Magnitude and Frequency of Avalanches in Relation to Terrain and Forest Cover

Transcription

1 Arctic, Antrctic, nd Alpine Reserch, Vol. 35, No. 1, 2003, pp Mgnitude nd Frequency of Avlnches in Reltion to Terrin nd Forest Cover D. M. McClung Deprtment of Geogrphy, University of British Columbi, Vncouver, B.C. V6T 1Z2, Cnd. Abstrct This pper contins n nlysis of mgnitude nd frequency of vlnches in reltion to terrin nd forest cover vribles. The nlysis ws pplied to 194 vlnche pths in four vlnche res long highwys in British Columbi with pproximtely 25,000 vlnches recorded. The mgnitude nd frequency for the vlnche pths were estimted from dt collected long the highwys by vlnche technicins. Results show tht men mgnitude nd men frequency re wekly correlted for set of vlnche pths in n vlnche re. In ddition, with mgnitude nd frequency viewed s response vribles, mgnitude nd frequency correlte with different sets of predictor vribles from one re to nother. This pper contins the first comprison of vribles which correlte with mgnitude nd frequency from one vlnche re to nother. The results show tht previous studies conducted for single res re simplistic. However, there is some consistency between res. Avlnche frequency is most directly relted to terrin steepness nd snow supply. Averge vlnche mgnitude ppers relted to terrin steepness, strting zone, nd trck confinement nd the scle (e.g., totl verticl drop of the pth) with only indirect evidence for link to snow supply. Introduction The mgnitude nd frequency of vlnches must be known or estimted to clculte risk to fcilities (highwys, rilwys, buildings) locted in terrin potentilly ffected by snow vlnches. In ddition, mgnitude nd frequency must be known or estimted to estimte risk to forest cover ffected by vlnches in nd below cler-cuts mde by logging nd for clercuts intersected by vlnche pths bove them. From previous study (McClung, 2001), I hve estimted tht pproximtely 10,000 cler-cuts in British Columbi, Cnd, hve been ffected either by vlnche initition in cler-cuts or vlnches descending into cler-cuts. In this pper, I present n nlysis of the mgnitude nd frequency of vlnches nd their reltion to terrin nd forest cover vribles. The nlysis is from 194 vlnche pths for four different vlnche res intersected by highwys in British Columbi for which mgnitude nd frequency of vlnches hve been estimted from dt records. The object of the study is to identify vribles which correlte significntly with mgnitude nd frequency s step towrd construction of models relting the vribles for guidnce bout decisions in lnd-use plnning nd forestry opertions. The pioneering work on frequency nd terrin vribles includes the work of Scherer (1977) nd Smith nd McClung (1997) for vlnche pths t Rogers Pss nd tht Gleson (1994) for n re in Montn. The present study is much more comprehensive thn previous works since it includes nlysis from 194 pths from four different res: Rogers Pss (Schleiss, 1989), Kooteny Pss, Three Vlley Gp, nd Ber Pss (Province of British Columbi 1982, 1983, 1989) in British Columbi. The present study includes mgnitude for the first time (Kooteny Pss, Three Vlley Gp, Ber Pss). The results show tht mgnitude nd frequency re relted to terrin nd forest cover vribles in complicted fshion with no generl multivrite reltionships yet vilble. Results bout mgnitude nd frequency probbility reltionships do show consistent results: men frequency for vlnche pths is pproximtely log-normlly distributed nd men mgnitude is pproximtely normlly distributed. However, there is generlly no significnt correltion between men frequency nd men mgnitude for set of vlnche pths in given re. Dt Description: Response Vribles The response vribles include the verge mgnitude nd verge nnul frequency of vlnches for ech vlnche pth. The dt used in this study consist of vlnche events recorded in four vlnche res long British Columbi highwys (Fig. 1). Tble 1 depicts bsic informtion bout the res nd informtion recorded. Mgnitude nd frequency dt were collected by stff of the British Columbi Ministry of Trnsporttion nd Highwys for Kooteny Pss, Ber Pss, nd Three Vlley Gp. Frequency dt for Rogers Pss were collected by stff of the Ntionl Reserch Council of Cnd. The dt included vlnche events which reched, exceeded, or cme close to highwys with continuous recording of events from November 1 through April 30 (181 dys: defined s one winter seson). The verge nnul vlnche frequency ws defined for ech pth s the totl number of events verged over the number of winters of records (Tble 2). Similrly, the mgnitude dt consist of the verge sizes of vlnches recorded for the five-prt Cndin size clssifiction system bsed on destructive potentil (see Appendix A for the size clssifiction system). The Cndin vlnche size clssifiction is somewht nlogous to the Merclli scle for erthquke mgnitude in tht the size cn be estimted fter the event tkes plce from simple field observtions relted to destructive potentil (McClung nd Scherer, 1993). Bsed on ex- 82/ARCTIC, ANTARCTIC, AND ALPINE RESEARCH 2003 Regents of the University of Colordo 23-00/03 $7.00

