Emmanuel Cohen

Wiedaad Slemming

Stephanie V Wrottesley

Alessandra Prioreschi

Shane A Norris

J ( Copans

Maternal perceptions of infant's body weight and childhood obesity in South Africa: A qualitative study in Soweto

Keywords: childhood, early years, education, health & well-being, food & diet Children & Society Lay norms, Body weight perceptions, Dietary practices, Childhood obesity, Soweto 15 16

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Over the last few decades in Western countries, modern values have favored a social 19 construction of the body oriented towards a permanent control of its natural expression. The 20 main societal aspiration promoted by media consists of fighting fatness, aging, illness and death 21 [START_REF] Brewis | Body norms and 523 fat stigma in global perspective[END_REF]Le Breton, 2011). In a postmodern era where one can modify their body 22 according to their fantasies, this demanding societal expectation, exacerbated by a constant 23 increasing technological development, acts as a social injunction to heal all life imperfections 24 (Foucault, 1976;Tratnik, 2017). However, the literature shows that in societies based on Following the recommendation on the methodologies of investigation in anthropological 146 studies, the qualitative analysis was based only from the participants' discourse. To achieve 147 this, we adopted an inductive approach without pre-identification/categorisation of mothers' 148 perceptions of their infants' body weight and feeding practices in Soweto. Indeed, the strategy 149 was to understand perceptions of mothers, considered by the researchers as the first experts of 150 their daily life in their community, and therefore reduced as much as possible the influence of 151 researchers' subjectivity (Copans, 2008). Four researchers using a thematic grouping approach 152 based on an exhaustive reading of all transcripts performed transcript analyses independently.

153

The main emerging themes were identified from the comparison of each researcher's thematic 154 grouping to avoid as possible the individual subjectivity of each researcher (Mason, 2002). We 155 retained the main common themes identified by all researchers, considered as the central topics 156 developed by participants. After identification of the main themes organised as a codebook, we used the constant comparative method (Corbin & Strauss, 1990) to categorise the main

249

The social aspiration to have a 'fresh' baby can reach such a high level that some mothers never Body Size" in adults and infants (Table 1).

261 ancestors' spirits, monotheist god, etc., which control the world [START_REF] Brown | An anthropological perspective on obesity[END_REF]; de country, the historical influences of these body weight animist conceptions persist through the 392 inheritance of elders (McFarlane, 2015;Schierenbeck et al, 2016), who have still experienced

393

during their youth some pre-industrial rural conditions.

394

Thus, in emic norms relative to societies still connected to a pre-industrial lifestyle, fatness has 395 often a spiritual value, perceived as the expression of an essential sacred fluid under the control 396 of these mystic entities [START_REF] Bird-David | Animism" revisited: Personhood, environment, and relational 511 epistemology[END_REF][START_REF] Bosire | I'd 520 say I'm fat, I'm not obese': Obesity normalisation in urban-poor South Africa[END_REF]. In this perspective, fatness is 397 commonly not a sign of illness in these societies, especially because in pre-industrial lifestyles 398 and their cultural inheritances, food access constitutes a daily hardship and morbid obesity is 399 rare [START_REF] Boëtsch | Les variations historiques et culturelles de la morphologie corporelle[END_REF][START_REF] Brown | An anthropological perspective on obesity[END_REF][START_REF] Cassidy | The good body: When big is better[END_REF]. Being rich means first of all being 400 well fed, being fat. Eating is always good, it originally represents a gift from this sacred nature, associated with an HIV positive status, as observed in this study [START_REF] Ashforth | An epidemic of witchcraft? The implications of AIDS for the post-509 apartheid state[END_REF]Rispel et al., 415 2015).

416

In African animist conceptions of the body reported by several studies, survival is an expression 417 of a constant unstable balance between endogenous and exogenous mystic vital energies lead to an unbalance between the body and the world leading to a "catastrophic" weight loss -427 the mystic entities "eat" the body [START_REF] Bosire | I'd 520 say I'm fat, I'm not obese': Obesity normalisation in urban-poor South Africa[END_REF]. Many South African women in our study still 428 believed, through their traditional medicine, in these mystic conceptions of the body, as 429 described in other rural and urban South African studies [START_REF] Bosire | God, Church water and 517 spirituality: Perspectives on health and healing in Soweto, South Africa[END_REF]Fottrell et al., 430 2012;Hundt et al., 2004).

431

Historically, if the valorization of stoutness appears well-adapted in rural areas where South Africa and Ghana [START_REF] Appiah | Preferred body size in urban Ghanaian 506 women: Implication on the overweight/obesity problem[END_REF]Cohen et al., 2013;Micklesfield et al., 2013).

440

And this sociocultural exposure to obesity also affects children, the familial environment 441 transmitting these body weight representations and practices from one generation to another, as 442 observed in South African families (Mchiza et al., 2011;[START_REF] Wrottesley | Maternal perspectives on infant feeding practices in Soweto, South Africa[END_REF].

443

The potential divergences between lay and Western conceptions of health in Africa is a major 444 challenge that concerns all aspects of public health, between emic/etic etiologic interpretations, towards their infants appeared ill-adapted to their nutritional health [START_REF] Bosire | I'd 520 say I'm fat, I'm not obese': Obesity normalisation in urban-poor South Africa[END_REF]

250"

  heard about how to make a child lose weight (Interview 3)". Hence, most mothers attested 251 concerning infants' body size that in their community: "The ones that I know and the ones that 252 I see when I go to the clinic, the kids are 'fresh', they're 'chubby' (Interview 4)". Overweight 253 is almost never perceived as a real danger, especially for babies, because the community 254 considers that infants need energy -even in excess -to grow and live: "Overweight? As long 255 as he's growing I think that he's fine (Interview 11)". This perception of fatness as a symbol of 256 normality and health is common in the community, and also expected in adults, especially in 257 women: "I want to be fat (laughs), I'm tired. I need a bigger body, I need to change, I think I'll 258 eat more than I do now (Interview 10)". And we can observe that this expectation in adults -259 in our case in mothers -is projected on children, as a relative relationship between the "Desired 260

401

  described byFarb and Armelagos (1980) and deGarine (1996) respectively in Bantou and 402 Massa ethnic-groups. In Cameroon,Cohen et al. (2013) showed that in Bamiléké lay norms, a 403 normal weight must intrinsically contain a relative excess of weight, such as a necessary 404 protective adipose tissue for the survival. This normalization of fatness is observed in this study 405 and also identified by Bosire et al. (2020) in another South African study, while thinness, and 406 particularly weight loss, is associated with a potential misfortune/illness. 407 Thus, an HIV positive status -often demonized according to interviewees -has a double-408 representation in societies which have maintained vitalistic conceptions of weight into urban 409 areas (Marenko, 2014). Since it represents basically an external attack against the individual410that can lead to a rapid weight loss, this symptomatology also generates codifying 411 "catastrophic" interpretations associated with a divine/magic punishment(Liddell et al., 2005).412Hence, several South African studies showed that overfeeding is valued and promoted (Morris 413 & Szabo, 2013;[START_REF] Wrottesley | Maternal perspectives on infant feeding practices in Soweto, South Africa[END_REF], while leanness as a "contagious curse" is often

432

  undernutrition is prevalent, this psycho-cultural inclination, as a persisting cultural inheritance, 433 becomes rapidly ill-adapted within the fast urbanization process of Africa. Indeed, sociocultural 434 traits valuing fatness as a symbol of health can expose populations to obesity in this context of 435 urbanization leading to a rapid nutrition transition. Through the development of the obesogenic 436 urban physical environment (e.g. motorized transports, high-calorie processed foods), such a 437 sociocultural environment (e.g. valorization and normalization of overweight/obesity, fattening 438 practices) can become a major risk factor for obesity in urban areas, as identified in Cameroon,

445

  compliance to treatments, biomedical practitioners and patient care relationships and 446 therapeutic trajectories, as described by Scherz (2018) in Uganda.[START_REF] Bosire | God, Church water and 517 spirituality: Perspectives on health and healing in Soweto, South Africa[END_REF] in Soweto 447 found that many participants of their study associated their co-morbidities (e.g. HIV positive 448 status and diabetes) with magic actions. Pelto and Pelto (1997), as well as Colvin et al. (2013), 449 found that African mothers living respectively in Gambia and Nigeria adopted etiologic 450 interpretations of acute respiratory infections and diarrhea in their children, attributed an 451 importance of these diseases, and mobilized therapeutic strategies that were ill-adapted to their 452 efficient treatments. In our study, lay maternal perceptions of body weight and dietary practices 453

  Following the standard procedure, we asked mothers to point out on the BSS their

	140	undernutrition to severe obesity, to give a concrete visual expression of body weight
	142	"Desired Body Size".
	143
	144	Data analysis
	145
		R e v R e v R e v R e v R e v
		i e w i e w i e w i e w i e w
		C C C C C
		o o o o o
		p y p y p y p y p y
		7

25 community life, a reduced technical development and a persistent animist sacralization of 26 nature, particularly in farmer and hunter-gatherer populations, the biopolitics of body have not 141 perceptions.

normalization of fatness 224 Fatness as a norm. In

  Through this perspective, being too thin, for both infants and adults, is the lay (communitarian) body weight norms described by interviewees,

