Influence of DEM resolution and domain discretization on the snow avalanche dynamics modelling

INFLUENCE OF DEM RESOLUTION AND DOMAIN DISCRETIZATION ON THE SNOW AVALANCHE DYNAMICS MODELLING Ma cos Sanz-Ramos1*, Pe e Olle 2,3, and E nes Bladé1 1 Flumen Resea ch Ins i u e (Uni e si a Poli ècnica de Ca alunya [UPC Ba celonaTech] – In e na ional Cen e o Nume ical Me hods in Enginee ing [CIMNE]), Ba celona, Spain 2 GeoNewRisk, Ba celona, Spain 3 Riskna g oup (Uni e si y o Ba celona), Ba celona, Spain ABSTRACT: Nume ical modelling o snow a alanche dynamics equi es necessa ily he u ilisa ion o e ain opog aphy o upda e he ele a ion o he calcula ion meshF ee dis ibu ed opog aphical da a is cu en ly a ailable wo ldwide h ough digi al e ain models (DTM), om coa se o ine esolu ions. This wo k aims on in es iga ing he in luence o he DTM esolu ion, bo h in he ho izon al and e ical accu- acy, on he esul s o he bulk dynamics o dense snow a alanches. To ha end, he nume ical ool Ibe , a dep h-a e aged hyd odynamic nume ical ool ecen ly enhanced o he simula ion o non–New- onian shallow lows such as snow a alanches, was used. Se e al calcula ion scena ios, based on wo well-documen ed e en s, we e ca ied ou u ilising combina ions o di e en mesh sizes and DTMs. The indings e eal he impo ance o DTM esolu ion o mid-low size a alanches. When compa ing iden i- cal mesh esolu ions, he e ical p ecision o he DTM has a mo e signi ican impac on he a alanche dynamics han he ho izon al esolu ion o he DTM. E en wi h a i e- old imp o emen in spa ial eso- lu ion, which cu en ly includes LiDAR echniques, he ou comes de i ed om he 5-me e DTM closely esembled hose o he 2-me e DTM, he compu a ional cos being educed no ably. LiDAR-based opog aphical da a allows he gene a ion o DTM and DEM (digi al ele a ion models), being he la es use ul o ep esen he obs uc ions on he low dynamics due o he ege a ion and p o iding a closes ep esen a ion o he a alanche dynamics o he obse a ions. KEYWORDS: DTM/DEM, nume ical modelling, Ibe , smoo hing, ill sinks. 1. INTRODUCTION Snow a alanches a e apid lows o snow down a slope, posing signi ican isks o li e, in as uc- u e, and ecosys ems in moun ainous egions (CCA, 2016; McClung e al., 2002). Unde s and- ing and p edic ing hese e en s a e c ucial o e - ec i e isk managemen and mi iga ion s a e- gies. Snow a alanche modelling is a scien i ic ap- p oach ha aims o simula e he dynamics o a - alanches o p edic hei beha iou , pa h, and po- en ial impac a eas. These models ange om simple empi ical o mulas o sophis ica ed nume - ical simula ions ha conside a ious physical p ocesses in ol ed in a alanche ini ia ion, low, and deposi ion (Egli e al., 2020). A undamen al componen o a alanche model- ling is he in eg a ion o opog aphical da a, which desc ibes he e ain o e which a alanches oc- cu . Topog aphy in luences many aspec s o a - alanche dynamics, including he s a ing zone, low pa h, and un-ou dis ance (Maggioni and G ube , 2003). Accu a e opog aphical da a, ob- ained om sou ces such as digi al e ain/ele a- ion models (DTM/DEMs), ae ial pho og aphy, and sa elli e image y, p o ides c i ical in o ma ion abou slope angles, aspec , cu a u e, and ough- ness, all o which a e essen ial pa ame e s in modelling e o s (G ube and Hae ne , 1995; Maggioni e al., 2013). Topog aphical da a allows o he de ailed map- ping o po en ial a alanche elease a eas and pa hs, enhancing he p ecision o a alanche haz- a d assessmen s. As compu a ional echnologies and emo e sensing me hods ad ance, he accu- acy and eliabili y o a alanche models con inue o imp o e, making hem indispensable ools in he ield o snow science and haza d manage- men . The cu en wo k explo es he in luence o he opog aphical da a (xy- esolu ion and z-accu acy) and he domain disc e iza ion on he modelling o he a alanche dynamics. To ha end, he nume - ical model Ibe (Bladé e al., 2014) ecen ly en- hanced o