2 TABLE 1 Frequency nd mgnitude informtion for four vlnche res Are Number of Avlnche Pths Winters of Record Frequency Anlyzed Mgnitude Anlyzed Rogers Pss Kooteny Pss Ber Pss Three Vlley Gp 24 No FIGURE 1. Mp of British Columbi showing the four vlnche res. perience using the clssifiction system in Cnd for more thn 20 yers, it hs been shown tht most observers cn gree on size designtion for hlf sizes for individul events. Therefore, vlnche forecsters recording sizes hve recorded dt using hlf sizes in the dtbses used here. The verge mgnitude for n vlnche pth ws defined s the sum of the sizes of ll the vlnches recorded divided by the number of vlnches recorded. The dt used in this study do not generlly include smll vlnches (size 1) which my hve stopped well bove the highwys. Poor visibility often prevents recording these smll vlnches nd they re not of gret interest in highwy opertions. Therefore, the dt used in this study will represent underestimtes of true vlnche frequency for some vlnche pths nd overestimtes of vlnche mgnitude (size) in some cses. The dt records should be very complete for lrger vlnches (size 2 nd greter) nd those smller thn size 2 which run close to the highwys. For ech vlnche re, norml probbility plots were compred with verge vlnche frequency for the set of vlnche pths in the res. These showed tht verge vlnche frequency hs logrithmic chrcter. Accordingly, the dt were trnsformed by tking the nturl logrithm of the men frequency for ech pth. When the trnsformed dt were compred with Gussin (norml) distribution much better fit ws found. When verge vlnche frequency ws used in regression nd correltion studies in this pper, the log trnsformed dt were used s the response vrible, which is equivlent to n pproximtely lognorml distribution of men vlnche frequency. Figure 2 shows norml probbility plots for f (verge frequency) nd ln (f) for Ber Pss. The results from the three other res show similr dependence. Other distributions were lso tried including extreme vlue distributions [Type I (Gumbel) nd Type II, Benjmin nd Cornell, 19] but the lognorml provided the best overll empiricl reltion to fit the dt s evidenced by visul inpsection of probbility plots for the vrious distributions. Norml probbility plots were constructed for verge vlnche size, M, for ech re. It ws found tht vlnche size my be pproximted s norml distribution nd this ssumption ws used in the nlysis below. Figure 3 shows verge vlnche size compred to norml distribution for Ber Pss. Similr results were obtined for Kooteny Pss nd Three Vlley Gp. Since the Cndin vlnche size system is constructed to increse roughly in logrithmic mnner, it ws expected tht tht vlnche size is roughly normlly distributed nd therefore M nd ln f both my be pproximted to fit norml probbility density function. Bsed on these results, M nd ln f were used s response vribles. In generl, I found tht verge frequency nd verge mgnitude for set of vlnche pths re nerly unrelted. The only re for which men mgnitude correlted significntly with ln f ws Kooteny Pss, which showed wek, negtive correltion of M with ln f. Figure 4 shows the sctter plot of M versus ln f for Kooteny Pss. The Spermn rnk correltion coefficient, r s 0.3 (N 48 vlnche pths) implying P 0.03 where P is the probbility tht two vribles re not independent. For Ber Pss, r s 0.1, N 65, nd for Three Vlley Gp, r s 0.06, N, neither of which is significnt. For this pper, significnt correltion is defined when P 0.05 nd highly significnt for P These levels imply tht r s 0.24 (for P 0.05) nd r s 0.34 (for P 0.01) for N t Kooteny Pss. The correltion results imply tht model construction for ln f nd M s response vribles my involve substntilly different terrin nd forest cover predictor vribles since the verge mgnitude nd frequency re so wekly relted nd this is illustrted in the nlysis sections below. Tble 2 gives bsic descriptive dt bout vlnche frequency nd mgnitude for the four res. Accurcy nd Determintion of Predictor Vrible Dt from Avlnche Atlses The predictor vrible informtion ws tken from vlnche tlses compiled by stff of the British Columbi Min- TABLE 2 Descriptive sttistics for men vlnche frequency, f, nd men vlnche mgnitude, M, for four vlnche res Are Men Stndrd Devition N Rnge Avlnche frequency, f (men number per yer per vlnche pth) Kooteny Pss Ber Pss Three Vlley Gp Rogers Pss Avlnche size (M) (size on Cndin scle) Kooteny Pss Three Vlley Gp Ber Pss N is number of vlnche pths D. M. MCCLUNG /83

