Anthropogenic climate change and glacier lake outburst flood risk: local and global drivers and responsibilities for the case of lake Palcacocha, Peru

Abstract. Evidence of observed negative impacts on natural and human systems from anthropogenic climate change is increasing. However, human systems in particular are dynamic and influenced by multiple drivers and hence identifying an anthropogenic climate signal is challenging. Here we analyze the case of lake Palcacocha in the Andes of Peru, which offers a representative model for other glacier lakes and related risks around the world because it features a dynamic evolution of flood risk driven by physical and socioeconomic factors and processes. Furthermore, it is the object of a prominent climate litigation case, wherein a local Peruvian citizen sued a large German energy producer over risk of flooding from lake Palcacocha. Adopting a conceptual model of cascading impacts and multiple drivers of risk, we first study climatic and other geophysical drivers of flood risk. We find that an anthropogenic signal from flood risk to greenhouse gas emissions is traceable. In parallel, flood risk has been strongly shaped (and increased) by interacting socioeconomic, institutional and cultural processes over the past few decades. The case raises important questions about the differentiation of responsibilities relating to flood risk of both global and local agents, which are, however, difficult to address in cases like Palcacocha, where we reveal a complex network of interlinked global, national and local drivers. Following from this, we outline a normative framework with a differentiated perspective on responsibility, implying that global emitters commit to support strengthening capacities in affected regions and localities and that local institutions and societies engage in local risk reduction measures and policies in collaboration with and driven by local communities.


Introduction
Impacts of climate change are increasingly observed in many natural and human systems worldwide (Cramer et al., 2014;Hoegh-Guldberg et al., 2018). Shrinking glaciers are among the most visible indicators of climate change, as the mountain cryosphere is especially prone to warming (Dussaillant et al., 2019;Hock et al., 2019;Zemp et al., 2015). While glaciers are widely monitored from the ground and from space, the impacts of glacier changes on natural and human systems are often more difficult to observe, and attribution of the observed changes to causal factors can be challenging (Carey et al., 2017;Hansen and Stone, 2016;. Changes in water resources and natural hazards are thereby the most substantial effects and have been documented in many mountain regions of the world (Casassa et al., 2009;Cramer et al., 2014;Harrison et al., 2018). Glacier lake outburst floods (GLOF) are among the most destructive and farreaching hazards related to glacier changes and have killed Published by Copernicus Publications on behalf of the European Geosciences Union.
Glaciers will continue to shrink and impact downstream natural and human systems in the coming decades, although emission pathways will have a crucial effect on the extent of the process and impacts (Hock et al., 2019;Huss and Hock, 2018;Kraaijenbrink et al., 2017;Schauwecker et al., 2017). Adaptation to cryosphere impacts is of fundamental importance and has so far taken place in the majority of countries (McDowell et al., 2019). Recent research has emphasized the importance of comprehensively understanding adaptation around socio-cryospheric and socio-hydrologic systems, with accumulating evidence from the Himalayas (Mukherji et al., 2019), including Ladakh Nüsser and Baghel, 2016) and Tsho Rolpa, Nepal (Sherry et al., 2018); the Andes ; and comparative analyses . Some of this research has pointed to adaptation to cryosphere change potentially reaching certain limits, e.g., with the disappearance of glaciers in regions that are highly dependent on glacier meltwater or large slope instabilities making certain areas uninhabitable or existing livelihood strategies unviable, thus resulting in losses and damages . Loss and damage (L&D) as a concept in global climate policy has been defined as the impacts that cannot or have not been avoided through mitigation and adaptation (Okereke et al., 2014;Warner and van der Geest, 2013), but there is still missing clarity and debate about what L&D comprises (Calliari, 2018;Lees, 2017;. In the Paris Agreement, L&D was anchored in a separate article, but at the same time the agreement specifies that this article does not provide any basis for liability and compensation. Despite this disclaimer at the level of international policy, important questions of responsibility and justice emerge from negative effects and risks related to climate change in general and to the mountain cryosphere specifically, such as which natural and social processes can be identified as drivers of risk; to what extent are global greenhouse gas emitters contributing to these risks; who must be held accountable to reduce local loss of lives and goods; and under what circumstances are local people, institutions, and governments able to manage these risks? There is currently only limited research that offers evidence for and responses to these questions. In this paper, we analyze these aspects from different disciplinary perspectives and associate