simula e non–New onian shallow lows (Sanz-Ramos e al., 2024), such as dense snow a alanches (Sanz-Ramos e al., 2023c), was u i- lised o simula e se e al well-documen ed snow a alanche e en s. The simula ions we e ca ied ou by conside ing i e ypes o opog aphic da a, oge he wi h pa icula op ions o Ibe o imp o e he ep esen a ion o he e ain. 2. MATERIALS AND METHODS 2.1 S udy si es and e en s Di e en s udy si es and a alanche e en s we e chosen o analyse he in luence o he opog aph- ical da a in he snow a alanche dynamics, o- ge he wi h some p ocedu es o enhance he ele- a ion da a in he nume ical model. All s udy cases a e loca ed on he sou he n side o he Py - enees ange (Figu e 1). On Janua y 2014 a slab a alanche occu ed in Bonaigua alley, c ossed a oad and s opped ew me e s below wi h a unou dis ance o a ound 650 m. The a alanche spli in o b anches a he deposi ion a ea. A wide desc ip ion o he e en besides da a u ilised in he nume ical model is de- ailed in Sanz-Ramos e al. (2023b). Figu e 1: Loca ion o he s udy si es. On Feb ua y 2018 an a alanche occu ed nea o Coll de Pal pass, be ween 1900 and 2200 m.a.s.l and s opped on a oad and ew me e s below. The e en was cha ac e ized ew days a e he e en showing a unou dis ance o 370 m wi h e ical d op o 215 m. A ull desc ip ion o he su ey and he nume ical pa ame e s a e de- sc ibed in Sanz-Ramos e al. (2021b). The las case s udy is he a alanche occu ed in in 1996 in Bo des d'À eu, a small illage ha was pa ially des oyed in 1803 by ano he a alanche e en (Olle e al., 2020). 2.2 Topog aphical da a All opog aphical da a u ilised come om he In- s i u Ca og à ic i Geològic de Ca alunya (ICGC, 2021), who p o ide DTMs o di e en ho izon al and e ical esolu ions and LiDAR da a, among o he p oduc s. The DTM o 15x15m and 5x5m o cell size a e gene a ed om he opog aphical base a 1:5000 scale. The 2x2m o cell size DTM is based on he 2nd e sion o LiDAR. Finally, he cloud o poin s come om LiDAR da a, being he 1s e sion ob- ained om 2008 o 2011 while he 2nd e sion om 2016 o 2017. LiDAR da a we e il e ed aim- ing o ob ain he g ound, key poin s and, when is necessa y, he ege a ion ( om low o high heigh ), and hen con e ed in o a DTM o DEM in as e o ma . Table 1 summa izes he main speci ica ions o he opog aphical da a employed o upda e he el- e a ions o he mesh a each nume ical model. Table 1. Speci ica ions o he opog aphical da a. Name Resolu ion Accu acy Sou ce DTM15x15 15m 0.90m 1:5000 DTM5x5 5m 0.90m 1:5000 DTM2x2 2m 0.15m LiDAR LiDAR 1* 0.5p/m2 0.06m LiDAR LiDAR 2* 0.5p/m2 0.06m LiDAR *Wi h and wi hou ege a ion. 2.3 Nume ical ool: Ibe The case s udies we e simula ed wi h Ibe (Bladé e al., 2014), a ee dis ibu ed wo-dimensional hyd odynamic ool ecen ly enhanced o simula e non–New onian shallow lows such as dense snow a alanches, mud lows, laha s, wood laden lows, e c. (Ruiz-Villanue a e al., 2019; Sanz- Ramos e al., 2023b, 2023c, 2024). Ibe sol es he shallow wa e equa ions (2D- SWE) h oughou a pa icula nume ical scheme based on he Roe scheme (Roe, 1986). I ensu es he balance be ween he lux and p essu e g adi- en s and he ic ion sou ce e m, a oiding nume - ical ins abili ies and achie ing non–ho izon al ee su ace acco ding o he heology o he luid e en in i egula geome ies and sloping e ain (Sanz- Ramos e al., 2023c). The cha ac e iza ion o he esis ance o ces can be done by means o di e en heological models, such as Voellmy (1955) join ly o no wi h cohe- sion (Ba el e al., 2015), simpli ied Bingham (Bingham, 1916; Chen and Lee, 2002; Nae e al., 2006), Manning (Chow, 1959), dila an - and is- cous-like (Macedonio and Pa eschi, 1992), quad- a ic (O’B ien and Julien, 1988), and (He schel and Bulkley, 1926). Based on p e ious s udies, he Voellmy-Ba el heological model was u i- lized in he simula ions. Addi ionally, Ibe includes se e al ea u es o i- en ed o imp o e he nume ical pe o mance o he model. Specially hose o opog