3 FIGURE 2. () Probbility plot of men vlnche frequency for Ber Pss. If men vlnche frequency obeyed Gussin distribution, the points would fll on the stright line. (b) Lognorml probbility plot for men frequency for Ber Pss. The plot shows men frequency is pproximtely lognormlly distributed. istry of Trnsporttion nd Highwys (Province of British Columbi, 1982, 1982, 1989) nd the vlnche tls from Rogers Pss (Schleiss, 1989). The dt were obtined from vriety of sources: contour mps (scle 1:50,000); ir photos (scles 1: 10,000 to 1:,000), field mesurements using clinometers for ngles nd distnce mesurements in the field (ccurte within severl meters) nd distnces tken from mps 1:50,000 mps with contour intervls of 100 feet with ccurcy within bout hlf contour intervl (50 feet). Most of the distnces in runout zones were mesured in the field. Terrin nd vegettion descriptions in the tlses were determined from combintion of ir photo nlysis nd field observtions. PREDICTOR VARIABLE DESCRIPTION AND ANALYSIS PROCEDURE In ddition to the response vribles (ln f; M), 19 predictor vribles were retined for Kooteny Pss, Three Vlley Gp nd Ber Pss. For Rogers Pss, one response vrible (ln f) nd 23 predictor vribles were used. The predictor vribles included continuous terrin vribles (14 for Rogers Pss; 10 for Kooteny Pss, Ber Pss nd Three Vlley Gp) nd 10 ctegoricl vribles relted to terrin configurtions, exposure to drifting snow, nd vegettion types. The study of predictor vribles ws on two levels: 1. First, single vrible correltions nd tests of significnce for vlnche frequency (ln f) nd vlnche mgnitude (M) were completed. For this prt of the study, Spermn rnk correltions were clculted nd only vribles which were significnt (0.01 P 0.05) nd highly significnt (P 0.01) were retined. 2. To supplement the nlysis bove, step-wise multiple lest squres regression nlysis between response vribles (ln f; M) nd predictor vribles which were significnt or highly significnt in the correltion studies were performed. The nlyses yielded significnt reltionships for frequency t Rogers Pss nd Kooteny Pss nd for vlnche size (mgnitude) t Ber Pss. FIGURE 3. Probbility plot of men vlnche size for Ber Pss. The plot shows tht men vlnche size pproximtely follows Gussin distribution. DEFINITION OF CATEGORICAL PREDICTOR VARIABLES Ctegoricl predictor vribles were determined from photos of the vlnche pths in published vlnche tlses com- 84/ ARCTIC, ANTARCTIC, AND ALPINE RESEARCH

4 TABLE 3 Rnge nd number of vlnche pths (N) for ctegoricl vribles for four vlnche res Vrible Are Rnge N FIGURE 4. Sctter plot of men vlnche size versus ln f for vlnche pths t Kooteny Pss. The plot shows wek negtive correltion for men vlnche size versus frequency: men size decreses s men vlnche frequency decreses. For the other res in this study (Ber Pss nd Three Vlley Gp) the correltion is not significnt. bined with other quntittive informtion obtined from mps nd in the published descriptions for ech pth in the tlses, such s spect, determined by the uthors of the vlnche tlses. Descriptions of ctegoricl vribles re contined in the list below. Tble 3 gives the rnges of the ctegoricl vribles nd number of vlnche pths for ech study re. Wind Index (Scherer, 1977; Smith nd McClung, 1997): The Wind Index is introduced to give progressively higher index (rnge 1 5) s more snow is expected in the strting zone. The ctegories re: 1. Strting zone completely sheltered from wind by surrounding dense forest cover 2. Strting zone sheltered by open forest or fcing the direction of the previling wind 3. Strting zone n open slope with rolls or other irregulrities where locl drifts cn form (e.g., gullies or bowls) 4. Strting zone on the lee side of shrp ridge 5. Strting zone on the lee side of wide rounded ridge or open re where lrge mounts of snow cn be moved by wind Strting zone, trck, nd runout zone type ccording to downslope terrin configurtion (3 ctegoricl vribles): 1. Deeply chnnelized 2. Contining shllow gully or gullies 3. Open slopes with essentilly no deep chnnels or gullies Strting zone, trck, nd runout zone vegettion density (3 ctegoricl vribles): 1. Very Sprse ( 100 stems per hectre) 2. Sprse (severl hundred stems per hectre) 3. Dense ( 1000 stems per hectre) Strting zone type Strting zone density Strting zone veg. Trck type Trck density Trck veg. Runout zone type Runout zone density Runout zone veg. Wind Index Avlnche res: Rogers Pss, Ber Pss, Kooteny Pss, Three Vlley Gp. The ctegories were determined for vegettion of heights greter thn 1 m nd higher nd by estimting verge spcing with the bove mounts from tls photos. Strting zone, trck, nd runout zone vegettion type (3 ctegoricl vribles): 1. Coniferous or deciduous trees (greter thn 1-m height) 2. Brush, grss, shrubs 3. Rocky The ctegories were determined by exmining tls photos nd tls descriptions. As the ctegory number increses, verge height of vegettive cover decreses. Aspect (Compss spect divided into 4 sectors): 1: 1 90; 2: ; 3: 181 2; 4: The vlues were determined from mps nd tlses. D. M. MCCLUNG /85