them with a normative responsibility framework to identify responsibilities for action. This paper focuses on the glacier lake Palcacocha and associated flood risk for the downstream city of Huaraz in the Peruvian Andes (Fig. 1) to help answer these questions in a specific context and to offer larger insights into climate change risks and responsibilities. While being attentive to a diversity of risk frameworks and concepts (Blaikie et al., 1994;Oliver-Smith, 2013;Wisner et al., 2004), we understand risk as a function of physical hazard, human exposure and vulnerability of people and assets (IPCC, 2014). Lake Palcacocha offers a representative case for other glacier lakes and related risks around the world because it features many physical and social dynamics found elsewhere: a shrinking glacier that led to the formation of a large glacier lake where ice previously existed; continued lake instability due to glacier retreat and moraine dam instability; a past glacier lake outburst flood that killed thousands of local residents and partially destroyed a city and other communities and infrastructure; repeated flood prevention and lake drainage engineering works; a history of glacier lake monitoring and ongoing scientific studies; contested knowledge, science, and perceptions about the lake and its risks among experts, policymakers, local residents, and other groups; a complex political and institutional context with periods of increased attention and neglect of the problem by authorities and the local population; unclear responsibilities among different government agencies and levels; and, overall, a dynamic evolution of risk driven by physical and socioeconomic factors and processes. Our objective is to analyze to what extent we can identify natural and social processes as factors and drivers of risk at lake Palcacocha and in Huaraz and to discuss whether this analysis can inform the conceptualization of responsibilities related to managing the negative impacts of anthropogenic climate change.
This analysis is timely not only because glacierized mountain regions are increasingly grappling with unstable glacier lakes but also because lake Palcacocha recently made headlines worldwide because of a legal case, Saúl Luciano Lliuya vs. RWE (Frank et al., 2019). This case, pending at a Ger-man court, 1 emerged when a local resident of Huaraz (Luciano Lliuya), sued the German energy producer RWE over flood risk from glacier lake Palcacocha, threatening his property if the lake were to cause a flood. Luciano Lliuya argues that Palcacocha is unstable as a result of anthropogenic emissions (to which, he alleges, RWE made a significant contribution), which caused glacier retreat and the growth of lake Palcacocha, making the lake unstable and threatening downstream communities. The case was initially dismissed at a local German court but then admitted by a higher appeals court. As the first lawsuit of its kind to reach this stage, it was considered a significant breakthrough in climate litigation (Ganguly et al., 2018;. Although the literature on climate litigation is steadily growing (Marjanac and Patton, 2018;McCormick et al., 2018), questions of responsibility, and possibly liability, in a case like Palcacocha, remain mostly unanswered and hence call for studies that analyze risk and responsibility during climatic, cryospheric and societal change. The purpose of this paper, however, is not to analyze legally relevant questions of causality but rather to substantiate and situate the Palcacocha case in a broader context and within the concept of responsibility.
To achieve a comprehensive picture of flood risk in Huaraz and its relation to climate and socioeconomic change, we make use of existing data and information and conduct additional research where needed, including hazard field studies, numerical flood modeling, satellite data analysis, census data and interviews. We structure our paper as follows: we first analyze the physical evolution of lake Palcacocha from the mid-19th century Little Ice Age (LIA) to the present (Sect. 2). We then disentangle the different drivers of GLOF risks following the aforementioned IPCC-based risk concept. We begin with the physical hazard component of risk, studying how global drivers of anthropogenic greenhouse gas emissions affect the local conditions of GLOF hazard (Sect. 3). We collected remote sensing and fieldwork-based information to document the evolution of lake Palcacocha. We analyzed the hazard conditions at and around the lake to develop a number of flood scenarios that we then implemented in a physically based GLOF flow model following established methodologies to evaluate the downstream hazard in Huaraz. We then look at how social, economic, institutional and cultural aspects become drivers of risk exposure and vulnerability . For this purpose, we used a mixed methods approach to elucidate various environmental and sociocultural drivers that contribute to risk. Our historical analysis of risk development in Huaraz derives primarily from historical document analysis, literature review and interviews with contemporaneous figures. The more recent analysis of sociocultural and institutional factors contributing to risk (since 2009) draws on qualitative data from participant observation in institutional, urban, and rural settings, as well as interviews with people from these three spaces.