	190 215	Results beautiful baby is fat; I see with how they treat mine (Interview 8)". Indeed, having a fat baby is HIV positive people take and you didn't take it', then the children don't grow properly
	166 216	We identified three main themes characterizing infants' body weight norms and feeding (Interview 4)". The necessity to be "fresh" is essential until the point that some mothers were
	167 217	practices in families living in Soweto. These include: a valorization of fatness, a normalization afraid to have a thin baby which could be stigmatized by adults, as a constant social pressure to
	168 218	of fatness and an obesogenic familial environment; and one more theme related to a progressive match the body weight norms promoted by the community: "Every time you walk next to your
	219	'fresh' baby, people greet and call him, but with a tiny one you get scared that someone tells
	220	you: 'No man this baby…' (Interview 5)"; "If the baby isn't 'fresh', they'll make snide remarks
	221	like: 'Ouu she's so filthy and skinny'. They criticize the baby (Interview 9)".
	222
	R e v R e v R e v there is an overlap between fatness, expressed by the terms "chubby" and "fresh", and the A 225 223 R e v
	226 227	i e w i e w i e w normality: "In my language, a normal body weight for baby is 'fresh' (Interview 1)"; "Babies who are 'chubby' are considered normal (interview 4)"; "Babies with a normal body are i e w
	228 229	C o C o C o 'chubby', proportional, they're fine (Interview 11)". Thus, for many mothers, being normal for C a baby is only to be not 'too fat': "My baby has to be on the right level, not too fat (Interview o
	230 231	p y p y p y 10)"; "My baby is fine, not too fat or slender, he's just in the middle (Interview 11)". Therefore, the vernacular definition of excessive body weights is consciously defined by mothers, and p y
	232	apparently their community, by a category above "fat":"We prefer normal babies, not fat, not
	233	'that fat' [sdudla fehlefehle]…, because there's fat [sdudla] and then there's fat, fat, fat [sdudla
	209 234	illnesses. In most cases, a thin silhouette means that something is potentially wrong: "When fehlefehle]. Fat [sdudla] is 'fresh' (Interview 2)".
	210 235	you have a child that's a bit on the thin side you aren't happy (Interview 4)"; infants not Difficulties in detecting overweight. Accordingly, some mothers, able to observe these lay
	161 211 236	(SCRC Co., Manhattan Beach, CA, USA) to group, analyse and synthesise the main outcomes "chubby" must be fed more: "In the community, they have this notion that children don't get body weight norms with a relative distance, said: "Maybe people can't differentiate between
	162 212 237	of the semi-structured interviews. full (Interview 6)". If both mother and their infant are not "fresh", catastrophic interpretations fat and normal... (Interview 5)". Thus, different quotes also attested that many mothers
	163 213	can emerge in the community: "Even if I'm HIV negative, they simply won't believe you. They'll
	164 214	say: 'No…, how come the child looks like that?' And they'll say: 'You should take the pill that
		9 10

158 information within each as subthemes. The themes and subthemes were analysed and compared 159 with each other to create a consistent presentation plan of the results. All results were presented 160 by the most relevant quotes illustrating the participants' discourse. We used Dedoose 8 software 191 a good way to receive positive remarks from peers concerning his or her health status, and feel 192 him/her considered by the community: "If we're walking down the streets, people will shout: 193 'sdudla sdudla' [fatty fatty], because they like him (Interview 8)"; "When you're walking down 194 the street with your child and people come to play with her, they'll say: 'She's so 'fresh'' and 195 they'll play with her (Interview 9)". 196 Phobia of thinness. 197 unfortunate for the community. For mothers, "that's the language that we get confronted 198 with…, because when you lose a bit of weight it's difficult to even go back home to visit. Because 199 they all feel sorry for you (Interview 4)". Indeed, losing weight in a short time is not perceived 200 as natural by the community; the weight loss expressing a suspicious reduction of vital energy 201 and wellbeing in vernacular conceptions. The worse situation is a significant weight loss in 202 infants, which is interpreted in terms of severe illnesses: "The baby's weight loss is the main 203 worry of most mothers (Interview 11)". Thus, in seTswana and seSotho cultures, a traditional 204 mystic and common infant disease named "Kokwana" presents symptoms of weight loss caused 205 by evil spirits which aim to steal the vital energy of humans: "The 'kokwana' eats the child 206 from inside, the kid becomes weak, the child doesn't eat properly because that illness ravages 207 him from the inside, they lose weight (Interview 7)". 208 According to interviewees, the lack of fatness is a symbol of poverty, being cursed, sorcery and 238 consciously defined infants' normal weight above the Western and biomedical criteria : "A 239 child growing properly, that has like… let me say 2 years old children wear clothes for 2 to 3 11 240 years old, or 3 to 4; so that's a child that we can say is normal (Interview 6)". These 241 conceptions of body weight are so omnipresent that they historically penetrated the linguistic 242 field. Thus, in both Zulu and Tshivenda languages, a fat person -also defined as overweight -243 is normal, healthy and valued by the society. "In Zulu, we say 'sdudla' for a fat person. Babies 244 like that eat delicious food, they grow nicely (interview 8)"; "In Tshivenda, the name for a baby 245 with a normal body weight is 'ngwana wa vhudi' [a good-looking baby]. […] The baby is fat 246 or 'chubby', happy like she just looks normal. […] For overweight babies, it is 'vhumkhede' 247 [fat]. The baby might be fat, like 'chubby'. […] There is no real difference with 'ngwana wa 248 vhudi' (Interview 9)".

Table 1 262 An obesogenic familial environment

 1 In many cases, when the mother refused to follow these familial 290 injunctions, older women at home took the responsibility -when they had the opportunity -to 291 feed the baby according to their own views: "If I leave my baby to my grandmother, she will

	265	familial pressure and injunction to overfeed the babies and not respect the dietary practices
	268	"They feel bad when they're eating something and the baby isn't, they say: 'I can't eat
	269	something while my baby isn't' (Interview 5)". In these lay communitarian conceptions of
	270	weight, gaining a constant weight for a child is a necessity as a proof of healthy growing: "When
	271	a child is thin, like he was fat when he was young but he's losing weight because he's more
	272	active…, he eats a lot but he's active; so they think that something is wrong (Interview 1)".
		R e v
		i e w
		C
		o
		p y
	286	around they want our kids to be thin (Interview 4); "Nurses just give us an attitude like: 'Your
	287	child is not normal!', others are born like that and they think that you feed the child… (Interview
	288	12)".
		12

263

Familial sociocultural pressures. For mothers, several obesogenic feeding practices 264 commonly adopted by the community's members were often a consequence of a constant 266 recommended by the clinic: "We stay with old women (grandmothers), like maybe if the baby 267 is crying at night, they'll be like: 'This child is not full, that's why he's crying' (Interview 2)"; 273 Hence, the older women at home permanently give advices to feed children with calorie rich, 274 solid food at early ages: "My mother and grandmother recommended that cream of maize to 275 me (Interview 10)". And these advices in many cases become orders when the communitarian 276 dietary practices are not sufficiently integrated by mothers: "Most of us, black people, feed our 277 children [a lot]. Because you know how our parents are: 'Feed the child. There's no this and 278 that (e.g. porridge)! A child must eat, they're hungry!' (Interview 12)". 279 The Table S2 synthesizes mothers' body weight perceptions and practices towards their infant 280 according to the five subthemes already treated. We could observe that mothers are at least 281 concerned by one of these subthemes, showing as a main tendency that they adopt -or 282 experience communitarian social injunctions to adopt -perceptions and practices favoring a 283 rapid infant's weight gain. Indeed, for mothers, clinics are often perceived by the community 284 as social spaces conveying intrusive biomedical Western (etic) values overvaluing thinness as 285 the acceptable body weight standard: "Some people just say that these nurses are messing us 13 Overfeeding by elders.

297 that it's their granny and she'll give them whatever they want (Interview 6)". For mothers, 298 many older women at home adopt fattening practices, using for instance pap (maize meal), soft 299 porridge, mash, samp and "maas" [fermented milk] to make the baby rapidly bigger from birth: 300 "Upon being born, at three days, the infant is fed with porridge mixed with Rama (margarine), 301 those things are fatty. At 7 days, the child's being fed with potatoes and other things (Interview 302 4)"; "Since birth you find that these babies are big compared to others, it's because of what 303 they eat. You find that the baby eats EVERYTHING, EVE-RY-THING (Interview 5)".

304

These feeding practices identified are not only perceived to be obesogenic within the mind of 305 some mothers; they are indeed obesogenic practices with rapid deleterious effects on infant's 306 body size: "He was growing and becoming fat, because he wasn't like babies from his age.

307

When people asked me: 'How old is this baby?', they said: 'You're lying, this child looks six 308 months old!' you know? The nurses at the clinic said: 'This child is not normal'. So I didn't 309 know what to do (Interview 12)". Hence, Figure 1 synthesizes the main processes leading to an 312 obesogenic rapid weight gain in babies.

322

dietary practices acting as lay social injunctions for making babies "chubby": "Some force their 323 kids at a young age to eat, and the child is fat, like obese; the child is obese, it's not normal, 324 above normal weight (Interview 1)".