5 TABLE 4 Descriptive sttistics for continuous terrin vribles: Rogers Pss, B.C. Vrible Strting zone ngle () Trck ngle () Runout zone ngle () Verticl drop (m) Pth length (m) Strting zone elevtion (m) (m) Aspect () Are of ctchment (h) Strt zone roughness height (m) 30-Yer Mx. Ann. Wter Equivlent (mm) Loction (km) Men Std. Devition Rnge N b See text for discussion of these vribles. b N is the number of vlnche pths nlyzed CONTINUOUS PREDICTOR TERRAIN VARIABLES: LIST AND DESCRIPTION Other terrin nd vegettion predictor vribles included those tking on continuous rnge of vlues. A list with ccurcy description ppers below. Strting zone elevtion (m): Elevtion of top of the strting zone (ccurcy 30 m); determined from mps. (m): Elevtion of top of the runout zone (ccurcy 30 m); determined from mps from experience, slope ngle chnges, nd vegettion ptterns. Verticl drop (m): Elevtion difference between top of strt zone nd bottom of runout zone (ccurcy 50 m); determined from mps. Strting zone ngle (): This represents verge downslope slope ngle in the strting zone. Determined from mps. The definition of the strting top nd bottom long the slope ws estimted by experience. The mximum ccurcy is 1. Trck ngle (): Averge downslope ngle in the trck. Determined s per strting zone ngle with similr ccurcy. Runout zone ngle (): This represents verge slope ngle in the runout zone. Determined from field mesurements with clinometer if possible, otherwise from mps. The ccurcy is similr to strting zone nd trck ngles. Tbles 4 nd 5 contin descriptive sttistics for continuous terrin nd vegettion vribles for Rogers Pss (Tble 4) nd Kooteny Pss, Ber Pss nd Three Vlley Gp (Tble 5). Aspect is lso included in Tbles 4 nd 5, even though it is ctegoricl vrible s defined in this pper. ADDITIONAL VARIABLES FOR ROGERS PASS There re four continuous vribles vilble t Rogers Pss which were used by Smith nd McClung (1997) which re potentilly importnt for the frequency study in this pper. 1. Strt zone roughness height (m): The vrible represents the verge ground roughness height in the strting zone TABLE 5 Descriptive sttistics for continuous terrin vribles for Kooteny Pss (), Ber Pss (), nd Three Vlley Gp () Vrible Are Men Std. Dev. Rnge N Strting zone elev. (m) Runout zone elev. (m) Verticl drop (m) Aspect () Strting zone ngle () Trck ngle () Runout zone ngle () in meters wter equivlent of snow. The ccurcy is bout 0.05 m. 2. Loction: Stright-line distnces in kilometers, est-west from Rogers Pss summit, to where ech pth intersects the highwy. The ccurcy is better thn 0.5 km. Negtive vlues re est of the summit nd positive vlues re west of the summit. 3. Thirty (30)-Yer Mximum Wter Equivlent (mm): This vrible is bsed on snow depth mesurements tken t severl sttions ner Rogers Pss. Over period of to 20 yers, mximum snow depth nd density mesurements were tken once yer t six sttions incresing in elevtion on both the est nd west sides of the summit. The 30-Yer Mximum Wter Equivlent ws clculted from the cube-root norml distribution (recommended by Atmospheric Environment Service, Cnd to stbilize the vrince) to give n estimte for ech strt zone elevtion. 4. Are of ctchment: Mximum re (h) vilble for strting of vlnches determined from mps nd photos by experience (see lso Smith nd McClung, 1997). Results RESULTS OF FREQUENCY CORRELATION STUDIES: NONPARAMETRIC STATISTICS Since vlnche frequency is not Gussin vrible, I clculted mtrices for Spermn rnk correltions of frequency with the predictor vribles. The dvntge of rnk correltions is tht the ssumption tht response nd predictor vribles re linerly relted, both being Gussin vribles, s with the ordinry Person correltion coefficient, is voided. Furthermore, mny of the vribles studied here re ctegoricl rther thn continuous, numericl vribles so tht rnk correltion is more meningful. I retined only vribles for which correltion is 86/ ARCTIC, ANTARCTIC, AND ALPINE RESEARCH

