Glciolog, 26, Schneebeli, M., C. Pielmeier nd J. B. Johnson, Mesuring snow microstructure nd hrdness using high-resolution penetrometer, Cold Regions Science nd Technolog, 3, Schweizer, J. B. Jmieson, 23. Snowpck properties for snow profile nlsis, Cold Regions Science nd Technolog, 37(3), Schweizer, J. nd J. B. Jmieson, 27. A threshold sum pproch to stbilit evlution of mnul snow profiles, Cold Regions Science nd Technolog, 47(1-2), S chweizer, J., J. B. Jmieson nd M. Schneebeli, 23. Snow vlnche formtion, Reviews of Geophsics, 41(4). Sihvol, A. nd M. Tiuri, Snow Fork for field determintion of densit nd wetness profiles of snow pck, Trnsctions on Geoscience nd Remote Sensing, GE-24, Tlor, F. J., Principles of Signls nd Sstems, McGrw-Hill.