This case demonstrates the inherent links between local and global activities to manage climate risks and how they drive localized climate-related risks. The local-global linkages raise many questions about causality, liability, responsibility and justice (Sect. 7). Our assumption is that a better understanding of the diverse drivers of risk in a case like Palcacocha allows us to clarify the differentiation of responsibilities and the challenges ahead vis-à-vis impacts and risks of loss and damage.

Lake Palcacocha
The evolution and history of lake Palcacocha in Peru's Cordillera Blanca is linked to glacier retreat, driven by both natural and anthropogenic forcing, large flood disasters, and human intervention and flood mitigation at the lake (see Table 1). According to the lichenometric dating, the moraine that later dammed the lake developed between 1590 and 1630 (Emmer, 2017) due to advancing glaciers from the southwestern slopes of Palcaraju (6274 m a.s.l.) and Pucaranra (6156 m a.s.l.) mountains. This period corresponds to the beginning of the first, more distinct, phase of the LIA in the Cordillera Blanca (Thompson et al., 2000;Solomina et al., 2007). It is not known precisely when the lake formed; however, based on the available evidence we estimate that it was likely after the second phase of the LIA in the second half of 19th century. The Palcacocha drainage outlet nourishes the Paria river, joins other waterways downvalley and flows into the Quillcay River that runs through downtown Huaraz, the capital city of Peru's Ancash Region, with approximately 140 000 inhabitants today.
The first scientific expeditions and observations of the lake were undertaken by Austrian and German researchers led by Hans Kinzl in the late 1930s, a time before anyone realized the threat that Palcacocha posed to downstream communities (Carey, 2012;Portocarrero, 2014;Wegner, 2014). Shortly after, on 13 December 1941, lake Palcacocha's moraine dam failed, resulting in a GLOF with a volume of >10 million cubic meters and peak discharge in excess of 10 000 m 3 s −1 , causing devastating impacts on the city of Huaraz, located ca. 25 km downstream of the lake (Mergili et al., 2020;Somos-Valenzuela et al., 2016). The flood killed nearly 2000 people and destroyed one-third of the city of Huaraz, focused particularly in its most developed downtown area and modern commercial district (Carey, 2010;Wegner, 2014). This event is considered among the worst floods ever documented worldwide resulting from natural dam failure (Carrivick and Tweed, 2016;Costa and Schuster, 1988). Although the precise cause is not known, the 1941 flood likely followed an impact of an ice avalanche into the lake or failure related to piping in the dam (Oppenheim, 1946). After the 1941 GLOF, a small "residual" lake remained, dammed by the basal moraine (elevated part of the former bottom of the lake basin). The lake volume remained relatively stable for several decades (Figs. 2, 3), even when a heavy earthquake on 31 May 1970 (M = 7.9) caused disastrous effects on the region (Lliboutry et al., 1977). In the early 1970s, after almost 3 decades of minimal lake growth or stagnation, a permanent drainage canal and two artificial dams were constructed, lowering the lake water level by 1 m and stabilizing it at 4 566 m a.s.l., with 7 m of freeboard and 0.515 × 10 6 m 3 of water (Table 1). The contemporary period of glacier retreat and downwasting accompanied by lake expansion started by the end of the 1970s and extends to the present (Vilimek et al., 2005).