325

Through medical messages and the recurrent exposure to obesity in Soweto with its dramatic 326 consequences, mothers globally tended to be more aware -although they still remained 327 influenced by their culture -than the older generation toward this burden: "Ah babies in the 328 township eat everything, they like junk food man. You'll find someone going to buy chips for a 329 1 year old baby, saying: 'My baby likes fat cakes'. He likes fat cakes?! Where does a 1 year old 330 baby know fat cakes from? They're ruining babies man (Interview 5)". Thus, this lay 331 valorization of fatness as a symbol of health, wellbeing and prosperity seemed to be questioned 332 by some mothers: "I think that babies 'sdudla fehlefehle

' [excess of fat]

are going to contract 333 a lot of diseases, like heart disease and diabetes… (Interview 1)"; "I see a difference between 334 me and my community concerning babies, I don't like 'sdudla' [fat] babies (Interview 2)". 337 about our children's lives; we do things because our grandmothers did the same thing. But 338 things are different today from what they were back then, we no longer live the same way that 347 we ate from day one or three days. With these babies, we wait a bit and watch what's going on, 348 so it's not the same (Interview 5)"; "I started to feed my baby with solid food from 2 months, 349 and my mom's age group started earlier. As soon as you got back home from Bara, they fed the 350 baby (Interview

11

)". The frequent early feeding of infants with solid foods, whereas the 351 medical recommendation is an exclusive breastfeeding until 6 months, did not represent 352 anymore an absolute norm for some mothers: "With my child, when he wasn't eating, they said 353 I must make him spinach and pap and peanuts and he would eat, but I didn't do that because I 354 don't know anything about that way of doing things (Interview 4)".

355

Therefore, other communitarian practices such as constantly forcing the baby to eat when he 356 refused to be fed seemed to be progressively abandoned by few mothers: "If the baby doesn't 357 want to eat, you leave her; but us we were forced even if we didn't want to eat, they'd fed us 362 we feed them, like kota (South African sandwich filled with processed meat) and all that 363 (Interview 7)". Overall, most mothers reproduced -at least partially -communitarian body 372 community may lead to early obesity. Under a constant communitarian pressure, most mothers 373 tended to socially value and normalize fatness and reject thinness of infants. This propensity 374 led mothers, and particularly older women at home for the interviewees, to adopt high-calorie 375 feeding practices towards infants potentially obesogenic. An emerging questioning from 376 mothers about these emic norms related to infants' nutritional health appeared, although older 377 women's authority and legitimacy maintained lay norms on body weight and feeding practices 378 as the dominant social schema of infant's health, especially in response to biomedical (etic) 379 messages promoting thinness as the unique body weight standard for the community.

380

Several qualitative studies showed that many African populations have maintained historical 381 representations of body weight strongly different to those adopted over the last decades in 382 modern societies. Whether in South Africa, Cameroon or Senegal, body fat is intrinsically 383 perceived as an expression of wellbeing, as observed in our study

(Cohen et al., 2019; Dapi et 387

considered as a capacity to survive in uncontrolled natural environments where the lack of vital 388 energy constitutes the main worry, and often interpreted as an action from mystic entities,

Table 1 .

 1 Relationships between mothers' body weight perceptions for themselves and their offspring Underweight For babies very thin, I think they are born naturally like that. is normal…, they are 'sdudla' [fat], they have weight.Overweight When you have a child that's a bit on the thin side, you aren't happy. has big cheeks, and just a big body; maybe he's 1 year but wears clothes for 3 to 4 years, they're just big babies.OverweightThin children, they're lifeless, like they're weak, they have no life or energy in them.OverweightMy child is fat. I'm happy with his weight, he's just fine.Normal weightChildren with a low body weight? Sometimes, that's just their natural body weight. Articulation between maternal and communitarian body weight perceptions and dietary practices favoring childhood obesity

	457	the Western representations (etic) where the biomedical discourse tends to -systematically -
	458	associate the promotion of fatness with a potential risk for obesity, and on the other side the lay
	459	representations (emic) valuing fatness -even in excess -as a sign of health. If younger African
	460	generations have experienced a modern acculturation process leading them to criticize the
	461	obesogenic aspect of lay body norms transmitted by elders, as observed in these mothers and

, and 454 can constitute a sociocultural determinant of early obesity during childhood, as suggested in 455 other South African studies

(Mvo et al., 1999;[START_REF] Wrottesley | Maternal perspectives on infant feeding practices in Soweto, South Africa[END_REF]

.

456

Mothers were at the frontier between two systems of body weight representations. On one side 462 other South African or Cameroonian studies

(Cohen et al., 2019; Dapi et al., 2007)

, some 463 cultural resistances towards the apology of thinness as "the norm" cannot be neglected. Through 30 Figure 1.

Table S1 :

 S1 Infancy in-depth interviews

	Infant's Mother	Infant's Age
	Interview 1	1 month
	Interview 2	6 weeks
	Interview 3	4 months
	Interview 4	6 months
	Interview 5	7months
	Interview 6	8 months
	Interview 7	12 months
	Interview 8	13 months
	Interview 9	17 months
	Interview 10	18 months
	Interview 11	19 months
	Interview 12	23 months
	R e R e R e R e R e R e
	v v v v v v
	i e i e i e i e i e i e
	w w w w w w
	C o p C o p C o p C o p C o p C o p
		y y y y y y

Children & Society

Garine & Pollock, 1995; Ndoye, 2001). Even though South Africa is now a middle-income

marker of their "Africanity" and "traditions" in the context of modernization of Africa

(Onebunne & Obasi, 2019), as found by[START_REF] Bosire | I'd 520 say I'm fat, I'm not obese': Obesity normalisation in urban-poor South Africa[END_REF] in Senegal.

An undergoing acculturation process 315

Questioning the valorization of fatness. Despite the strong influence of older women on residing inside and outside the body (Warnier, 2009;[START_REF] Zempleni | Between "sickness" and "illness": From socialization to individualization 667 of the "disease[END_REF]. Thus, traditional 419 medicines, as the mystic treatment of the "kokwana" which "eats" the child from inside in our 420 study, usually adhere to a fundamental paradigm consisting of the maintenance of this balance 421 (Scheper-Hughes & Lock, 1987). The so-called "gift-giving" of Mauss has a mystic dimension 422 through offerings to supernatural entities to guarantee in turn positive energy and vitality in the 423 community [START_REF] Bondaz | Gift, Sacrifice, and Sorcery: The Moral Economy of Alms 515 in Senegal[END_REF]. As long as these entities are satisfied, the mystic 424 fluids crossing the body are under control. However, a rupture in harmony with these 425 supernatural entities, often associated with a rupture in social interactions [START_REF] Zempleni | Between "sickness" and "illness": From socialization to individualization 667 of the "disease[END_REF], Such an identitarian closure faced with acculturation processes has already been identified, as 468 observed in African migrants living in Europe (Luque et al., 2006). Thus, Thomas and DeCaro 469 (2018) found in African Americans that the so-called "traditional" perceptions commonly


Steffi Woo

Fuhui Shao

Nianjheng Wu

Robert Schneider

Ashish Arora

Johann Preuß

Benjamin Carey

Steffen Michaelis De Vasconcellos

Andrew Mayne

Rudolf Bratschitsch

Strain Relaxation and Excitonic Absorption of Atomically-Reconstructed WSe2 Moiré Superlattices

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Strain Relaxation and Excitonic Absorption of Atomically-Reconstructed WSe2 Moiré Superlattices

Steffi Y. Woo 1 , Fuhui Shao 1 , Nianjheng Wu 1,2 , Robert Schneider 3 , Ashish Arora 3,4 , Johann A. Preuß 3 , Benjamin J. Carey 3 , Steffen Michaelis de Vasconcellos 3 , Andrew J. Mayne 2 , Rudolf Bratschitsch 3 , Luiz H.G. Tizei 1,* 1 Laboratoire de Physique des Solides, Université Paris-Saclay, CNRS, Orsay, France 2 Institut des Sciences Moléculaires d'Orsay, Université Paris-Saclay, CNRS, Orsay, France 3 Physikalisches Institut, Westfälische Wilhelms-Universität Münster, Münster, Germany 4 Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, 411008 Pune, India * Corresponding author: luiz.galvao-tizei@universite-paris-saclay.fr Atomically-thin layers of semiconducting transition metal dichalcogenides (TMDs), namely tungsten diselenide (WSe2), have attracted considerable interest because of new properties that can be obtained when artificially fabricated into van der Waals superlattices. Interlayer coupling is responsible for various properties, including the indirect-to-direct band gap cross-over from bulk and few-layered to monolayer TMDs. It has also been demonstrated that twist angle can be used to tune the interlayer coupling strength in bilayer MoS2 [1] and WS2 [2] homostructures. In this work, the high spatial and spectral resolution of monochromated electron energy-loss spectroscopy (EELS) coupled with four-dimensional scanning transmission electron microscopy (4D-STEM) in an aberration-corrected STEM are used to investigate the excitonic response of twisted bilayer WSe2 with a low moiré angle and the strain relaxation of those that are atomically reconstructed. Monolayered WSe2 flakes were mechanically exfoliated from synthetic bulk crystals, and transferred onto SiO2/Si wafers prior to assembly. The twisted bilayer WSe2 structures were fabricated using a viscoelastic 'tear and stack' stamping method for controlled stacking and twist angle [3], before depositing onto a Quantifoil holey carbon TEM grid. Monochromated EELS and nano-beam electron diffraction with 1 mrad convergence angle were performed on a modified Nion HERMES-S200 (or ChromaTEM) operated at 60 kV with the sample cooled using liquid nitrogen (T ~ 150 K).