aphical da a ea men in hyd ological modelling (Cea and Bladé, 2015; Ga cía-Alén e al., 2022; Sanz- Ramos e al., 2020, 2021a), such as ‘ ill sinks’ and ‘smoo hing’ can be also use ul o snow a a- lanche modelling. * Co esponding au ho add ess: C/ G an Capi à s/n, Flumen Resea ch Ins i u e, Uni e si a Poli ècnica de Ca alunya (UPC Ba celonaTech) – Cen e In- e nacional de Mè odes Numè ics en Enginye ia (CIMNE), 08034 Ba celona, Spain; el: +34 934054251; email: ma cos.sanz- am[email p o ec ed], [email protected] 25 km N B ie ly, he ‘smoo hing’ op ion adjus he ele a ion o a node acco ding o he nodes ele a ion o i s icini y; while he ‘ ill sinks’ op ion inc ease he el- e a ion o he dep essed nodes o he op ele a- ion o he su ounding o dele e na u al o unna - u al dep essions. 2.4 Scena ios and domain disc e iza ion Se e al simula ions we e ca ied ou pe each s udy si e by eeding he model wi h he o iginal da a, conside ing wo il e s o he opog aphical smoo hing ha Ibe inco po a es (2 and 10 passes) and he u ilisa ion o DTM (no ege a ion land co e ) o DEM ( ege a ion land co e ) in Li- DAR based simula ions. Thus, h ee simula ions we e done pe each opog aphical sou ce, excep o LiDAR in which h ee addi ional simula ions we e ca ied ou conside ing he ‘ ill sinks’ op ion o Ibe . The domain was disc e ized by means o iangu- la elemen s, de ining a side leng h equal o he esolu ion o he DTM in a e age. Thus, he ele- men side anges om 1 o 15 m. 3. RESULTS Due o he la ge numbe o simula ions, he mos ele an esul s o he in luence o he opog aph- ical da a in he a alanche dynamics is p esen ed. 3.1 Coll de Pal 2018 The pa ame e s o he heological model (Voellmy-Ba el ) we e selec ed acco ding o Sanz-Ramos e al. (2021b), being he u bulen coe icien o 1250 m/s2, he Coulomb ic ion co- e icien o 0.34, and he cohesion o 100 Pa. Figu e 2 shows he map o dep h when he a a- lanche s opped. As expec ed, as he elemen size is educed and he e o e he accu acy o he opo- g aphic da a is inc eased, he esul s i mo e closely o wha was obse ed ( anspa en whi e polygon). The DTM15x15 p o ided coa se esul s due o he low esolu ion and accu acy o he opog aphy and he size o he a alanche. A 5x5m DTM shown a good ep esen a ion o he a alanche, wi h a de en ion a ea shi ed o he eas as ob- se ed. When a 2x2m esolu ion is u ilised, he esul s adjus ed o he obse a ions, no only in he a alanche’s ex en bu also in he snow accu- mula ed on he oad (Sanz-Ramos e al., 2021b). Models ed wi h LiDAR da a also pe o med ade- qua ely, wi h di e ences in bo h scena ios ela ed o ege a ion g ow h (no ably highe in LiDAR 2 e sus LiDAR 1). In such cases, he shape o he ege a ion was included in he mesh ac ing as an obs acle o he low, gene a ing accumula ion up- s eam o he ees and expanding he de en ion zone (Naaim e al., 2004). MDT15x15 MDT15x15_s2 MDT15x15_s10 MDT5x5 MDT5X5_s2 MDT5X5_s10 MDT2X2 MDT2X2_s2 MDT2X2_s10 LiDAR 1 LiDAR 1_s2 LiDAR 1_s10 LiDAR 2 LiDAR 2_s2 LiDAR 2_s10 Figu e 2: Coll de Pal. Map o dep h when he a - alanche s opped. 3.2 Bonaigua 2014 The s udy a ea was disc e ized in 3705 elemen s o he coa se DTM o 15x15, while he numbe o elemen s almos each 750,000 o he LiDAR- based models. The pa ame e s o he heological model ha bes i o he obse a ions a e 500 m/s2 o he u bulen coe icien o and 0.125 o he Coulomb ic ion coe icien (Sanz-Ramos e al., 2023c). This case highligh s he bene i o using he ‘ ill sinks’ (_ s) op ion o Ibe since al eady exis s some poin s o he LiDAR cloud wi h w ong ele- a ion da a despi e he da a ha e been ea ed p e iously. This gene a es un eal dep essions on he e ain (Figu e 3, uppe ) ha , some imes, a e di icul o de ec e en using ad hoc LiDAR o /and GIS so wa e. Figu e 3: Bonaigua. Map o e ain: LiDAR 1 (up- pe ) and LiDAR 1_ s (lowe ). Values lowe ha 1975 m a e plo ed in black, which ep esen s he dep ession (highligh ed in a ci cle). Figu e 4: Bonaigua. Map o maximum snow ele- a