GLACIAL QUARRYING AND DEVELOPMENT OF OVERDEEPENINGS IN GLACIAL VALLEYS; MODELLING EXPERIMENTS AND CASE STUDIES AT ERDALEN, WESTERN NORWAY Julien Seguinot This work was done at Norges Geologiske Undersøkelse (Geological Survey of Norway) in Trond- heim, between March and August 2008, under the supervision of Ola Fredin. It is within the scope of a five-month-long internship included in my first year of master studies at the Terre-atmosph`ere- oc´eandepartment of the Ecole´ normale sup´erieurein Paris. 1 Contents Abstract 1 Literature review 3 Erdalen valley in western Norway exhibit a set 1.1 Glacial overdeepenings . 3 of several sediment-filled overdeepened basins 1.2 Large-scale erosion modelling . 4 carved in the rock by the Quaternary glaciers. 1.3 Process of plucking or quarrying 6 This is a common phenomenon in presently or 1.4 Plucking quantification . 8 previously glaciated regions of the world. De- spite of numerous glacial erosion theories, the 2 Field area description 9 origin of glacial overdeepenings remains confuse. 2.1 Geographical setting . 9 The present study attempts to take a step fur- 2.2 Geological setting . 9 ther in the comprehension of the underlying pro- 2.3 Quaternary geological setting . 9 cesses. The results of a numerical model of 2.4 Morphology . 11 glacial erosion, based on shallow ice flow mod- elling, bed separation and glacial plucking by 3 Glacial plucking model 11 sub-critical crack growth in conjunction with ob- 3.1 Ice flow model . 12 servations on Erdalen geology and geomorphol- 3.1.1 Continuity equation . 12 ogy shows that small-scale overdeepenings are 3.1.2 Navier-Stokes equation . 13 mainly the expression of bedrock resistance vari- 3.1.3 Flow law . 13 ations and flux pattern of the glacier. Glacial 3.1.4 Sliding speed . 14 plucking, as modeled in this study, mainly con- 3.1.5 Non-dimensionalization . 14 tributes to headwall steepening. 3.2 Bed separation calculation . 15 3.3 Fracture growth and erosion rate 16 3.4 Numerical implementation . 17 R´esum´e 4 Results 18 4.1 Observed erosional features . 18 Arrachement glaciaire et d´eveloppement d'om- 4.1.1 Plucking and abrasion . 18 bilics dans les vall´ees glaciaires; mod´elisation 4.1.2 Exploitation of the bedrock 18 et ´etude de cas `a Erdalen en Norv`ege. La 4.2 Bedrock geology . 18 vall´eeErdalen dans l'ouest de la Norv`egeoc- 4.3 Modelling results . 19 cidentale pr´esente une s´erie de bassins rem- 4.3.1 Unviable bed separation . 19 plis de s´ediments et surcreus´es dans la roche 4.3.2 Pre-existing overdeepening 20 par les glaciers quaternaires. Les ombilics glaciaires se rencontrent commun´ement dans 5 Discussion 20 les r´egions qui sont ou furent couvertes par 5.1 The too high sliding velocity . 20 les glaces, et malgr´e les nombreuses th´eories 5.2 Geomorphologic effects . 21 d'´erosionglaciaire, leur origine demeure mal ex- 5.3 Erdalen basins . 22 pliqu´ee. Cette ´etudea pour but de faire un pas dans la compr´ehensiondes processus sous- jacents. Les r´esultatsd'un mod´elenum´erique d'´erosionglaciaire fond´esur l'approximation de 2 couche mince, le d´etachement du lit rocheux subglacial water pressure, or water pressure tem- et l'arrachement par croissance de fracture poral fluctuations (Hooke, 1991; Iverson, 1991). sous-critiques sont associ´es`ades observations Since the last deglaciation, many alpine land- g´eologiques et g´eomorphologiques effectu´ees `a scapes became very unstable, because of the of- Erdalen pour montrer que les petits ombilics tentimes very steep slopes exposures and weath- sont en g´en´erall'expression de variations dans la ering of rock by the glaciers (Terzaghi, 1962; r´esistancede la roche m`ereet dans la forme du Augustinus, 1995; Ballantyne, 2002), leading flux de glace. L'arrachement glaciaire tel qu'il a to the formation of numerous fluvial and rock ´et´emod´elis´edans cette ´etude explique en outre avalanches deposits in the valley floors. Still la formation d'ar^etes. today, and especially in Norway, the landscape remains strongly active and rockfall and rock- fall induced tsunami hazards are serious (Blikra Introduction et al., 2006). Understanding glacial erosion pro- cesses and glacier bed morphologies could help In past glaciated areas, ice has been a very ef- unravel the localization of such events. ficient erosional agent during the Quaternary The aim of this study is to gain a better glaciations, overprinting the existing fluvial net- understanding of the formation of small scale work. Glacially eroded valleys are often easily overdeepenings, relying on previous works in this identified by their characteristic U-shaped trans- area, field observations in Erdalen (Sogn og Fjor- verse profile, but in most of the cases, they also dane, Norway,) and a numerical processes-based show a very typical, stepped longitudinal profile, glacial erosion model. consisting of alternating bedrock thresholds and basins. These basins are called overdeepenings and are presently oftentimes filled with seawa- 1 Literature review ter, lakes or sediments. 