On 19 March 2003, the left lateral moraine along lake Palcacocha slid into the lake and produced a displacement wave that overtopped the dam and caused a small lake outburst flood further down the valley. This flood, combined   Table 1).
with an inaccurate but high-publicity NASA announcement 1 month later in April 2003 about glacier instability above Palcacocha, reopened discussions about the lake's threat to the city of Huaraz (Carey, 2010;Kargel et al., 2011). Given the more than 110 000 inhabitants of Huaraz at the time, these events led to a number of new hazard and risk assess-ment studies (e.g., Hegglin and Huggel, 2008;Vilimek et al., 2005). The lake volume at that time was determined as being 3.690 × 10 6 m 3 (+640 % in 29 years; Zapata et al., 2004), although some doubts have arisen concerning the accuracy of this 2003 lake bathymetry, and the lake area in fact would suggest a higher lake volume. The existing hazard mitigation measures built in the 1970s were no longer found to be sufficient . In 2009, a new bathymetry revealed that the lake had grown to 17.325 × 10 6 m 3 (Portocarrero, 2014). As a response, six siphons were installed in 2011 to temporarily reduce lake volume prior to the implementation of a permanent engineering solution. This project progressed slowly in the context of institutional instability, and volume regulation remains ongoing in 2019 with a set of 10 siphons.
With a volume of 17.403 × 10 6 m 3 in 2016 (i.e., +3380 % in 42 years; UGRH, 2016), lake Palcacocha is among the largest moraine-dammed lakes in the Cordillera Blanca. Further potential for lake growth is, nevertheless, limited by topographic constraints of lateral side moraines and bedrock slope reached in the rear part of the lake. According to the recent lake inventory and GLOF susceptibility assessment , Palcacocha is among the lakes susceptible to the production of a GLOF, which could be triggered by rapid landslide processes from surrounding moraines, ice and rock slopes. A detailed study of a potential landslideinduced outburst flood was performed by Klimeš et al. (2016) and flood and inundation hazard modeling for Huaraz was published by Somos-Valenzuela et al. (2016) and Frey et al. (2018), suggesting a decreasing hazard level if the water level is lowered. The population of Huaraz has increased from approximately 12 000 residents at the time of the 1941 GLOF to about 140 000 today, with tens of thousands inhabiting the path that the 1941 followed along the Quillcay River.

Physical drivers of risk
In this section we explore to what extent flood hazard and risk from lake Palcacocha can be attributed to anthropogenic climate change and to other physical drivers of risk. This is a challenging task with hardly any precedents and first needs some conceptual considerations, drawing on recent understandings of how impacts can be attributed to (anthropogenic) climate change (Cramer et al., 2014;Stone et al., 2013). A formal attribution study investigates whether a particular system has shown any observable trend and whether this trend can be attributed to anthropogenic climate change. Figure 4 visualizes a cascade of impacts from anthropogenic emissions to climate change, glacier shrinkage, and lake growth and eventually to GLOFs and the resulting flood hazard and damage. If we want to decipher the influence of climate change on GLOF hazard we need to analyze each component of this cascade of impacts, considering that a varying number of confounding factors (i.e., factors not related to climate change) interact at each stage.
In this cascade, we start with climate change where attribution research has a long and advanced track record and would typically conclude with a statement such as to what degree the observed climatic changes or trends can be attributed to anthropogenic emissions (Bindoff et al., 2013;Stott et al., 2000).
Specific studies on the attribution of observed climatic trends in the tropical Andes to anthropogenic emissions so far hardly exist. Global-scale attribution studies and assessments, however, have considered the broader Andes and Pacific coastal region. Bindoff et al. (2013) and Jones et al. (2013) show that temperature changes in this region are broadly in line with climate model runs that include anthropogenic forcing and clearly deviate from model runs with natural forcing only. Further research has analyzed the observational temperature and precipitation record of the region over the past few decades, as well as the link to phenomena of climatic variability such as the El Niño-Southern Oscillation (ENSO) (Heidinger et al., 2018;Vuille et al., 2008). Schauwecker et al. (2014) and Vuille et al. (2015) concur that temperatures in the Andes of Peru, including the Cordillera Blanca, have increased since the beginning of the observational record in the 1960s at rates of about 0.2 to 0.3 • C per decade, with reduced warming rates during the last ca. 30 years (∼ 0.1 • C per decade).