ion: LiDAR 1 (uppe ) and LiDAR 1_ s (lowe ). Values lowe ha 1975 m a e ep esen ed in whi e (highligh ed in a ci cle). As expec ed, his ab up change in he opog a- phy no ably modi ied he dynamics o he a a- lanche because he dep ession ends o be illed. An un eal inc ease o eloci y was p oduced due o he change o slope, while he dep ession could no be illed depending on he a alanche dynam- ics gene a ing an un eal snow ele a ion p o ile (Figu e 4, uppe ). The ‘ ill sinks’ op ion o Ibe nume ically ill hese dep essed a eas, sol ing he a o emen ioned is- sues and p o iding a eliable snow a alanche dy- namic modelling. Rega ding he pe o mance o he model wi h he di e en opog aphical da a, in all cases he e- sul s show a de en ion a ea spli in wo b anches, e en o he coa se DTM o 15x15m. 3.3 À eu 1996 The snow a alanche o À eu 1996 was well e- p oduced wi h all opog aphical da a due o he size o he a alanche. The de en ion zone was p oduced in he Mona s Go ge and À eu Ri e junc ion. Figu e 5 (uppe maps) shows he a a- lanche a he end o he simula ion when using a 15x15 (up), 5x5 (middle), and 2x2 (down) DTM. Figu e 5: À eu. Map o dep h when he a a- lanche s opped (uppe maps). Map o slopes (lowe map), colou ed map il e ed om 0 o 1 m/m (black colou ep esen s slopes highe han 1 m/m). This ag ees wi h he selec ed heological p ope - ies o he a alanche and he slope, he Coulomb ic ion coe icien being o 0.35 (Figu e 5, low map). As he DTM cell size is educed, he de ini ion o he junc ion, as well as he es o he alley, im- p o es, p o iding a mo e de ailed and accu a e desc ip ion o he a alanche dynamics. The junc- ion is almos pe pendicula ; hus, when he a a- lanche a i es ends o con inue lowing in he o iginal di ec ion gene a ing an accumula ion a highe al i udes o he i e bed. À eu case s udy also p esen ed p oblem wi h he opog aphical da a, especially in LiDAR da a wi h some poin s below o he eal opog aphy. This issue was also sol ed wi h he ‘ ill sinks’ op ion o Ibe . 4. DISCUSSION 4.1 On he da a sou ce and pe o mance All da a u ilised come om cu en echniques and ollowed se e al s anda ds ha modelle s u i- lise o eed nume ical models aiming o simula e di e en en i onmen al lows. Pa icula ly o dense snow a alanches, cu en ly exis s a wide ange o esolu ions hanks o he con inuous e olu ion in he acquisi ion o opo- g aphical da a. Fine esolu ion commonly implies highe accu acy, being his las ac o a key in nu- me ical modelling (Chojnacki e al., 2010; Do o i e al., 2013), especially in moun ain a eas whe e he accu acy is limi ed by he echnique u ilised o ob ain i . This also implies he possibili y o building up mo e de ailed nume ical models. The s udy cases we e disc e ised using a mesh o iangula ele- men s, which i in ol es a densi y o elemen s pe hec a e anging om ~88 o 20000. The compu- a ional e o when ine meshes a e u ilised in- c eases no ably o nume ical models based on a nume ical scheme explici in ime (Cou an e al., 1967). Thus, he applica ion o gene al-pu pose compu ing on g aphics p ocessing uni s being manda o y o ca y ou simula ions in a easible compu a ional ime, such is al eady done in he hyd odynamic and sedimen anspo module o Ibe (Dehghan-Sou aki e al., 2024; Sanz-Ramos e al., 2023a) and i will be ealized in u u e e - sion o he non–New onian module, eaching speed-up abo e 100- imes. 4.2 On he land co e (DEM s. DTM) LiDAR da a is a cloud o poin s usually classi ied acco ding o he LiDAR e u n/in ensi y as g ound, low-mid-high ege a ion, buildings, wa- e , e c. Depending on he p ocedu e o ob ain his cloud o poin s, and la e ea men , LiDAR da a can be di ec ly used o upda e he ele a ion o he nodes o a calcula ion mesh. Figu e 6 exempli ies he di e ences in he u ilisa- ion o opog aphical da a as DTM (le , wi hou ege a ion land co e ) and as DEM ( igh , wi h ege a ion land co e ) o he simula ion o he e en o Coll de Pal. In bo h cases he unou