Well-defined hexagonal moiré patterns with nanometer periodicity are apparent for the low twist angles with high-resolution imaging. At twist angles below ~3°, some of the highsymmetry stacking regions become more energetically favorable, leading to an expansion of selected high-symmetry points into domains by atomic reconstruction. A low-angle annular dark-field (LAADF) image can be used to visualize the domain boundaries [4]. The domain boundary geometry has been demonstrated to differ between those of R-type (AA) and H-type (AA') stacking order in twisted TMDs that designates layers without and with inversion symmetry, respectively. R-type takes on a triangular geometry [Fig. 1(b,c)], while H-type resembles a kagome-like pattern [Fig. 1(d)]. 4D-STEM of the reconstructed bilayers reveals the nanoscale deformation that correlates perfectly with the location of the domain boundaries [Fig. 2]. The excitonic absorption signatures of these nanometric twisted bilayers [Fig. 1(e)] demonstrate a good general correspondence to the thickness dependence of the exciton resonances, namely a pronounced decrease in C exciton energy with the number of layers [5]. Comparing different twist angles in the bilayers also shows sizable blueshifts in the C exciton energy up to 200 meV, with extremes between the zero-twist and towards the anti-aligned (28°) case, indicating underlying differences in interlayer coupling with respect to the moiré angle.

Figure 1 .

 1 Figure 1. STEM-LAADF images of WSe2 twisted bilayers (2Ls) with (a) 4.1° twist angle, and (b,c) AB (R-type) stacking, (d) AA' (H-type) stacking with atomic reconstruction. (e) Monochromated EELS spectra from twisted bilayers with various moiré angles compared to a representative monolayer (1L) and trilayer (3L) with zero twist. Spectra are offset in energy relative to the A exciton, and the dotted lines are to help guide the eye in the different exciton energy positions.

Figure 2 .

 2 Figure 2. Strain maps obtained using 4D-STEM of the boxed region from Fig. 1(b), including axial strains, εxx, εyy, shear strain, εxy, and rotation ωxy, showing strain relaxation corresponding to the distribution of alternating AB/BA domains, as a result of the atomic reconstruction.

Acknowledgements: The authors acknowledge funding from the ANR, program of future investment TEMPOS-CHROMATEM (No. ANR-10-EQPX-50), and support by the European Union in the Horizon 2020 Framework Program (H2020-EU) under Grant Agreement No. 823717 (ESTEEM3).


Florence Penna

P Magnin

B Nicolet

R L Etzelmüller

M Hermanns

L Böhme

F Kristensen

M Nöel

J F Bredal

Dehls

I M Penna

R L Hermanns

M Böhme

L Kristensen

M Bredal

J F Dehls

PERMAFROST CONTROLS THE DISPLACEMENT RATES OF LARGE UNSTABLE ROCK-SLOPES IN SUBARCTIC ENVIRONMENTS

Keywords: Subarctic, Permafrost thawing, Unstable rock-slopes, Displacement rates. 1. INTRODUCTION B,M., Investigation, Methodology

Permafrost controls the displacement rates of large unstable rock-slopes in subarctic environments

combining thermal ground conditions with paleo-slip rates of six unstable rock-slopes [START_REF] Hilger | Permafrost as a first order control on long-term rock-slope deformation in the (Sub-)Arctic[END_REF]. This work postulated that the frequency of slope failures could increase under warming conditions. But is the relationship so straightforward? Answering this question has implications for understanding landscape evolution and geohazard scenarios and establishing appropriate development strategies in high-mountain settings and arctic and subarctic regions. Norway, with more than 500 LURSs identified through a vast program for systematically mapping large unstable rock-slopes (LURSs; fig. 1; [START_REF] Blikra | Rock slope failures in Norwegian fjord areas: examples, spatial distribution and temporal pattern[END_REF][START_REF] Hermanns | Systematic Mapping of Large Unstable Rock Slopes in Norway[END_REF], and with current and past permafrost conditions covering large part of its territory [START_REF] Lilleøren | The relative age of mountain permafrost -estimation of Holocene permafrost limits in Norway[END_REF]Gisnås et al., 2016a;[START_REF] Magnin | Permafrost distribution in steep rock slopes in Norway: measurements, statistical modelling and implications for geomorphological processes[END_REF], is a perfect natural laboratory to build into this knowledge. Our study statistically explores the link between permafrost and displacement rates of LURSs, by combining ground surface deformation rates determined from satellite remote sensing for all of Norway [START_REF] Dehls | INSAR.No: A National Insar Deformation Mapping/Monitoring Service In Norway --From Concept To Operations[END_REF] and in-situ measurements, with modelled current and past ground thermal conditions [START_REF] Magnin | Permafrost distribution in steep rock slopes in Norway: measurements, statistical modelling and implications for geomorphological processes[END_REF]Gisnås et al., 2016b). Furthermore, the study expands the debate on how landslide hazards in current permafrost areas might change with warmer climate conditions.

METHODOLOGY

Characterisation of large unstable rock-slopes

In this work we analyse 509 LURSs with volumes larger than 100 000 m 3 identified and mapped by the Geological Survey of Norway (NGU) through a national systematic mapping and monitoring programme, which started in 2007 (fig. 1;[START_REF] Oppikofer | Database and online map service on unstable rock slopes in Norway-From data perpetuation to public information[END_REF]. Their identification was conducted by using highresolution (1-m or better) aerial photos and digital terrain models (DTM) and the use of a full national satellite-based ground motion service (insar.ngu.no). The assessment of LURSs carried out by NGU includes field mapping, structural and kinematic analyses, monitoring of displacement rates, and in some cases, the dating of sliding surfaces.

In this work we computed the average orientation of each LURS using the 10m DTM of Norway and the perimeter of the LURSs. We derived from the DTM the aspect (geodesic method) and slope in ArcMap and used these inputs to calculate the normal vector in each cell of the DEM. We computed then a weighted sum of all the normal vectors inside each LURS's polygon. We used the inverse of the cosine of the slope to weight the sum since sloping cells of a DTM represent a larger surface area. Finally, the aspect and slope of the surface represented by the resulting normal vector was computed.

Once the orientation was calculated for each LURS individually, we calculated the average orientation of all the LURSs in a region. To achieve this, we derived a horizontal unit vector from the aspect of each LURS calculated previously and then sum all those vectors. If the LURS are all oriented in the same direction, the resulting vector will be long, while if they are randomly distributed, this vector will be short. To measure this, we compute the strength of the resulting vector (or mean resultant length), which is defined as its length divided by the number of vectors summed [START_REF] Borradaile | Statistics of Earth Science Data[END_REF]. Thus, a value of 1 means that all the vectors have the same orientation, while a value close to 0 reflects the absence of preferential orientation.

We calculated the LURSs' volumes using the sloping local base-level (SLBL) method [START_REF] Jaboyedoff | A review of methods used to estimate initial landslide failure surface depths and volumes[END_REF], which is an iterative method considering that the volume above a sloping surface connecting the surrounding points, in that case the limits of the instability, can be eroded. A tolerance can be used to create a curved surface, and the value of the tolerance controls the curvature. We implemented this method in an ArcGIS toolbox (https://github.com/ngu/pySLBL). The developed tool calculates the tolerance automatically for each LURS by drawing a profile going through the centre of the LURS's polygon and following the average slope direction. The horizontal length (𝑙) of the LURS and its altitude difference (∆𝑧) along this profile are used to estimate the tolerance (𝑐) using the following formula:

𝑐 = 2 • (1 -√2) • ∆𝑧 • ( 𝑥 2 𝑙 2 )
where 𝑥 is the cell size of the DTM. This formula gives a tolerance that is half of the maximum tolerance defined in [START_REF] Oppikofer | Metodikk for konsekvensanalyse av fjellskred[END_REF] From our experience, the tolerance as calculated in this study can be considered acceptable. The volume is given by the difference between the original DTM and the resulting DTM after applying the SLBL method, which represents the thickness of the LURS. The sum of all the pixels of the raster of thickness, multiplied by the area of a pixel results in the volume of the LURS.

Measurement of displacement rates

Displacement rates of 296 out of 509 LURSs have been used in this work. Displacement rates were extracted from the NGU database and own measurements using InSAR Norge portal. We use the displacement rates that are representative of the whole LURSs, not of single scenarios. Within the framework of the hazard classification system done by NGU [START_REF] Hermanns | Recommended hazard and risk classification system for large unstable rock slopes in Norway: NGU rapport[END_REF], six classes of displacement have been defined: 1. No movement; 2. <0.5 cm/y; 3. 0.5-1 cm/y; 4. 1-4 cm/y; 5. 4-10 cm/y; and 6. >10 cm/y. LURSs with unknown displacement rates are located mainly on slopes with dense vegetation coverage, are in shadow zones of the Sentinel-1 satellites or are on inaccessible slopes.

The methods used for the monitoring of displacement rates are as follows:

Differential Global Navigation Satellite System (dGNSS): used to measure displacement rates on 95

LURSs. The time the LURSs have been monitored is variable, the longest monitored period with this method spans from 2003 to 2018, and the time interval between the measurements depends on the degree of activity each LURSs, accessibility, estimated risk, among other factors. The measurements rely on the installation of a network of one or several fixed points in stable outcrops and several points on the unstable rock-mass. GNSS antennas are mounted for each acquisition campaign on bolts fixed to the rocks. Static phase measurements are performed with an interval of a minimum of one year between acquisitions. The measurements are then post-processed using the fixed point(s) as reference. The displacement rate of the LURSs is considered significant if both the following conditions are met:

 the displacement rate obtained by linear regression (𝑣) is higher than the average measurement accuracy (𝜎 𝑡𝑜𝑡 ) multiplied by the square root of two and divided by the time interval between the first and the last measurement (∆𝑡) in years:

𝑣 > √2 • 𝜎 𝑡𝑜𝑡 ∆𝑡

 the displacement follows a coherent trend over at least three measurements.

