AN EXPERIENCE OF AVALANCHE DIAGNOSTIC AND FORECAST MODELS VERIFICATION

Pavel Chernouss*Center of Avalanche Safety of "Apatit" JSC, Kirovsk, Russia

ABSTRACT. Verification of several types of avalanche occurrence diagnostic and forecast modelsused by the Centre of Avalanche Safety in the Khibiny Mountains are described. Validity of one andtwo-dimensional empirical models, multi-dimensional statistical and stochastic models applied toseparate avalanche sites and the whole area is considered. Wind speed and direction andprecipitation or snowdrift intensity were used for the simple empirical models as predictors. Somemore standard meteorological and snowdrift parameters were used in different schemas ofdiscriminant analysis and by the method based on Bayes' formula. The data for last 10 - 20 yearswere treated. Categorically and probabilistically formulated forecasts were analysed. A correlationcoefficient between forecasted and observed situations - Obukhov's criterion is calculated forcategorical forecasts and Brayer's criterion for stochastic ones. Comparison of the different modelsquality was carried out. Warnings made by avalanche forecasters with the models and their subjectiveexperience are evaluated too. Quality of the slushflbw diagnostics is considered separately.

1. INTRODUCTION

As far as ideal avalanche forecastmodels are absent, there are some reasons toverify existing models, for example, to choosethe best one or to evaluate possible losses dueto forecast errors. Verification also can beuseful for an analysis of errors and improvingof the forecast models. So forecast makersand users both are interested to know theresults of the verification. Of course theforecast castomers most of all want to knowspatial and temporal evaluations of anavalanche risk- characteristic which takes intoaccount the avalanche occurrence possibility,its dynamics and interaction with an object,vUlnerability of the object. Unfortunately thereare no such integrated models and in practicethe risk evaluations are making subjectively.The models. for avalanche occurrencediagnostic and forecast are discussed here.The models used at the Center of AvalancheSafety of "Apatif' JSC (CAS) from late thirtiestill now where selected for verification. Socalled, "scientific verification" was made, whenforecasted avalanche occurrence wascompared with reality on a base of specialcriteria. .

2. DIAGNOSTIC AND FORECAST MODELS

Corresponding author address: PavelChernouss, Center of Avalanche Safety of"~patif' JSC, 33a, 50 years of October St.,Klrovsk, Murmansk Region, 184250 Russia;tel: +781531 96230; fax: +47789 14124; email:P.Chernous@apatit.com

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Diagnostic and forecast models areconsidered as a set of formal rules forinterpretation of input data and gettingquantitative or qualitative conclusion on itsbase about avalanche occurrence possibility.Really the models which forecast an exact timeand exact place of avalanche occurrence havenot been used in CAS. Usually they just givean opportunity to say whether a period with adefinite avalanche occurrence probability havebegun or not. Thus it is rather a real-timeavalanche diagnostics than a forecast andsome models are just rules for classification ofthe situations which say nothing whenavalanche can occurred before an a momentof diagnostics or after. When the categoricalconclusions such as "avalanche situation" and"non-avalanche situation" are used thecalculated and threshold probabilities are abase for them. Some of the models are appliedto all genetic types of avalanches, but some ofthem to certain ones only. Brief description ofthe models is given below.

Zelenoy's (1937) method - anempirical rule worked out for a small area 5x 3km with about 50 avalanche sites. It wasconsidered that at least one avalanche releasecould occur in days when the wind speed atthe valley weather station was more than 10mS-1. The wind speed 10m S-1 is very close tothe threshold wind when snowdrift starts.

Akkuratov's (1956) model - anempirical rule, which instead of indirectsnowdrift characteristics uses snowdriftintensity measurements at the top of the

mountain. The model was used for so calledsnowstorm avalanches, which are formed offresh snowstorm snow and release in time ofthe snowstorm. Avalanche period starts whentotal amount of snowdrift with intensity 0.25 kgm -2 S-1 in 2 cm near surface layer isovercoming 1000 kg/m. This rule is applied tothe same area as Zelenoy's model.