ob- ained was simila , bu conside able di e ences we e obse ed in he dynamic and s a ic phases, specially below he oad. Figu e 6: Coll de Pal e en simula ed wi h Li- DAR 1: DEM (uppe le ) and DTM (uppe igh ); map o maximum dep h wi h opog aphical da a as DEM (lowe le ) and as DTM (lowe igh ). This a ea is co e ed by mid-low dense ege a ion ha co esponds o a ela i ely young o es . When he DEM is u ilised, he ege a ion is inco - po a ed in o he model as an addi ional ele a ion ha ac s as mac o- oughness. This has an e ec on he a alanche pa h and de en ion since lows wi h enough ene gy pa ially accumula es up- s eam o he ege a ion; while he es con inue lowing gene a ing an i egula de en ion zone in compa ison wi h he DTM simula ion, which is smoo h. In such case, he esul s ha bes i wi h he obse a ion may be in an in e media e si ua- ion: DTM wi h ege a ion in he g ea es ees and an inc ease o oughness in he es . Conside ing he ege a ion o he DEM in he snow a alanche modelling could no be ep e- sen a i e o he eal beha iou : he sh ub ege a- ion is ei he co e ed wi h snow, o has a lexible beha iou owa ds he a alanche as occu in lu- ial loods (Cheng, 2011; Nep , 2012; Sanz- Ramos e al., 2018; S ephan and Gu knech , 2002), and some ees will wi hs and he impac , bu o he s will b eak. Thus, DEM da a conside s all hese elemen s as a pe manen and in a ian mac o- oughness h oughou he simula ion, no being as ealis ic as wi h DTM da a. The use o DEM can be mo e use ul o small a alanches, which do no ha e enough ene gy o b eak ees, han o la ge a alanches, whe e he e is a lo o o es des uc ion. Howe e , u he in es iga ion is needed o ully unde s and he ole o DEM in snow a alanche modelling. 4.3 Fine- uning opog aphy wi h Ibe Addi ionally, despi e he classi ica ion and ea - men o LiDAR da a, which is done by he p o ide o he sou ce ollowing s ic s anda ds, some e - o s and ou lie s can emain. This was he case in Bonaigua case s udy, in which a ew poin s o he cloud ha e an ele a ion e y a om he poin s o i s icini y, e en a e applying he same ea - men as o he es o LiDAR da a. In such cases, he ‘ ill sinks’ op ions o Ibe allowed o co ec he opog aphical da a illing he sink wi h an ele a- ion equal o he lowes node o he su oundings. This is also use ul o ill dep essed a eas ha usu- ally cumula es snow du ing snow e en s (e.g. up- s eam o b idges, cul e s, e c.) and migh condi- ion he a alanche dynamics. The op ion ‘smoo hing’ o Ibe plays a ole simila o hose ob ained when simula ing an a alanche wi h coa se DTMs. Howe e , his op ion allows modelle s o use e y ine esolu ions and ob ain a smoo h ep esen a ion o he e ain, e en when using summe opog aphy. Fu he in es iga ion on he u ilisa ion o ‘smoo hing’ o Ibe is neces- sa y, mainly o ien ed o compa e he esul s o summe opog aphy wi h ‘smoo hing’ and he win- e opog aphy (Maggioni e al., 2013). These op ion helps he modelle o deal, wi hou addi ional ea men s and in he simula ion p o- cess, wi h some p oblems in he opog aphical da a when simula ing dense snow a alanches. 5. CONCLUSIONS Se e al opog aphical sou ces we e u ilised o e- p oduce well-documen ed snow a alanche e en s wi h Ibe , a dep h-a e aged hyd odynamic nume ical ool ecen ly enhanced o simula e non–New onian en i onmen al lows. Depending on he size o he a alanche, coa se mesh and opog aphical da a (e.g. 15m) canno be able o ob ain a sui able ep oduc ion o an a - alanche e en . Fine meshes and de ailed opo- g aphical da a, despi e inc ease he compu a- ional e o , p o ide high esolu ion esul s. The u ilisa ion o DEMs (DTMs wi h ege a ion) can be u ilised conside ing he ege a ion as mac o- oughness, especially o small and medium a a- lanches, bu u he esea ch is needed. A di ec u ilisa ion o DTM/DEMs o 15, 5, 2, and 1 m o as e cell size is possible, bu some issues migh be gene a ed especially wi h LiDAR da a. 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