While ENSO and the Pacific Decadal Oscillation (PDO) exert an important influence on an interannual or decadal scale, anthropogenic radiative forcing has been identified as the most likely cause of the longer-term warming (Vuille et al., 2015).
We proceed along the impact cascade ( Fig. 4) with glaciers. Glaciers are closely coupled to the climate system, but surprisingly only very few studies that explicitly attribute glacier change to anthropogenic climate change exist worldwide. If we revisit glacier decay in the Cordillera Blanca, including the Palcacocha area, we find a phase of rather strong glacier retreat in the late 19th century, followed by a slowdown in the early 20th century with small advances in the 1920s (Kinzl, 1969). Later, a period of strong glacier shrinkage in the 1930s and 1940s led to a phase of slow retreat in the 1950s to 1970s, eventually followed by very marked glacier loss since the late 1970s up to the present (Georges, 2004;Hastenrath and Ames, 1995;Kaser and Georges, 1997;Rabatel et al., 2013). The continuous mass loss since the late 1970s was enhanced (or reduced) by variations in the Pacific sea surface temperatures and El Niño-La Niña phases, respectively, with ENSO exerting a significant effect on Andean glaciers on interannual timescales. The long-term glacier-shrinking trend, however, cannot be explained by ENSO-related variability (Schauwecker et al., 2014;Vuille et al., 2015), and therefore climate change clearly plays a significant role. This is also reinforced by the IPCC, who attributed glacier retreat in the Andes to climate change with very high confidence (Magrin et al., 2014).
A global-scale study finds that more than two-thirds of the 1991-2010 global glacier mass loss is due to anthropogenic forcing, while for tropical regions (including the Cordillera Blanca) an anthropogenic signal in observed glacier mass loss of recent decades is detectable with high confidence (Marzeion et al., 2014). A new study, however, focusing specifically on Palcaraju glacier (the glacier driving the growth of lake Palcacocha), concludes that close to 100 % of the observed temperature trend of 1.3 • C warming since 1880 can be attributed to anthropogenic climate change and that the glacier's retreat is entirely attributable to the observed temperature trend (Stuart-Smith et al., 2020).
We now analyze how Palcacocha lake growth relates to glacier shrinkage and anthropogenic climate change. Lake Palcacocha extends on a relatively flat area that was previously occupied by glacier ice and is dammed by LIA and early 20th century moraines. Lake growth at Palcacocha can therefore be attributed to glacier retreat in a straightforward way, as glacier ice was simply replaced by lake water and close to 100 % of the lake growth can be explained by glacier retreat (Fig. 2). Thermal energy of lake water accelerates ice mass loss at the glacier front, generating a positive feedback between glacier retreat and lake growth (Kääb and Haeberli, 2001). Lake growth was strongest in the 1990s and 2000s (Fig. 3), coinciding with the period of high anthropogenic emissions. Considering our well-documented glacier retreat and lake growth and new evidence on attribution of Palcaraju glacier's retreat from (Stuart-Smith et al., 2020), we therefore conclude that the growth of lake Palcacocha over the past 3 decades cannot be explained by natural variability and has a clear and high anthropogenic signal.
How GLOF hazard and risk in Huaraz or elsewhere can be attributed to anthropogenic climate change is still an open field of scientific debate. Physically, flood risk in Huaraz is determined by GLOF hazard, which is a function of the magnitude (or intensity, such as flood height) of a hazardous process at a given location and its probability of occurrence (Raetzo et al., 2002;UNISDR, 2009). A number of factors influence and determine GLOF magnitude and probability of occurrence at lake Palcacocha, notably lake volume, dam stability, and freeboard, as well as landslides from unstable moraines or ice/rock avalanches impacting the lake (Emmer and Vilímek, 2013;Schneider et al., 2014). Some of the factors (such as lake formation) are closely related to climate change, while others are associated with geologic or geotechnical conditions (e.g., dam stability) or are explicitly influenced by human intervention aiming at reducing the risk of GLOFs (e.g., lake freeboard determined by the height of the constructed drainage canal). In addition to effects on glacier retreat, climate change can influence some of these hazarddetermining factors, e.g., increasing temperatures can degrade permafrost and thus destabilize the flanks of the steep headwalls surrounding lake Palcacocha or alter thermal conditions and stability of steep glaciers Faillettaz et al., 2015;Haeberli et al., 2017).