Linear discriminant analysis -discriminate situations with a linear function inmultivariate space of diagnostic parameters.There have been used two types of a lineardiscriminant analysis. First one (Chernouss,1975) was worked out for avalanche situationsrecognition in a grope of four avalanche siteslocated very close one to another and havingalmost the same starting zone inclination andaspect. The model was applied for snowstormavalanches. Nine weather and snowdriftcharacteristics, which characterise snowfallfrom the beginning to the moment ofdiagnostics, were taken as the diagnosticparameters. In a second schema (Chemoussand others, 1998) of the analysis snowfallswere classified on avalanche and non­avalanche. A snowfall is considered asavalanche one when at least one avalancherelease is observed in the area (the model isapplied to the same area as Zelenoy's andAkkuratov's models. The discriminant functionswhere obtained for each sixth hour sincesnowfall beginning. An advantage of thismodel relatively first one is an opportunity touse different evaluations of mathematicalexpectations and variances of the parametersat different stages of the classification. Lineardiscriminant analysis was also applied forrecognition of days with and withoutslushflows. Situations were described withdaily water income (a parameter calculated ona base of standard meteorologicalobservations) and snow height.

Bayes' formula - the model wasworked out by Zuzin (1989) and has beenused in CAS since 1978. The model isapplicable for all genetic types of avalancheswithout any differentiation. A situation isconsidered as avalanche one when at leastone avalanche release is observed in the areafor which all above-mentioned models havebeen used. On a basis of meteorologicalmeasurements and avalanche release recordstwo groups of the empirical probabilitydensities of such parameters as: snow height,daily precipitation, mean daily wind speed,mean daily temperature - were obtained fordays with and without avalanches. Bayes'formula is using these distributions to

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recalculate apriori probability of avalanChesituation taking into account the data oncurrent situation, described with the samparameters. In practice 24 h gliding averagesare used as input parameters for classificationof gliding one day periods on avalanche andnon-avalanche. Bayes' formula was alsoapplied for recognition of days with and withoutslushflows. Situations were described sameway as for discriminant analysis.

Statistical simulation - the main idea Ofthe method to generate input data fordeterministic models of snow cover mechanicalstability on mountain slopes (Chernouss,1994). The data are generated in accordancewith statistical lows of the snow coverparameters spatial distributions. The simulationwas used for two dimensional slope of arbitraryconfiguration. Parameters of the snow coverwere represented by stochastic functions andsnow stability for real slopes was calculated forseparate profiles. Evaluations of snow height.density and shear strength mathematicalexpectations, their variances andautocorrelation functions were used as inputparameters for the model. The results of theclassification were the probabilities· of snowrelease for different segments of the profileand probability of avalanche release.

Synoptic model - It is for snowstormavalanches forecasting. The model(Izhboldina, 1975) binds avalanche releaseswith previous synoptic situations (24 hoursbefore). Each situation was described with aset of parameters to evaluate avalanchereleases probability. Later (Polkhov andIzhboldina, 1977) the method was formalisedby discriminant analysis using.

3. CRITERIA FOR THE MODELSVERIFICATION

The categorical and probabilisticforecasts were verified with differentcharacteristics and criteria using: 1) PX 100%- percentage of correct forecasts, whenforecasts coincide with observations, 2) "postagreement" - PaX 100% - percentage ofcorrect forecasted avalanche situations.PoX 100% - percentage of correct forecastednon-avalanche situations, 3) "prefigurance" ­pax 100% - percentage of correct "avalanche"forecasts, pox 100% - percentage of correct"non-avalanche" forecasts, 4) Q - Obukhov'Scriterion (1955) for alternative forecasts, 5) "criterion, 6) Brier's criterion (1958) torprobabilistic forecasts. Contingency tableswere a base for calculations of all criteria tor

categorical forecast verification. Obukhovs'

criterion:

Q=1-0-13

where a =1 - Pa and ~ =1 - Pn, changing fromo for random, climatological, inertial or other"blind" forecast models to 1 for an ideal model,make a sense of. correlation coefficientbetween forecasts and observations. Thehigher Q the better th~ model. To evaluate asignificance of the differences between theresults obtained with tested forecast modeland some "blind" model t criterion is applied.Briers' criterion expression for probabilisticforecasts is:

1 2 N

E= 1- -IICPij _E;)22N j=! i=l .

where: j - 1,2 - numbers of classes, j = 1 ­avalanche situations, j = 2 - non-avalanchesituations, i-number of situation, Pij ­

calculated probability that i-situation belongsto j - class, Eij are 1 or 0 depending onwhether i-situation belongs to j - class or not.As for Obukhov's criterion, it is equal 1 for idealforecasts when all situations have beenforecasted with probability equal 1.