6 TABLE 6 Spermn rnk correltion coefficients of frequency with predictor vribles Rogers Pss Highly significnt: Strt zone elevtion Strt zone roughness 30-Yer Mx. Ann. Wter Equivlent Loction W or E of Rogers Pss Strting zone vegettion density Ber Pss Highly significnt: None TABLE 7 Vribles which hve highly significnt correltion with men vlnche frequency or which re significnt in multivrite reltionships with vlnche frequency Predictor Vrible Strting zone roughness or type 30-Yer Mx. Ann. Wter Equiv. Strting zone elevtion Strting zone incline b Trce incline b Runout zone incline b c Sign of correltion Significnt: Runout zone incline Strt zone type Trck veg. density Runout zone veg. type Strting zone veg. type Significnt: Aspect Strting zone incline Trck veg. type Denotes possible reltion to snow supply. b Denotes possible reltion to terrin steepness. c is likely to hve positive correltion with frequency since higher elevtions imply shorter distnces to strt zones so tht more vlnches rech the runout zone where frequency is estimted. Kooteny Pss Highly significnt: Strting zone incline Trck incline Strt zone elevtion Three Vlley Gp Highly significnt: Strting zone incline Trck incline Significnt: Significnt: Runout zone incline 0.31 Runout zone incline Runout zone veg. Trck veg. type Denotes possible link to forest cover significnt (0.01 P 0.05) or highly significnt (P 0.01) ccording to definitions given by Wlpole nd Myers (1978). Vrible correltions re summrized in Tbles 6 nd 7. It is cler tht there re no generl reltionships between verge vlnche frequency, terrin nd forest cover vribles becuse different vrible sets re importnt in different vlnche res. However, there re vribles tht re physiclly meningful nd stisfy either of the following criteri: (1) highly significnt correltion in t lest two res or (2) vribles which re significnt enough to pper in multivrite reltions between men frequency nd predictor vribles (presented in lter section). The vribles retined while meeting either of these two criteri re contined in Tble 7. Tble 7 lso includes Mx. Annul Wter Equivlent which is highly significnt t Rogers Pss: the only re where estimtes were vilble. Most of the vribles in Tble 7 cn be indirectly relted to either snow supply or terrin steepness nd this forms possible correspondence with the model of McClung (2000) where return period in the runout zone is relted to overll terrin steepness nd locl vlnche frequency (relted to snow supply) through the distribution of extreme runout distnces for set of vlnche pths in mountin rnge. Higher snow supply in the strt zone insures higher overll probbility of vlnching (e.g., Slm, 1997) nd steeper terrin (strt zone, trck nd runout zone) my imply higher probbility tht vlnches which relese continue to rech the runout zones where the frequency estimtes were mde for this study. RESULTS OF MAGNITUDE (AVALANCHE SIZE) CORRELATION STUDIES A compnion study of Spermn rnk correltion of men vlnche size with predictor vribles ws mde using the sme criteri for retention s the frequency study: highly significnt if P 0.01 nd significnt if 0.01 P The results re given in Tbles 8 nd 9. Using the sme criteri for selection of vribles identified s possibly importnt in Tble 7 for vlnche frequency, tble of vlues ws constructed for mgnitude (Tble 9). The vribles retined re listed in Tble 9 must be physiclly meningful nd stisfy t lest one of the two following criteri: (1) highly significnt correltion with mgnitude for t lest two res or (2) significnt in multivrite lest squres regression with vlnche size. The reltionships of the predictor vribles (Tble 9) to vlnche mgnitude hve plusible physicl interprettions. Higher strting zone elevtion nd higher verticl drop my imply greter destructive effects which re implicit in the size clssifiction scheme (McClung nd Scherer, 1993). Incresed trck incline possibly implies tht smller-size vlnches cn be kept in motion to rech runout zones. Hence, smller mgnitudes on verge cn rech the runout zone, resulting in negtive correltion with incresing trck inclintion. Positive correltion of men vlnche size with runout zone incline ws found but there is no cler physicl interprettion so this correltion should be discounted until good physicl explntion is provided. Slm (1997) notes tht smller vlnches tend to hve higher bsl friction thn lrger vlnches on verge. Slm s suggestion implies tht the correltions of vlnche size with runout zone incline should be negtive. Strting zone type nd trck type hve negtive correltion (the prmeter increses s the terrin is less chnnelized) with mgnitude, possibly implying tht more chnnelized terrin delivers lrger vlnches, on verge, to the runout zone. This my be relted to snow entrinment with more mss dded in chnnelized terrin but this ide cnnot be proven with the dt in the present study. Positive correltion with Wind Index comes only from the D. M. MCCLUNG /87