To assess how GLOF hazard at lake Palcacocha translates into flood hazard in the city of Huaraz, we draw on numerical mass flow simulations by Frey et al. (2018) and Somos-Valenzuela et al. (2016), who modeled different scenarios of avalanches impacting the lake and producing damovertopping waves and downstream-propagating floods (see Supplement). They follow state-of-the-art hazard assessment approaches (GAPHAZ, 2017), which were also applied to others lakes in the Cordillera Blanca (Schneider et al., 2014). Corresponding model results indicate that an urban area of similar size as that destroyed by the 1941 GLOF is threatened by high GLOF hazard and thus by potential devastating effects (Fig. 5). Previous studies estimated about 40 000 people living in the inundation zone with a potential death toll of close to 20 000 (Somos-Valenzuela, 2014). Based on spatial census data from the National Statistical Institute of Peru (INEI), here we found that about 22 500 inhabitants living in the high-hazard zone are highly exposed to GLOF (Fig. 5). However, because the high-hazard zone intersects with the central business and market places of Huaraz, the number of people present during the day is much higher, possibly up to 50 000.
While recent studies quantitatively attributed the retreat of Palcaraju glacier to anthropogenic climate change (Stuart-Smith et al., 2020), it remains to be clarified whether quantitative attribution can also be achieved for GLOF hazard encountered at Huaraz or whether only qualitative statements are possible at the current state of science. Overall, despite the non-climatic factors also influencing GLOF hazards, we can confidently state that the clear and strong signal of anthropogenic emissions in the growth of lake Palcacocha translates to GLOF hazard in Huaraz. In the absence of anthropogenic climate change, the flood hazard would be much lower, primarily because the size of the lake would be substantially smaller, and a longer, flat glacier tongue, as was present in 1941, would significantly attenuate the impact energy of potential ice or rock and ice avalanches (Mergili et al., 2020). build their towns on valley floors in riparian zones, a pattern that contrasted with pre-Columbian populations that implemented a form of hazard adaptation by settling in upland areas away from alluvial fans (Oliver-Smith, 1999). The 1941 Palcacocha GLOF illustrated the consequences of this placement and the city's long-term exposure to Cordillera Blanca hazards (Wegner, 2014).
Following the flood, authorities attempted to reduce hazard zone inhabitation by prohibiting construction in the GLOF path, but residents and newcomers ignored the hazard zoning policies, and the government did not enforce its mandate (Carey, 2010). After the devastating 1970 earthquake destroyed much of Huaraz, the government again prohibited reconstruction in the 1941 GLOF path due to new concerns about unstable glacier lakes above Huaraz (Bode, 1990;Carey, 2010;Oliver-Smith, 1986). Once again, residents defied government hazard zoning, both rebuilding downtown Huaraz and expanding upstream along the banks of the Quillcay River toward Palcacocha and other glacier lakes. According to flood hazard assessment and mapping presented in Fig. 5, the Huaraz inhabitants most exposed to a future Palcacocha GLOF are clustered along the Quillcay river in the districts of Nueva Florida, Antonio Raimondi, Centenario, parts of San Francisco, Huarupampa, Nicrupampa, José Olaya and Patay, which have largely expanded in the past decades (Bode, 1990;Carey, 2010;Wegner, 2014). Figure 6 spatially compares the urban area of Huaraz from the immediate aftermath of the 1941 GLOF to the current situation, revealing enormous urban growth including the most hazard-exposed areas. Census data from a similar timeframe also show an enormous population increase from about 11 000 in 1940 to more than 140 000 in 2017 (Fig. 7). Several reasons motivated inhabitants to resettle and build within the potential path of a Palcacocha GLOF, even though they recognized the GLOF risks. Analysis of these reasons helps illuminate socioeconomic drivers of GLOF risk that are useful not only for understanding Palcacocha but also for evaluating GLOF and worldwide hazard risk.