1.1 Glacial overdeepenings The formation of glacial overdeepenings is not very well understood and there are many hy- If few overdeepenings have been observed under potheses explaining the processes involved (Sug- present glaciers (Hooke, 1991), rather they have den and John (1976, p. 182), Benn and Evans been exposed during the last deglaciation as flat- (1998, p. 348), MacGregor et al. (2000).) First, bottomed valleys, glacial lakes, or fjords (fig. 1.) the basins could be due to of bedrock resistance These basins have however been identified as ev- variations (lithology, foliation, preexisting frac- idence for glacial erosion for a long time, since tures.) Second, some overdeepenings are situ- rivers do not transport eroded material upslope, ated in the valley confluence points, which in which indeed glaciers can do. turn suggest tributary glaciers could play an Numerous glacial overdeepenings can be quali- important role. Finally, overdeepenings could tatively explain. They are very commonly delim- be formed by self-driven glacial processes lead- ited down-valley by a threshold of harder rock, ing to localisation of glacial erosion (Anderson as the glacier erodes deeper into the less resis- et al., 2006), under the effect of climatic varia- tant materials (Veyret, 1955; Beaudevin, 2008; tions (Oerlemans, 1984), spatial distribution of Benn and Evans, 1998, p. 348). As we will see 3 later, preglacial joints density may play an even more important role in their formation (Matthes, 1930; King, 1959; Gordon, 1981). Finally, it is generally assumed that the local erosion rate of the bedrock is increasing with the ice dis- charge (Harbor et al., 1988; Anderson et al., 2006), and some superficial velocity measure- ments shows valley glaciers can locally accelerate just below, and sometime just above a conflu- ence point (Gudmundsson, 1997; Wangensteen et al., 2006; NASA, 2008). This can explain why so many overdeepened basins are found at the junction point of one or several tributary glaciers (Veyret, 1955; King, 1959; MacGregor et al., 2000). Aside from of all these different explana- tions, there are still some cases of stepped and overdeepened valleys, apparently carved in ho- mogeneous bedrock, trough a regular channel of constant width. This is precisely the case of Erdalen, whose longitudinal profile exhibit sev- eral basins of depths around 50 m and lengths around 1 km. Some authors discussed the im- portance of pre-existing fluvial morphology and meltwater erosion in their formation (Benn and Evans, 1998, p. 349), but this both points will not be brought up in the present study. Rather we will focus on glacial processes, which justify glacial erosion modelling. 1.2 Large-scale erosion modelling A very simple glacial erosion model was pro- posed by Anderson et al. (2006). This model does not require any flow law for the ice, as Figure 1: Sediment enfilling of glacial over- the glacier movement is not described in term deepenings. After the glacier retreats, the basins of velocity field and ice depth, but only ice dis- are filled with water, glacial till, then glaciola- charge per unit width, which means integrated custrine, glaciofluvial and eventually fluvial de- velocity over the entire ice depth. The equa- posits. tions are resolved in one dimension along the 4 1000 glacier erode faster than the equilibrium line re- treats up-valley. A numerical implementation of 800 Anderson et al. (2006) simplest model (uniform ) valley width, linear mass balance) shows that m ( 600 n o the valley floor is rather preferentially eroded i t a v 400 up-slope than really overdeepened (fig. 2.) An e l e overdeepening can only be obtained if the equi- 200 librium line stay at the same position, and this means either that the valley floor is raising or 0 0 2000 4000 6000 8000 10000 the ELA is lowering. down-valley distance (m) Oerlemans (1984), which is a pioneer in long- profile glacial erosion modelling, used a slightly Figure 2: Simple model of glacial erosion of a lin- different model based on temperature-dependant ear valley profile. Valley floor elevation at 10 k.y. ice flow and an empirical abrasion law, obtained intervals. Glacial erosion progressively retreats the same results and concluded that overdeep- up-valley while the glacier bed is flattened, but enings are `favoured by a gradually deteriorating never overdeepened. climate, or slow uplift of the entire region.' The first hypothesis concerns but two phenomenons on very different time scales. The measured longitudinal profile and erosion is assumed to glacial erosion rates are usually at the order be proportional to the ice discharge per unit of magnitude of one millimeter per year (Burki width.