7 TABLE 8 Highly significnt nd significnt Spermn rnk correltions for mgnitude with predictor vribles Ber Pss Three Vlley Gp Kooteny Pss Highly significnt: Highly significnt: Highly significnt: Strting zone elevtion Verticl drop Trck incline Runout zone incline Wind Index Strting zone type Strting zone density Strting zone veg. type Trck type Runout zone veg. density Strting zone elevtion Verticl drop Runout zone incline Strting zone type Trck type Trck veg. density Trck veg. type Trck incline Verticl drop Strting zone elevtion Significnt: Significnt: Significnt: Runout zone type 0.22 None Strting zone type Trck type Ber Pss re nd my indicte tht strting zones djcent to lrge res of open, unforested terrin, s is chrcteristic of Ber Pss, re more prone to lrger vlnches on verge. From Tble 9, there is positive correltion with vribles tht re relted to snow supply (Wind Index, elevtions), terrin steepness (trck nd runout zone incline) nd pth confinement (strting zone nd trck), nd scle of the pth (verticl drop, strt zone elevtions). However, ny vribles bove which my be relted to snow supply re only through indirect reltionships nd this mkes the link of snow supply to verge vlnche size somewht doubtful. There is cler physicl link of snow supply to vlnche frequency nd direct link through correltion studies nd the work of Scherer (1977), Smith nd McClung (1997), nd the work in this pper. However, direct link of mgnitude nd snow supply hs yet to be mde. EFFECTS OF FOREST AND VEGETATION VARIABLES Forest nd vegettion vribles hd significnt nd highly significnt correltion with vlnche frequency for ll four res (see Tble 6) but the most importnt vrible seems to be the Wind Index. The Wind Index ws highly significnt in two res nd significnt for the other two res (Tble 6). Similr comments pply for vlnche mgnitude: the Wind Index is the only vrible which stisfies one of the two criteri for identifying it s truly importnt: highly significnt in multiple regression reltionship (see next section). Thus, the vegettion/forest cover vribles pper to be of secondry importnce in this study. TABLE 9 Importnt predictor vribles correlting with men vlnche mgnitude MULTIVARIATE SIZE AND FREQUENCY REGRESSION ANALYSES Here, I estimte size nd frequency s functions of predictor vribles in multivrite sense. Since some of the predictor vribles re similr to others, proper multivrite reltionship hs the dvntge tht the only vribles retined re significnt in combintion with others so tht such redundncy is minimized. Therefore, I sought multivrite lest squres regression reltionships for ech re seprtely for both size nd frequency. Significnt multivrite reltionships for mgnitude were found for Ber Pss, Kooteny Pss, nd Three Vlley Gp. Multivrite reltionships for ln f were found for Rogers Pss nd Kooteny Pss. The equtions were ll derived from step-wise multiple regression nd explortory dt nlysis techniques including sctter plots nd significnce testing of vribles. 1. Mgnitude reltionships. For the equtions below, VD Verticl drop, RZE, WI Wind Index, SZE Strting zone elevtion, SZT Strting zone type nd M is vlnche size, R is correltion coefficient, F is F sttistic, SE is stndrd error, nd N is number of vlnche pths. Ber Pss: M (VD/1000) RZE WI t-sttistic: p-(2-til): R , F(3,62) 108, P 0.01, SE 0.18, N 66 Kooteny Pss: M SZE 0.4(VD/1000) t-sttistic: p-(2-til): R , F(2,46) 6.7, P 0.003, SE 0., N 48 Vrible Strting zone elevtion Verticl drop Trck incline Strting zone type Trck type Wind Index Sign of correltion Three Vlley Gp: M RZE SZT t-sttistic: p-(2-til): R , F(1,30) 16.2, P 0.001, SE 0.53, N Frequency reltionships. For the reltionships below, the following nottion pplies in ddition to tht bove for mgnitude reltionships: R Roughness, L loction est or west of 88/ ARCTIC, ANTARCTIC, AND ALPINE RESEARCH

8 Rogers Pss summit (in km) (see lso Smith nd McClung, 1997), TKE Trck elevtion. Rogers Pss: ln f R 0.08 WI 0.02 L t-sttistic: p-(2-til): R , F(3,37) 27, P 0.001, SE 0.12, N This represents n improved regression reltionship over tht presented by Smith nd McClung (1997) becuse ln f ws used s the response vrible insted of f s used by Smith nd McClung (1997). Kooteny Pss: ln f RZE TKE 0.39 WI t-sttistic: p-(2-til): R , F(3,45) 59.3, P 0.001, SE 0., N 48 Effects of Avlnche Control Some of the vlnche pths in the present study re subject to vlnche control by gunfire nd explosives nd it is possible the reltionships nd correltions could be ffected. I performed correltion, explortory dt nlysis, nd stepwise regression for 27 of the pths t Rogers Pss which were not subject to vlnche control. The result of the best stepwise regression gve: ln f R 0.08 WI 0.02 L t-sttistic: p-(2-til): R , F(3,23) 31.1, P 0.001, SE 0.10, N 27 This nlysis is nerly identicl to tht for the set of vlnche pths which included those controlled by gunfire. Similrly, I clculted t-tests for the differences between mens of the frequency dt nd the vribles which hd t lest significnt correltion with frequency nd the results of these clcultions showed no significnt differences between the mens. For the other res, the vlnche pths t Three Vlley gp re not normlly controlled by explosives nd t Ber Pss, only bout 10% of the