4. RESULTS AND DISCUSSION

As it was said already, all modelse~cept s¥noptic one can be considered as onlydiagnostic ones if real time input data are usedfor them. All of them can be used as forecastones if to use forecasted input parameters orextrapolate the output data in time. Heremainly the results of verification for diagnosticmodels are presented, special reservations aremaking for forecast models.

Zelenoy's model worked well foravalanche situations (Pa = 0.85), but it gavetoo many errors in recognising of non­avalanche situations (Pn = 0.25). Q criterionwas. equal 0.20 only. If to modify the model byadding two necessary conditions for avalancheOCCurrence - fresh snow presence and thawabsence - Pn grows to 0.50 and Q to 0.30, Padecrease very slightly to 0.80.

v. Akkuratov's model . It was difficult toerify this model for whole area which it was

;Orked out, because very frequently a geneticpe of released avalanches was

unrecogn· d WcI . I~e. hen the model was applied foraasslficatlon ?f situations for the group of fourvalanche sites (as in the first type of

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discriminant analysis) obtained Q - value was0.43. Of course for whole area Q will be higher.

Linear discriminant analysis. For thefirst type of discriminant analysis the nextresults were obtained: P =0.85; Pa =0.60; Pn=0.97; pa =0.91; p n = 0.83; a = 0.40; ~ =0.03; Q = 0,57. Correlation between forecastsand observations essentially higher than forZelenoy's and Akkuratov's methods. Thatcould be achieved due to using of additionalparameters for describing of the situations. Thecharacteristics of the verification of secondtype of discriminant analysis presented inTable 1.

iTime since Thresholdsnowfall probability

Omax Pa Pnbeginning for OmaxP

(h)6 0.10 0.23 0.87 0.36 0.4312 0.15 0.29 0.57 0.72 0.7018 0.15 0.36 0.67 0.69 0.6924 0.20 0.43 0.63 0.80 0.7730 0.20 0.43 0.67 0.76 0.7436 0.20 0.36 0.61 0.75 0.7242 0.20 0.45 0.73 0.72 0.7348 0.30 0.46 0.69 0.77 0.7554 0.35 0.57 0.72 0.85 0.8160 0.30 0.63 0.84 0.79 0.8166 0.30 0.60 0.89 0.71 0.7872 0.30 0.65 0.94 0.71 0.8078 0.40 0.79 0.94 0.85 0.8984 0.45 0.80 0.93 0.87 0.9090 0.50 0.84 0.91 0.93 0.92

Table 1. The results of snowfalls categoricaldiagnostics on "avalanche" and "non­avalanche" for different periods since snowfallbeginning. Snowfalls of 1980 - 84.

It is evident that quality of theclassification increases with time sincesnowfall beginning, that is averagedtrajectories avalanche and non-avalanchesnowfalls in a space of the diagnosticparameters diverge more and more with time.Classification of the snowfalls at differentstages is an advantage of this type of analysiscomparatively with first one.

Bayes' formula. Verification of themodel was made on data for ten winters. Theresult was extremely high - E = 0.85.Comparison of the calculated integralprobability of avalanche situations - P withempirical one - Pe (Zuzin, 1989) is given inTable 2.

5. CONCLUDING REMARKS

Observed situationsavalanche non-avalanche

349113=0.034

100709Pn=0.966pn=0.9998

l/)Q)~ 6e 0.Q e Pa=0.25iii m

:J (ij pa=0.002- >'0 m"0Q)-l/) Q)~ ~

~I 0 18e e

0 om u=0.75u. e-m>m

Table 4. Contingency table for subjective 3hour avalanche danger forecasts for each ofeight separate avalanche sites. Whether ornot an avalanche reach objects in the run outzone (railrQads, automobile roads, open pits).