Tape extensometers: used on 34 LURSs. Here, eye bolts are mounted on both sides of a structure (scarp, crack, etc.), permitting the installation of the instrument at the same location for each acquisition.

Repeated measurements are performed with an interval of at least a year. The displacement rates are given by the change of the length of the tape over the years. As for the GPS, a coherent trend shown by at least three measurements (i.e. at least 2 years between the first and last measurement) is necessary to consider the measured velocity reliable.

Interferometric Synthetic Aperture Radar (InSAR): compares microwave images acquired at different times, allowing the detection of surface displacement rates down to mm/y scale, by analysing changes in the phase of the returned microwave [START_REF] Massonnet | Radar interferometry and its application to changes in the Earth's surface[END_REF]. The monitoring can involve both satellite-based InSAR and ground-based InSAR (GB-InSAR) [START_REF] Wasowski | Investigating landslides and unstable slopes with satellite Multi Temporal Interferometry: Current issues and future perspectives[END_REF][START_REF] Bertolo | Decision support system (DSS) for critical landslides and rockfalls and its application to some cases in the Western Italian Alps[END_REF][START_REF] Kristensen | Movements, failure and climatic control of the Veslemannen rockslide[END_REF].

Satellite InSAR measurements are based on Sentinel-1 images acquired since 2015 (freely available at https://insar.ngu.no) and processed with the persistent scatterers method [START_REF] Ferretti | Nonlinear subsidence rate estimation using permanent scatterers in differential SAR interferometry[END_REF][START_REF] Ferretti | Permanent scatterers in SAR interferometry[END_REF]. Sentinel-1 has a spatial resolution of 5 by 20 m, a swath width of 250 km, and a revisit period of either 6 or 12 days between acquisitions. The measurements are one-dimensional along the radar line-of-sight (LOS) and depend on the acquisition geometry. Thus, the accuracy of the method depends on the angle formed by the LOS of the sensor and the vector of displacement of the LURS.

The LOS of the satellites is inclined either towards the west or the east. Therefore, LURSs with stronger northward or southward displacement will have their rates underestimated, but the vertical component will be measured anyhow. The larger the angle between the displacement vector of a LURS and the LOS of the satellite, the more we underestimate the real displacement of a LURS. However, since we are mostly interested in the magnitude of the displacement the measurements (divided in classes) are acceptable approximations of real displacement rates, but there is a risk of classifying some LURS in a lower class of displacement. Because snow coverage hinders the measurements in winter, 2 m-high corner reflectors have been installed on 23 LURSs to allow for measurements throughout the year.

Ground-Based InSAR has been used on 9 LURSs by the Norwegian Water Resources and Energy Directorate (NVE). The measurements were computed along the LOS of a radar mounted to the ground, typically in front of and below the LURS. This makes the instrument to have its LOS as parallel as possible to the expected displacement vector. The LiSALab radar system, that measures in the Ku band, with a central frequency of 17.2 GHz is used. The instruments can measure movements exceeding 1 m/day, but since for some LURSs the displacements range from a few mm to a few cm per year, periodic campaigns (about a week in length) are conducted two or more times in a season or over a few years. These campaigns are averaged to a single radar image, and the change of distance between the campaigns is calculated. If a LURS has a very fast displacement, its rate is measured on a daily basis.

Steep slopes permafrost mapping

To assess current permafrost conditions on LURSs, we extracted the minimum mean annual rock-surface temperature (MARST) value inside the polygon representing each LURS and the corresponding permafrost class (sporadic, discontinuous, continuous) from the 10 m resolution CryoWALL map from [START_REF] Magnin | Permafrost distribution in steep rock slopes in Norway: measurements, statistical modelling and implications for geomorphological processes[END_REF], covering all slopes > 40° in a 10 m resolution DEM (fig. S6). When more than a class of permafrost is present, we assign the one covering the largest area. For LURSs in gentler slopes, we assigned the class of permafrost using the regional permafrost model and MAGT temperatures from Gisnås et al. (2016b).

The MARST map derives from a multiple linear regression model, with mean annual air temperature (MAAT) and potential incoming solar radiation (PISR) as explanatory variables. [START_REF] Magnin | Permafrost distribution in steep rock slopes in Norway: measurements, statistical modelling and implications for geomorphological processes[END_REF] calibrated it with in-situ measurements (85 MARST measurement points), local MAAT records and computed PISR at each measurement point using GIS tools. The predicted MARSTs and their standard deviation were used to calculate a permafrost probability (probability that MARST is ≤0°C), and later converted into a map of permafrost classes, with sporadic permafrost designating areas with permafrost probability of 10 to 50%, discontinuous permafrost designating areas with probability ranging from 50 to 90% and continuous permafrost referring to areas with a probability of >90% [START_REF] Magnin | Permafrost distribution in steep rock slopes in Norway: measurements, statistical modelling and implications for geomorphological processes[END_REF]. Thus, "sporadic permafrost" indicates conditions where permafrost may be very patchy and subsists because of transient effects from past colder climates or because of locally favourable conditions (such as fractured outcrops with air ventilation); "discontinuous permafrost" indicates more wide-spread areas, but with permafrost temperatures closer to 0°C, while "continuous permafrost" indicates conditions favourable to permafrost persistence independent of ground characteristics (fractured or not) or debris/snow cover. A probability of 50 % corresponds to a MARST of 0°C.

For this study, we produced MARST and permafrost class maps for the Little Ice Age (LIA; ca. 250 y BP) using the air temperature coefficient of the multiple linear regression model (1.06) and the LIA known air temperature anomaly (compared to the 1961-1990 period). For the LIA anomalies, we used the value -1.5°C, which is considered to be reasonable value based on various studies in the wider North-Atlantic region (e.g. [START_REF] Lilleøren | The relative age of mountain permafrost -estimation of Holocene permafrost limits in Norway[END_REF][START_REF] Etzelmüller | Icelandic permafrost dynamics since the Last Glacial Maximum-model results and geomorphological implications[END_REF]. As a first step, the air temperature difference was calculated from the periods 1981-1990 and 1961-1990 from the SeNorge air temperature maps and applied to the CryoWALL map [START_REF] Magnin | Permafrost distribution in steep rock slopes in Norway: measurements, statistical modelling and implications for geomorphological processes[END_REF]. Then, we considered the LIA for back analysis and its respective air temperature anomaly of -1.5°C. For the LIA period, specific MARST, permafrost probability and permafrost class maps were created and used to determine permafrost conditions on LURSs on steep slopes. For LURSs of gentler slopes, the presence of permafrost during LIA was evaluated using the map of Lillehøren et al. ( 2012) who modelled the distribution of Holocene permafrost in Norway. Figure S1 shows an example of the MARST map and permafrost maps for the LIA and current times (CT) for a LURS from northern Norway.

Statistical analyses

We performed statistical analyses to investigate the relation of different variables, namely permafrost, minimum temperature, slope, area and lithology with the displacement rates of LURSs. Other aspects such as the structural control or the glaciation history where not considered as they are difficult to investigate at that scale. To further identify if the considered variables are spatially related, the analyses were done for the entire country, the South, the North, and two specific regions of the North: Troms and Finnmark. Thus, the groups are not independent since Troms and Finnmark are included in the North, which, together with the South, are included in the entire country. Because of the different nature of the studied variables (Table 1), various tests were performed. The Chi-squared method [START_REF] Pearson | On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling[END_REF] is applied here when both variables are categorical. The observed Chi-squared is given by:

Χ 2 = ∑ (O 𝑖 -E 𝑖 ) 2 E 𝑖 𝑛 𝑖=1 (eq. 1)
where O 𝑖 is the observed number of events in class 𝑖 and E 𝑖 is the expected number of events in the same class assuming no correlation (null hypothesis). The p-value is then calculated from the Chisquared distribution using the corresponding degrees of freedom, calculated as follows:

𝑑𝑜𝑓 = (𝑚 -1) * (𝑛 -1) (eq. 2)
where 𝑚 and 𝑛 are the number of classes for the two parameters, respectively. The p-value gives the probability for the Chi-squared, assuming the null hypothesis, to be higher than the observed Chisquared. Thus, the lower the p-value, the less likely the data is to fulfil the null hypothesis. It is commonly considered that the null hypothesis is rejected for p-values below 0.05 [START_REF] Borradaile | Statistics of Earth Science Data[END_REF], which implies that the alternative hypothesis (i.e., that the variables are correlated) is then accepted.

Here, we considered the correlation to be significant for p-values below 0.01, partly significant for pvalue between 0.01 and 0.1 and not significant for p-values above 0.1. It is recommended to apply the Chi-squared method only when the expected number of events is at least 5 for each class [START_REF] Borradaile | Statistics of Earth Science Data[END_REF]. Here we classify the velocities in fewer classes (no movement, significant movement <1cm/y, >1cm/y) to avoid having classes with too few values, and only use the classes of the other parameters (rock type or permafrost type) when there are at least ten values in them. Even when using fewer classes, we do not always reach the minimum expected value of 5 events in each class, so we present the minimum expected value as a control so that the analyses where this threshold is not reached can be interpreted more carefully (Table S1).