pths re regulrly controlled using explosives so the dt there re not sufficient to ssess the effects of vlnche control. Kooteny Pss is the lone exception here in tht nerly ll pths re regulrly controlled by explosives nd gunfire. I conclude tht the reltionships from Kooteny Pss my be significntly ffected by vlnche control but the effects of vlnche control on the dt from the other res is likely to be smll. Summry The present study of high-frequency vlnche pths is much more comprehensive thn previous work (Scherer, 1977; Smith nd McClung, 1997; Gleson, 1994) ttempting to predict frequency from terrin nd snow supply vribles. In the present study, more predictor vribles re included nd dt from four vlnche res re included insted of one re. Furthermore, the present study includes vlnche mgnitude (size) for the first time s well s selection of forest cover nd vegettion predictors. Primry results of this study re tht frequency my be pproximted s lognormlly distributed for ech of the four res nd vlnche size (mgnitude) is pproximtely normlly distributed. Furthermore, there is nerly no reltion between verge mgnitude nd verge frequency except for Kooteny Pss, where there is wek but significnt reltion between size nd frequency: s verge frequency increses verge size decreses. This ltter result my be ffected by vlnche control t Kooteny Pss. I conclude tht there is no strong reltion between verge mgnitude nd frequency for the res studied here. This result is lso indicted by the multiple regression results: different sets of predictors pper for mgnitude nd frequency for the sme re. This suggestion should not be extrpolted to comprison of pirs of vlnche pths but it my hve some importnce for comprison between res. For exmple, n individul pth with lower verge frequency my be expected to hve higher verge mgnitude thn one with higher verge frequency in n re with similr snow supply but this reltion does not seem to hold for collection of pths in n vlnche re. Importnt predictor vribles for frequency re clustered in two sets: those relted to snow supply (Wind Index, strt zone roughness, 30-yer Mximum Annul Wter Equivlent, strt zone elevtion) nd terrin steepness (strting zone, trck nd runout zone inclines). The results with respect to trck incline (steeper trck implies higher frequency) re comptible with those of Scherer (1972) bsed on dt t Rogers Pss. However, the results of this pper re not comptible with Scherer s (1972) result tht chnnelled trcks hve higher frequency thn open slope trcks either for Rogers Pss or the other three res in the study. Further, correltion of frequency with trck steepness is much weker thn in the study of Scherer (1972). Insted, the present study indictes tht chnnelled trcks tend to hve higher verge mgnitude. Since 30-Yer Mximum Annul Wter Equivlent from Rogers Pss is directly relted to elevtion through snow course dt, it is likely tht this vrible nd strt zone elevtion (ppering from correltions t both Rogers Pss nd Kooteny Pss) re providing similr informtion. Importnt vribles for vlnche size re relted to pth scle (strt zone elevtion, verticl drop), snow supply (Wind Index), nd pth confinement nd steepness chrcteristics (strt zone nd trck type, trck incline). All these vribles cn be justified s physiclly plusible. Even though strt zone elevtion showed highly significnt positive correltion with vlnche size for Ber Pss nd Three Vlley Gp, the correltion ws negtive for Kooteny Pss. The physicl explntion of this result is lcking but it my be relted to the specific terrin fetures t Kooteny Pss. Strt zone elevtion lso is lso present in the multivrite regression nlysis for Kooteny Pss with negtive sign so tht there is consistency with the sign of the correltion result for Kooteny Pss. The collective results of this pper show tht the prediction of verge mgnitude nd verge vlnche frequency is very complex with no generl multivrite reltionships vilble. However, both vlnche frequency nd vlnche mgnitude (ssuming tht size s defined by the Cndin system includes logrithmic increse in destructive potentil between sizes) re pproximtely lognormlly distributed for the res studied. The results bout men frequency in reltion to runout zone incline my be reveling something importnt bout vlnche behvior. Frequency hs positive correltion with runout zone incline, implying tht men frequency increses s runout zone incline increses. There is lso plusible explntion: steeper runout zones mke it esier for higher frequency of events to rech the highwy loctions where dt were collected. Even though the ppers s significnt in some D. M. MCCLUNG /89