First, inhabitants recognized key economic factors: some believed they would incur direct economic losses if they moved away, while others thought that inhabiting the area along the Quillcay River adjacent to Huaraz would yield economic gains. This dynamic emerged as early as the 1940s, and residents were outspoken about defending their rights to live in the potential GLOF path -often based on economic reasoning -starting in the 1950s (e.g., Anonymous, 1956Anonymous, , 1951Anonymous, , 1945. Inhabitation of flood-prone areas and other places susceptible to natural disasters, even when people understand the risks, is not unusual (e.g., Steinberg, 2000;Wisner et al., 2004). In Huaraz, however, many worried that the government would not compensate them for their lost land or provide them with a comparable plot and home elsewhere. Others were concerned that relocation of the city or even moving upslope to safer terrain would diminish Huaraz's position as the region's financial hub, where jobs and markets offered opportunities, transportation and commercial centers attracted people, and banks and credit institutions existed (Doughty, 1999;Oliver-Smith, 1977, 1999. While many were reluctant to leave Huaraz for these economic reasons, others migrated into the city for related motives, such as receiving relief and disaster aid following the catastrophe (Walton, 1974;Wrathall et al., 2014).
One part of Huaraz, the Nueva Florida district adjacent to the Quillcay River, exemplifies these economic incentives outweighing GLOF risks. Ethnographic research we conducted in the area provided insights that exemplify the historical and contemporary factors playing into this dynamic. Quechua-speaking farmers from the highlands above Huaraz began buying inexpensive property in Nueva Florida after the 1970s. This previously vacant land was not only affordable but also offered proximity to employment, public services and an overall higher standard of living for historically marginalized people. In the 1990s, new multinational mining operations near Huaraz triggered an influx of mine workers, who frequently settled in Nueva Florida. Given the district's growth, authorities built paved roads and installed electricity and sewage networks in Nueva Florida in the early 2000s. Today, Nueva Florida is a flourishing district, attracting even more people to the area along the Quillcay River. While authorities have officially prohibited construction in Nueva Florida since Palcacocha GLOF risk concerns arose again in 2009, residents attest that officials tolerate the construction of smaller buildings. Over time, living in Huaraz provided a unique opportunity for Quechua-speaking villagers to access social and economic opportunities in Huaraz. According to a survey we conducted in 2017 (see the Supplement), most Nueva Florida residents showed little concern for the risk of flooding either in the past or today. Though many were aware of recent public and media discussions about the threat of a Palcacocha GLOF, they contended that such warnings were exaggerated. It appears that economic and material benefits of inhabiting Nueva Florida outweigh the potential flood risk.
Second, social status among Huaraz residents -influenced primarily by racial and class divisions -has been another key factor influencing GLOF risk and explaining some inhabitants' continued occupation of the Quillcay riparian zone. Cities like Huaraz have long been inhabited by the ruling classes -the Spanish-speaking residents and supposedly non-indigenous people (Oliver-Smith, 1999). Living higher and more rurally, on the other hand, signified a poorer, more indigenous status in this culturally constructed schematic of race-class dynamics (Walton, 1974). Post-disaster urban zoning after the 1941 GLOF and 1970 earthquake that attempted to relocate populations to safer ground higher above the river came to symbolize, for some, a government-imposed assault on ruling-class privilege, downward social mobility and loss of socioeconomic status (Bode, 1977(Bode, , 1990Carey, 2010;Doughty, 1999).