Kendall's 𝜏 calculates the association between two rankings. It is calculated from the following equation:

𝜏 = 𝐶-𝐷 √( 𝑛(𝑛-1) 2 -𝑇 𝑥 )( 𝑛(𝑛-1) 2 -𝑇 𝑦 ) (eq. 3)
where 𝐶 is the number of concordant pairs, 𝐷 the number of discordant pairs, 𝑛 the number of data points, 𝑇 𝑥 the number of ties on 𝑥 and 𝑇 𝑦 the number of ties on 𝑦 [START_REF] Agresti | Analysis of Ordinal Categorical Data[END_REF]. A concordant pair is a pair (𝑥 1 , 𝑦 1 ) and (𝑥 2 , 𝑦 2 ) where either 𝑥 1 > 𝑥 2 and 𝑦 1 > 𝑦 2 or 𝑥 1 < 𝑥 2 and 𝑦 1 < 𝑦 2 . Kendall's 𝜏 takes a value between -1 and 1, where -1 indicates a perfect monotonically decreasing relation, 1 indicates a perfect monotonically increasing relation and 0 indicates the absence of relation. Again, we calculated a 13 p-value, to test for the hypothesis that the two variables do not show a statistical correlation. Although the p-value, which is two-sided, differs from the one obtained using the Chi-squared method, they can be interpreted similarly. This test is applied without filtering or reclassification since it is not influenced by the number of values in a class.

RESULTS

Distribution of LURSs

LURSs are spatially concentrated in southern Norway ( 261 LURSs in northern Norway is 9.3 * 10 6 m 3 and 2.9 * 10 6 m 3 in the South (fig. 2B). The mean orientation of LURSs is 291° (WNW) with a vector strength of 0.14, indicating a weak preferential orientation (fig. 2C).

This is mostly influenced by the LURSs in the North (with a preferential orientation of 287° and a vector strength of 0.36), while there is almost no preferential orientation in the South (with a preferential orientation of 80° and a vector strength of 0.06). 82% of LURSs have preferentially developed on five lithologic units, as observed in Figure 2D. In the North, most LURSs developed on 1) mica-gneisses, micaschist, metasandstone and amphibolite, while a minor proportion developed on 2) metasandstones and mica-schist. The high proportion of LURSs in unit 1 (35%) is not representative of the distribution of lithologies in this region in which this unit is only outcropping in 10% of the surface (fig. 2D). In the South, most LURSs developed on 1) dioritic to granitic gneiss, migmatites, while a minor proportion developed on 2) phyllites, mica-schist. Here, the lithologies in which the LURSs developed better match the general distribution of outcrops in that region. The lithologies grouped as "Others" are underrepresented in the LURSs distribution in both regions. Medians are shown as orange lines.

Current displacement rates of LURSs

Displacement rates have been established for ca. 57% of the LURSs, and from this, ca. 61% (177) show active displacements. The number of active LURSs increases towards the North. Around 60% of the currently inactive LURSs are located in southern Norway. The proportion of LURSs with displacements slower than 0.5 cm/y is similar throughout Norway. More than 70% of the LURSs with displacements ranging 0.5-1 cm/y are located north of the Polar Circle, as are more than 80% of those displacing between 1-4cm/y (fig. 3).

Past and current permafrost conditions of LURSs

Steep slopes (> 40° on 10 m resolution DEM), represent around 6000 km 2 in cartographic area in Norway. Our model shows that approximately 3000 km 2 of those steep slopes had permafrost (continuous to sporadic) during the LIA. This represents 48 % of the steep slopes' surface area (fig. 4D), meaning that the other 52% had already no permafrost at that time. Our model further shows that 32% of the steep slopes' surface area currently has permafrost, which means that permafrost disappeared in around 16 % of the steep slopes between the LIA and now. In Finnmark (northern Norway), the sporadic permafrost extends down to sea level on coastal cliffs. In the southern extreme of Norway, the current lower limit is at around 700 m a.s.l. At that altitude, only extremely shaded slopes can have permafrost.

The lower modelled altitudinal limit of sporadic permafrost during the LIA was at sea level in northern Norway and ca. 270 m a.s.l. in the south.

From the modelled permafrost during LIA and the location of the LURs, we observe that during the LIA, a similar number of LURSs existed in permafrost-free and sporadic permafrost areas (fig. 4A). After the LIA, the reduction in the extent of the permafrost changed the ground conditions of several LURSs.

Controlling factors of displacement rates -Statistical analyses

The relationships between LURSs' volume, lithology, slope, and displacement rates, are presented in fig.

5. LURSs with smaller volumes seem to have slower displacement rates than the larger ones. However, the pattern is not very clear. Regarding the relation between volume and lithology, we observe that LURSs developed on dioritic to granitic gneiss and migmatites are smaller than those developed on other types of rocks. In addition, at the country scale, LURSs developed on this type of rock seem to present slower displacements. However, this is because this unit is significantly more represented in the South than in the North, where displacement rates are slower. Indeed, a similar relation is not observed when analysing the North and the South separately. The analysis of minimum MARST shows that displacement rates increase with decreasing temperatures (fig. 7A). This trend is more evident in northern Norway (fig. 7B) and more marked in Troms (fig. S2),

where the range of temperatures is wider. Currently, inactive LURSs have an average minimum MARST over +3°C, while it is close to +1°C for active LURSs. The analysis of the distribution of permafrost during the LIA and current time (CT), combined with current displacement rates, shows the link between permafrost conditions and the activity of LURSs (fig. 8). LURSs with permafrost conditions during the LIA are more likely to move than those that did not have permafrost. It is also interesting to observe that the LURSs having discontinuous permafrost during the LIA show less movement if they still have discontinuous permafrost than if they have now sporadic permafrost (fig. 8). LURSs with no permafrost during the LIA nor in CT are more likely to show no movement or insignificant displacement rates. Globally, ca. 30% of LURSs without permafrost conditions during the LIA are currently moving, while ca. 70% of LURSs with permafrost conditions during the same period show active displacements. 49% of LURSs with permafrost during the LIA but without current permafrost conditions show active displacements, which means that the probability of a LURS being active is 1.6 times higher if the permafrost did not completely thaw between the LIA and CT. These characteristics are visible at the country scale and in the North and South separately (fig. 8 and fig. S3).

Of the 25 LURSs in the South, where permafrost thawed completely after the LIA, 12 of them do not show current displacement. Of the 18 LURSs in the North with displacement information where permafrost thawed completely after the LIA, 10 do not show current displacement. In the results of the statistical tests (fig. 9), from the values of Kendall's 𝜏, we can observe that the current type of permafrost is positively associated with the displacement rates, although the association is moderate. The association is relatively stable for all geographic areas. It is slightly lower in the South, where permafrost is less widespread (0.16), and has values of 0.31-0.43 for the other regions. The results are statistically significant with p-values below 0.01, except for the South where the p-value is partly significant (0.05). The association is also positive for the combination of permafrost during the LIA and CT (0.21-0.39), with all p-values below 0.01. The association is negative for the minimum MARST and the displacement rates, meaning lower temperatures correspond with faster displacements. The association is moderate (-0.18 to -0.33), but statistically significant for all regions. On the other hand, the trend is not clear for the association of the volume and the displacement, since 𝜏 takes both positive and negative values, and since the associated p-value is significant in only one region (South), partly significant in three other regions (Norway, Troms and Finnmark) and not significant in the last region (North). In the South, the association is the largest (0.26), while the p-value is the lowest, which indicates a positive association between the volume and the displacement rates in this area. This is probably related to the large number of smaller LURSs developed in dioritic to granitic gneiss and migmatites that tend to have not-significant or no displacements. A relatively similar observation can be done for the association between the slope and the displacement rates. At the country scale, the association is negative (-0.15) and statistically significant, meaning LURSs on steeper slopes tend to present less displacement. Similar observations can be made in the South and in Troms, but are only partly statistically significant. No association is observed when looking at the North, and a positive, but statistically not significant association is observed in Finnmark.

The p-values obtained with the Chi-squared method (fig. 9) in northern Norway do not show a correlation between lithology and displacement rates. In the South, there is a partial correlation between these parameters. On the other hand, the current permafrost and the displacement rates, as well as the combination of permafrost during the LIA and CT in relation to displacement rates, show a statistical significance for all the regions, except for the correlation of displacement rates and current permafrost in the South, where the p-value is only partly significant. Both p-values (B and C) indicate the statistical significance of the tests, which are considered statistically significant below the green line, partly significant between the green and the red lines and not significant above the red line. Note that permafrost is positively associated with the velocity and the association is statistically significant. On the other hand, volume, area, slope, or rock type are less clearly related to the velocity.

DISCUSSION AND CONCLUSIONS

Uncertainties and limitations

Two major uncertainties and limitations arise from this study: [START_REF] Booth | Integrating diverse geologic and geodetic observations to determine failure mechanisms and deformation rates across a large bedrock landslide complex: the Osmundneset landslide, Sogn og Fjordane, Norway[END_REF] the statistical evaluation and (2) the co-existence of permafrost and large unstable rock-slopes.