9 of the correltions nd regressions described, it my hve limited usefulness in pplictions. The Wind Index, s defined, mixes terrin spect nd snow supply within the five levels of its definition so tht there is the possibility of redundncy with other vribles. Thus, for exmple, it cnnot be concluded tht correltion of Wind Index with vlnche size is relted directly to snow supply. Acknowledgments This reserch ws funded by Forest Renewl BC, Cndin Mountin Holidys, the Nturl Sciences nd Engineering Reserch Council of Cnd, the Vice President Reserch t the University of British Columbi, nd the Peter Wll Institute of Advnced Studies t the University of British Columbi. I m very grteful for these sources of support. Doug Sndilnds nd Peter Weisinger of the Deprtment of Geogrphy t the University of British Columbi provided invluble ssistnce with ssembling the dt. Ted Weick of the B.C. Ministry of Trnsporttion nd Highwys grciously provided frequency nd size dt for Kooteny Pss, Three Vlley Gp, nd Ber Pss. References Cited Benjmin, J. R., nd Cornell, A. C., 19: Probbility, Sttistics nd Decision for Civil Engineers. New York: McGrw-Hill, Inc. 684 pp. Gleson, J. A., 1994: Terrin prmeters of vlnche strting zones nd their effect on vlnche frequency. Proceedings of the Interntionl Snow Science Workshop, ISSW 94, P.O. Box, Snowbird, Uth, October 30 November 3: McClung, D. M., 2000: Extreme vlnche runout in spce nd time. Cndin Geotechnicl Journl, 37: McClung, D. M., 2001: Chrcteristics of terrin, snow supply nd forest cover for vlnche initition cused by logging. Annls of Glciology, : McClung, D. M., nd Scherer, P. A., 1981: Snow vlnche size clssifiction. Proceedings of Avlnche Workshop, 3 5 November, 1980, Vncouver, B.C. Technicl Memorndum No. 133, Committee on Geotechnicl Reserch, Ntionl Reserch Council of Cnd, Ottw, October: McClung, D., nd Scherer, P., 1993: The Avlnche Hndbook. Settle: The Mountineers Books. 293 pp. Province of British Columbi, 1982: Snow Avlnche Atls, Ber Pss, Stewrt-Hyder, B.C. Victori: B.C. Ministry of Trnsporttion nd Highwys. 202 pp. Province of British Columbi, 1983: Snow vlnche tls, Revelstoke Three Vlley Gp, B.C. Victori: B.C. Ministry of Trnsporttion nd Highwys. 175 pp. Province of British Columbi, 1989: Snow Avlnche Atls, Kooteny Pss, B.C. Victori: B.C. Ministry of Trnsporttion nd Highwys. 252 pp. Slm, B., 1997: Principles of vlnche hzrd mpping in Switzerlnd. In Izumi, M., Nkmur, T., nd Sck, R. L. (eds): Snow Engineering: Recent Advnces. Rotterdm: Blkem, Scherer, P. A., 1972: Terrin nd vegettion of snow vlnche sites t Rogers Pss, British Columbi. Mountin Geomorphology: Geogrphicl Processes in the Cndin Cordiller. Vncouver: Deprtment of Geogrphy, University of British Columbi. Geogrphicl Series 14: Scherer, P. A., 1977: Anlysis of snow vlnche terrin. Cndin Geotechnicl Journl, 14: Schleiss, V. G., 1989: Rogers Pss Snow Avlnche Atls. Revelstoke, B.C.: Environment Cnd, Cndin Prks Service. 313 pp foldout mp. Smith, M. J., nd McClung, D. M., 1997: Avlnche frequency nd terrin chrcteristics t Rogers Pss, British Columbi, Cnd. Journl of Glciology, (1): Wlpole, R. E., nd Myers, R. H., 1978: Probbility nd Sttistics for Engineers nd Scientists, 2nd ed. New York: Mcmilln Publishing Co. 580 pp. Size TABLE A1 Cndin vlnche size clssifiction Description Typicl Mss Typicl Pth Length Typicl Impct Pressures 1 Reltively hrmless to people 10 t 10 m 1 kp 2 Could bury, injure, or kill person 10 2 t 100 m 10 kp 3 Could bury cr, destroy smll building, or brek trees 4 Could destroy rilwy cr, lrge truck, severl buildings, or forest with n re up to 4 h 5 Lrgest snow vlnches known; could destroy villge or forest up to 40 h Ms submitted July 2001 Appendix A: Cndin Avlnche Size Clssifiction The Cndin vlnche size system is bsed on estimting the destructive effects of vlnche events. The system is similr in concept to the Merclli Scle for erthquke intensity nd like the Merclli Scle, it is possible to estimte destructive potentil. Guidelines for sizing depend on: (1) vlnche mss, (2) distnce moved long the incline, (3) estimted mximum impct pressure, nd (4) wter content of the debris i.e., dry snow vlnches or wet snow vlnches. The system hs been developed from experience nd mesurements to cover snow vlnche destructive potentil for snow vlnches of ll known size. The system hs 5 clsses for which pproximtely n order of mgnitude in destructive potentil is estimted for ech increse in size. In generl, the frequency of vlnches recorded decreses s the size increses. The pper by McClung nd Scherer (1981) contins the theoreticl rgument nd dt on which the system is bsed. It is customry in Cnd for vlnche observers to record events using hlf sizes (e.g., size 2.5). However, due to ssocited uncertinty, it is recommended to use whole sizes in pplictions. Tble A1 contins descriptions of the size clsses t 1000 m 100 kp 10 4 t 2000 m 500 kp 10 5 t 3000 m 1000 kp 90/ ARCTIC, ANTARCTIC, AND ALPINE RESEARCH