Q - value the forecasts almost same as for onlyavalanche occurrence prediction, but pa in fivetimes more worse.

Slushflow diagnostic models. Resultsof the discriminant analysis model verificationfor the Khibini Mountains: P = 0.85; Pa = 0.79;Pn = 0.86; Pa = 0.06; Pn = 0.997; 0= 0.21; ~ =0.14; Q = 0,65; and for mountains of Norway:P = 0.87; Pa = 0.76; Pn = 0.84; Pa = 0.40; Pn =0.97; a = 0.24; 13 = 0.16; Q = 0,60. Quality ofthe--diagnostics enough high for first numericalmodels.

Survey of the existed modelsapplicability for verification are reduced due toshort period of using. Some models exist justlike conceptual ones and are formalisedinsufficiently. As carried verification showed itis difficult to test some models intended forspecific genetic types of avalanches becauseof absence of reliable signs which permitindicate types by direct observations. It can be

Quality of such forecast is very IOnly one of one hundred "avalanche" forecais accurate. Only 26% of avalanche situatioare forecasted correctly. Q =0.23 is very lowBut test with t criterion showed that .probability 0.9999 there is significant differebetween these forecast and random ones. Anabove all such forecasts are real forecasts intime and space and are most valuable for theirconsumers. Only forecasts when besidesavalanche occurrence its run out distance isevaluated are some more valuable for theconsumers. In Table 4 the results Ofverification of such forecast are presented.

Table 3. Contingency table for sUbjective 3hour avalanche occurrence forecastsfor each of eight separate avalanche sites.

Statistical simulation. This model is notverified enough reliable because of dataabsence. Twenty situations (8 avalanche and12 non-avalanche ones) were discriminated onavalanche and non-avalanche (by highestprobability) and only one error was got, non­avalanche .situation was recognised asavalanche one.

Synoptic model. This models gives anopportunity to forecast avalanche releases aday before their occurrence with accuracy Pa =0.55 - 1.0 depending on a type of the synopticsituation. Due to big indefiniteness inforecasting of places where the avalanchescan occurred and absence of consumers forsuch forecasts in the Khibini Mountains theywere stopped as a formal procedure and nowsynoptic information is taken into account onlysubjectively.

Some results of verification ofsubjective conclusions on avalanche danger.In practice a final categorical formulation ofavalanche forecast are making sUbjectively ona base all available information. It is interestingto verify this forecast too. If to try to makeforecast formulations more definite in time andspace its validity drops sharply. The results ofthe forecast verification for nine winters arebelow.

Table 2. The results of comparison of thecalculated integral probability - P with empiricalone - Pe

P 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Pe 0.11 0.22 0.34 0.46 0.60 0.74 0.87 1.00

Observed situationsavalanche non-avalanche

Q)l/) ~ 41e 0 3812.Q e Pa=0.263iii ~ 13=0.037m pa=0.0112 >'0 m"0Q)-l/) Q)m 1002560 ~

Q) I 0 115 Pn=0.963... C C0 om u=0.737 pn=0.999u. C(ij

>m

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a reason of non-homogeneity of the testsamples and d~rease the ve~fi~tion re~ults.Good classification of the situations with amodel is not enough for good forecast.Besides the model should give preciseforecasts in time and space. Quality of themodels decrease strongly if to try forecastavalanches in a separate starting zone in ashort period of time, but the models for bigareas and long periods of time have a veryreduced number of forecast consumers. A partof the errors in categorical forecast formulation(high misclassification of avalanche situations)can be explained by incorrect choosing of thethreshold probabilities. At present there are noguidelines how to fix them and the forecastersdo that subjectively. Using of the statisticalsimulation with a reliable deterministic model ofsnow cover stability are perspective.Applicable for practice stochastic forecastmodels should be worked out. Presentedresults of the verification could be used forcomparison different models for a single areato choose best one or the same model indifferent areas to evaluate an influence ofspatial and temporal variability of predictors indifferent geographical conditions on forecastquality.

6. ACKNOWLEDGEMENT

The author wish to express sincerethanks to the engineer of the Centre ofAvalanche Safety of "Apatif' JSC TatyanaMuravieva for the help rendered in compilingthe data.

7.REFERENCES

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