Concerning [START_REF] Booth | Integrating diverse geologic and geodetic observations to determine failure mechanisms and deformation rates across a large bedrock landslide complex: the Osmundneset landslide, Sogn og Fjordane, Norway[END_REF], the Chi-squared and Kendall's 𝜏 tests do not differentiate cause-effect from autocorrelation. In our case, we limit the risk of autocorrelation by applying the tests at country-scale, to the North and the South separately and by dividing the North in two. Indeed, since permafrost is mostly present in the North, a correlation with the type of rocks is expected to be seen simply because lithologies are different in the South and the North, while this is less likely inside both regions independently. In addition, we look at different parameters that could explain the difference in displacements, such as size, slope angle, and lithology. Another effect that we do not consider is that Kendall's 𝜏 tests test for monotonically increasing or decreasing function. But we see that the relation between permafrost and displacement rates is not monotonical since lower displacement rates are observed and expected where permafrost is either absent or continuous, and higher displacement rates are expected for thawing permafrost (mostly sporadic). However, the low number of LURSs in continuous permafrost implies that we are mainly looking at the discontinuous, sporadic and no permafrost classes.

Concerning (2), the permafrost conditions are based on a temperature map derived statistically and for steady-state conditions. Other processes that are not accounted for in the statistical approach may impact permafrost conditions, such as topographical and transient effects [START_REF] Noetzli | Three-dimensional distribution and evolution of permafrost temperatures in idealized high-mountain topography[END_REF][START_REF] Noetzli | Transient thermal effects in Alpine permafrost[END_REF][START_REF] Myhra | Modelled Distribution and Temporal Evolution of Permafrost in Steep Rock Walls Along a Latitudinal Transect in Norway by CryoGrid 2D. Permafr[END_REF]. The topographical effects are related to the variable energy balance at the ground surface that is strongly controlled by direct solar radiation, which depends on sunexposure and latitude. In Norway, the control of the solar radiation on ground surface temperatures is less than in the European Alps [START_REF] Hipp | Permafrost in Alpine Rock Faces from Jotunheimen and Hurrungane, Southern Norway[END_REF][START_REF] Magnin | Permafrost distribution in steep rock slopes in Norway: measurements, statistical modelling and implications for geomorphological processes[END_REF] and induces temperature difference in the order of 2 to 4°C between north-exposed and south-exposed faces (this decreases with latitude). These differences affect the temperature fields at depth and permafrost that is not expected in a south face when considering statistically-derived surface temperature may exist due to the proximity of a colder north face. This is particularly the case for alpine topography with sharp peaks and spurs. Transient effects that result from the past climatic conditions add to this topographical control.

Here again, permafrost may persist at depth even if the predicted permafrost conditions indicate a low probability of its occurrence because of the transient effect of past colder climate. The permafrost map representing current permafrost conditions typically represents conditions for a 30-year period, partially accounting for the recent atmospheric warming . The effect of past and colder decades may persist at depth. In this respect, basing the permafrost classes on permafrost probability limits the risk of misinterpreting the results due to a lack of consideration for past climate because the map users are made aware that a low probability (e.g. probability falling under the sporadic permafrost class) doesn't necessarily mean the absence of permafrost. Other parameters that may favour the existence of permafrost even under low probability are the snow cover and bedrock fractures. Previous investigations show that permafrost might exist below positive surface temperature up to about 3°C depending on sun-exposure [START_REF] Hasler | Temperature variability and offset in steep alpine rock and ice faces[END_REF]. For example, the Jettan unstable rock-slope in northern Norway, with ice in deep fractures [START_REF] Blikra | A field-based model of permafrost-controlled rockslide deformation in northern Norway[END_REF].

Permafrost and current displacement rates

In Norway, geologic, landscape, and climate conditions control the development of LURSs, their extent and kinematics [START_REF] Böhme | Analysing complex rock slope deformation at Stampa, western Norway, by integrating geomorphology, kinematics and numerical modeling[END_REF][START_REF] Booth | Integrating diverse geologic and geodetic observations to determine failure mechanisms and deformation rates across a large bedrock landslide complex: the Osmundneset landslide, Sogn og Fjordane, Norway[END_REF][START_REF] Vick | Structurally controlled rock slope deformation in northern Norway[END_REF]. The destabilisation of rockslopes mainly occurred soon after the Younger Dryas deglaciation, as shown by cosmogenic nuclide dating of sliding surfaces and morphologic assessments [START_REF] Hermanns | Rock-Avalanche Activity in W and S Norway Peaks After the Retreat of the Scandinavian Ice Sheet[END_REF][START_REF] Hilger | Multiple rockslope failures from Mannen in Romsdal Valley, western Norway, revealed from Quaternary geological mapping and 10Be exposure dating[END_REF][START_REF] Hilger | Permafrost as a first order control on long-term rock-slope deformation in the (Sub-)Arctic[END_REF]. Differences in precipitation can not explain differences in displacement rates at country scale. While the mean annual precipitation is higher in the southwest coast [START_REF] Lussana | seNorge2 daily precipitation, and observational gridded dataset over Norway from 1957 to the present day[END_REF], the higher displacement rates of LURSs are measured in the North. The fact that the lithologies in which most LURSs developed better match the areal distribution of the lithologies in the South than in the North is primarily due to suitable relief conditions and does not mean LURSs have a higher tendency to develop on a specific lithology. Instead, the high relief areas occupy a larger extension in the South than in the North. Similarly, the lithological units classified as "others" are always underrepresented when considering the LURSs' lithology distribution simply because they are widespread in regions with low relief, where no LURSs developed and have therefore not been differentiated in this analysis. Regarding the activity of the LURSs, a recent study of nine LURSs in northern Norway showed their complex nature and pointed out a link between displacements and structural conditions [START_REF] Vick | Structurally controlled rock slope deformation in northern Norway[END_REF]. In southern Norway, actively displacing LURSs are mostly seen on phyllites and mica-schist. In four of those LURSs, the poor rock-mass quality was previously proposed as a key control of the active deformation [START_REF] Böhme | Analysing complex rock slope deformation at Stampa, western Norway, by integrating geomorphology, kinematics and numerical modeling[END_REF][START_REF] Penna | Large-Scale Rockslope Deformations in Sogn Og Fjordane County (Norway)[END_REF]. However, our results show that the correlation between lithologies and displacement rates is only partially significant in the South and not significant in the North. While geologic conditions alone cannot explain the northward increase of displacement rates or even differences in displacement rates in northern Norway, ground temperature variations can. Our results

show that permafrost and changes in permafrost co-vary with observed displacement rates, with faster displacement measured in LURSs with a MARST closer to 0°C suggesting permafrost at depth. This is caused by the cryostatic and hydrostatic changes induced by the warming of permafrost. The factor of safety of ice-filled fractured rocks decreases when ground temperatures get closer to the ice's melting point [START_REF] Davies | The effect of rise in mean annual temperature on the stability of rock slopes containing ice-filled discontinuities[END_REF]; it is equal to 1 or more when ice has fully melted or when temperatures are below the melting point. The shear stress decreases when ice-filled joints warm to temperatures close to 0°C [START_REF] Mamot | A temperature-dependent mechanical model to assess the stability of degrading permafrost rock slopes[END_REF]. In addition, the melting of ice increases the water circulation in jointed rocks, enhancing the hydrostatic pressure of the frozen fractured rocks [START_REF] Murton | Monitoring rock freezing and thawing by novel geoelectrical and acoustic techniques[END_REF].

Permafrost decline and the hazard paradigm

Since the deglaciation of the Fennoscandian Ice Sheet, the permafrost in Norway has undergone drastic variations [START_REF] Lilleøren | The relative age of mountain permafrost -estimation of Holocene permafrost limits in Norway[END_REF]. Fluctuations in the extent of permafrost have an impact on the strength of rock-slopes. Recent works discuss how the aggradation and degradation of permafrost undermine their stability (e.g. [START_REF] Voigtländer | Subcritical crack growth and progressive failure in Carrara marble under wet and dry conditions[END_REF][START_REF] Dräbing | The Efficacy of Frost Weathering Processesin Alpine Rockwalls[END_REF]. Our results

show that LURSs with discontinuous permafrost during the LIA are more likely to move if they currently have sporadic permafrost than if they currently have discontinuous permafrost. In addition, LURSs with permafrost remaining since the LIA are more likely to move than those with permafrost during the LIA that are currently permafrost-free. This has two main implications; firstly, permafrost degradation can increase displacement rates. This is consistent with the outcomes of recent studies on three LURSs of northern Norway, located on sporadic or discontinuous permafrost, showing that paleo-slip rates were half of the currently measured ones [START_REF] Böhme | Comparison of monitoring data with paleo-slip rates: Cosmogenic nuclide dating detects acceleration of a rockslide[END_REF][START_REF] Hilger | Permafrost as a first order control on long-term rock-slope deformation in the (Sub-)Arctic[END_REF]. Secondly, the complete thaw of permafrost can lead to a decrease in the displacement rates, and LURSs can decelerate until arrest. Both in the North and in the South, half of the LURSs whose permafrost thawed completely after the LIA have insignificant displacement rates or no movement. Therefore, the paradigm of permafrost degradation directly increasing the frequency of failures only partially addresses the effect of ground ice melt associated with the thawing of permafrost. This is because active displacements are often seen as the prelude to failure, and forecasts assume constant external forcing factors. But external factors change with time [START_REF] Carlá | Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses[END_REF]. The formation of a sliding surface requires the nucleation of cracks under appropriate environmental and geologic conditions. As environmental conditions change with time, the development of a sliding surface can be accelerated, deaccelerated, interrupted or reactivated. The complete thaw of permafrost removes the hydrostatic pressure and cryostatic pressure from the rock, leaving the shear force induced by gravity and pre-existing stresses as the main drivers of deformation [START_REF] Krautblatter | Why permafrost rocks become unstable: a rock-icemechanical model in time and space[END_REF]. Therefore, if during the period of permafrost and permafrost degradation the accumulated deformation was not enough to drive a slope to failure or to lead to the full development of a sliding surface, a LURS can decelerate and halt (dormant state) once permafrost has completely decayed. However, changes in environmental conditions can drive dormant LURSs to reactivate. In summary, while permafrost warming at temperatures closer to 0°C can increase the displacement rates of LURSs, thereby increasing the hazard level, the complete thaw of the permafrost can lead to a decrease in their displacements, thereby decreasing the hazard level. However, neither increase nor decrease of displacement rates assures or excludes the possibility of a LURS failing catastrophically.

Figure 1 .

 1 Figure 1. Observation of LURSs and distribution of permafrost on the mainland of Norway. A) Location of

  ) and north of the Polar Circle (241; fig.1). At a country scale, the median maximum altitude of the headscarps is ca. 700 m a.s.l. (fig.2A), although higher in the south than in the north. The spatial distribution of LURSs is associated with geologic and landscape conditions and the Quaternary history. LURSs in southern Norway developed mostly in overdeepened valleys and fjords, and those in northern Norway mainly developed in coastal cliffs carved on flat or gentle relief in Finnmark and in over-deepened valleys and fjords in Troms. The median volume of

Figure 2 .

 2 Figure 2. Characteristics of the LURSs. A) Boxplot with altitude of headscarps per region and for the

Figure 3 .

 3 Figure 3. Cumulative curves of classes of displacement rates from south to north. The location of the

  Seventyeight (45 in the South and 33 in the North) of 203 LURSs changed from sporadic permafrost to permafrost-free conditions and 66 (16 in the South and 49 in the North and 1 in the centre) of 103 from discontinuous to sporadic permafrost. Of the 237 LURSs with current permafrost in Norway, ca. 77% are located north of the Polar Circle. Figure4A and D show that the proportion of LURSs in the sporadic permafrost class (around 37% at CT) is higher than the proportion of the surface covered by sporadic permafrost (around 21% at CT), which gives a higher number of LURS per square kilometer in that class (fig.4 E).

Figure 4 .

 4 Figure 4. Temporal change of type of permafrost present in LURSs. A) Histogram showing the proportion

Figure 5 .

 5 Figure 5. Boxplots showing the distribution of volumes of LURSs by displacement rate class for the whole

Figure 7 .

 7 Figure 7. Boxplots with minimum MARST, and displacement rate classes with amount of LURSs present

Figure 8 .

 8 Figure 8. Stack bar showing the distribution of LURSs by type of permafrost and during the LIA and

Figure 9 .

 9 Figure 9. Results of the statistical tests for different combinations of variables. A) Kendall's 𝜏 indicates

Table 1 .

 1 Tested variables and corresponding data types.

	Variable	Type
	LIA-CT permafrost	Categorical ordinal
	CT permafrost	Categorical ordinal
	Min MARST	Interval
	Displacement rate	Categorical ordinal
	Area	Ratio
	Rock type	Categorical nominal
	Slope	Ratio

Note: The LIA-CT permafrost is a combination of two ordinal scales. It allows calculating Kendall's τ.

Displacement rate is considered on a categorical scale since the available displacement data does not always allow accurate measurement of the displacement rate. Here we sort the classes primarily by CT and secondarily by LIA to use the combination scale as an ordinal scale.

ACKNOWLEDGEMENTS

The authors acknowledge the Norwegian Water Resources and Energy Directorate for funding most of the research done in the framework of this study. Parts of the study are based on results from the project 'CryoWALL -Permafrost slopes in Norway' (243784/CLE) funded by the Research Council of Norway (RCN) at the University of Oslo, Norway. CONTRIBUTIONS P,I., Conceptualization, Investigation, Formal Analysis, Writing. M,F., Conceptualization, Methodology, Formal Analysis, Writing. N,P., Methodology, Investigation, Formal Analysis, Graphs, Writing. E,B., Conceptualization, Writing-reviewing. H,R.L., Investigation, Supervision. B,M., Investigation, Writing.

DATA AVAILABILITY

MARST data for current permafrost analysed during this study are included in [START_REF] Magnin | Permafrost distribution in steep rock slopes in Norway: measurements, statistical modelling and implications for geomorphological processes[END_REF] https://doi.org/10.5194/esurf-7-1019-2019) and its supplementary information files (https://doi.org/10.5194/esurf-7-1019-2019-supplement.).

The modelled permafrost map for the Little Ice Age is available from the corresponding author under request.

InSAR data is freely available at https://insar.ngu.no LURSs data is freely available at https://geo.ngu.no/kart/ustabilefjellparti_mobil/ Bedrock map available at: https://geo.ngu.no/kart/berggrunn_mobil/

ranges from the median. Medians are shown as orange lines. For (G), (H) and (I) where a class represents less than 10 LURSs, it is overprinted with a hashed pattern.

Concerning the relation between current permafrost and displacement rates, LURSs with no permafrost show lower displacement rates than those with permafrost in general (fig. 6). Sporadic permafrost hosts LURSs with relatively higher displacement rates than discontinuous permafrost (fig. 6 and fig. S1).


Fuhui Shao1

Steffi Y Woo1

Nianjheng Wu1

Robert Schneider3

Andrew J Mayne2

Steffen Michaelis3

Ashish Arora3

Benjamin J Carey3

Johann A Preuß3

Noémie Bonnet1

Cecilia Mattevi4

Kenji Watanabe5

Takashi Taniguchi6

Rudolf Bratschitsch3

Luiz H G Tizei1

Disentangling Exciton Linewidth Broadening Factors in Transition Metal Dichalcogenide Monolayer with Electron Energy Loss Spectroscopy

Monolayer two-dimensional transition metal dichalcogenides (TMDs) have invoked great interest for potential applications because of their strong light-matter interactions and direct energy gap. However, the external environment heavily influences the optical properties of TMD monolayers. Encapsulating TMDs in h-BN is recognized as the most effective way to preserve their intrinsic optical properties [1,2], and to obtain narrow excitonic linewidths. It has been proven that h-BN encapsulation can reduce the roughness of graphene from 114 ± 1 to 12 ± 5 pm [3]. Besides roughness, surface protection [1], charge disorder [2], and variations of dielectric environment [4] are also believed to be key factors that could induce inhomogeneous excitonic linewidth broadening of TMDs. However, no such study has comprehensively compared and disentangled the various proposed factors that contribute to excitonic linewidth broadening exists, because few techniques can address all factors single-handedly.

In order to explore the role of these factors, we investigated the roughness and absorption behavior by electron energy loss spectroscopy (EELS) of WS2 monolayers either supported or encapsulated by two different nanosheets (h-BN and Si3N4) in a scanning transmission electron microscope (STEM) [5]. Using this technique, the factors leading to exciton absorption linewidth inhomogeneity can be ranked in increasing order of importance: monolayer roughness, surface cleanliness, and substrate induced charge trapping. In Fig. 1., the EELS spectra of WS2 monolayers in different configurations are illustrated. Experiments were done on the ChromaTEM microscope, a modified Nion HERMES 200 equipped with an electron monochromator. The electron beam energy is set at 60 keV with a spread down to below 10 meV. The convergence half-angles for the EELS and diffraction measurements are 10 mrad and 1 mrad. Roughness was measured with the sample tilted with respect to the electron beam from 0 to 385 mrad as shown in Fig. 2, which is similar to previous experiments for graphene [3,6]. Corrugated monolayers are expected to show diffraction spots blurring as the tilt angle increases, whereas a flat monolayer does not. Additionally, numerical calculations for the diffraction patterns under different roughnesses are performed in QSTEM [START_REF] Koch | Determination of core structure periodicity and point defect density along dislocations[END_REF] to ascertain the corrugation of the monolayers in each configuration. This project has been funded in part by the National Agency for Research under the program of future investment TEMPOS-CHROMATEM (reference no. ANR-10-EQPX-50) and the MAGMA research grant (ANR-16-CE09-0027), and the JCJC grant SpinE (reference no. ANR-20-CE42-0020) and by the European Union's Horizon 2020 research and innovation programme under grant agreement No. 823717 (ESTEEM3) and 101017720 (EBEAM). This work has been supported by Region Île-de-France in the framework of DIM SIRTEQ.

Figure 1 .

 1 Figure 1. EELS spectra of WS2 monolayers in various configurations at 110 K. The linewidth of the A exciton increases in order: h-BN encapsulated, h-BN supported, freestanding CVD-grown, Si3N4 supported and Si3N4/h-BN encapsulated WS2 monolayers.

Figure 2 .

 2 Figure 2. (a) and (b) are the diffraction patterns of a WS2 monolayer on a 15-nm Si3N4 membrane, corresponding to the reciprocal space of a corrugated monolayer and Ewald sphere geometry in (d) and (e). The intensity profiles of the diffraction spots are plotted in (c), which are indicated in (a) and (b) by the purple and yellow box.