Analysis of GLOF risks, exposure and vulnerability must consider both how inhabitants rank their risks and how disaster prevention policies such as hazard zoning, building practices and urban planning affect socioeconomic status. It is difficult to pinpoint responsibility for people's decisions to inhabit the potential GLOF path below Palcacocha. Inequality driven by class and race divisions has led to the marginalization of some segments of the Peruvian population. As a result, their decision-making may be shaped by economics, livelihood and employment opportunities, social standing, and other socioeconomic factors that are usually impossible to assign to certain individuals but instead can be assigned to overall populations, such as racism, poverty and global inequality. Furthermore, the economic level of Peruvians, including the citizens of Huaraz, is also affected by global histories and legacies of colonialism, neoliberalism, resource extraction, political domination and economic marginalization. Parts of these historical processes continue to affect the lives of people in Huaraz, which contributes to making them, generally speaking, poorer compared to residents of the most developed nations, who tend to have lower levels of vulnerability and can afford to rank risks differently than Peruvians living beneath lake Palcacocha (Carey, 2010).

Institutional and governance-related risk drivers
Institutions, policies and governance also affect levels of GLOF risk. In particular, government instability, fluctuating support (funding and resources), and institutional inconsis- tency creating confusion about disaster-prevention roles and responsibilities have all exacerbated risk below lake Palcacocha. It initially took 10 years after the 1941 Huaraz disaster to form the first GLOF prevention office, the Control Commission of Cordillera Blanca Lakes (CCLCB). Since the establishment of the first glaciology and lake security office in 1951 to mitigate Cordillera Blanca GLOF risks, the agency has passed through four different ministries, had 12 different names and even disappeared completely for nearly 4 years in the late 1990s (Carey, 2010). Some disaster events (e.g., the 1950 Los Cedros GLOF and the 1970 earthquake and Mount Huascarán avalanche) and some authoritarian governments (e.g., Presidents Odría in the 1950s and Velasco in the 1970s) stimulated strong investments in Cordillera Blanca GLOF prevention. At other times, glacier disasters (1962 Ranrahirca avalanche) and authoritarian governments (President Fujimori in the 1990s) triggered little government response or even backward steps in GLOF risk reduction.
Decentralization of the national government has also exacerbated institutional inconsistency and instability, which also influences GLOF risk. Prior to the 2002 start of the decentralization process, Peru's 25 departmental governments functioned as administrative extensions of the national government, with departmental governors (prefects) appointed by the national government. During this period, the central government directed and consolidated Cordillera Blanca GLOF monitoring and mitigation. Decentralization created new, more autonomous regional governments that were independently elected (Arce, 2008;Dickovick, 2011). On paper, the reforms made the Ancash regional government primarily responsible for identifying and implementing Palcacocha risk reduction measures, but in practice decentralization generated confusion about jurisdiction, expertise, authority, funding and responsibility, often leading to stagna-tion and nonaction that left residents more vulnerable or exposed to potential GLOFs.
Amidst decentralization, the Ancash government has also experienced exceptional turmoil in recent years: since 2014, three governors of Ancash have been imprisoned over charges including corruption and assassination (El Comercio, 2018). Further, there remains a host of national governmental institutions and ministries with jurisdiction over the Cordillera Blanca, including the Glacier and Lake Evaluation Office (formerly the Glaciology and Water Resources Unit, UGRH) of the National Water Authority (ANA) and associated local and provincial water authorities and Huascarán National Park. They interact with the Ancash regional government; provincial and municipal authorities and their corresponding entities, such as civil defense; rural community jurisdictions (comunidades campesinas); and a host of other stakeholders including mining companies, Duke Energy, and non-governmental organizations (NGOs). More specifically for GLOF risk reduction, the national government agencies, ANA, and the National Institute for Glacier and Mountain Ecosystem Research (INAIGEM), founded in 2015, operate in the Cordillera Blanca but sometimes overlap in confusing ways, ultimately impeding institutional capacity to respond to increasing glacier risks.
This regional government instability and uneven decentralization has obstructed effective GLOF risk reduction measures at lake Palcacocha specifically. In 2003, Palcacocha overflowed and caused a small flood due to a landslide into the lake (Vilimek et al., 2005). While debate ensued about jurisdiction and responsibility (e.g., Congreso de la República, 2003), it took nearly a year to conduct a bathymetry study and repair the damaged flood protection dam at the lake. In 2009, when a new study revealed that Palcacocha contained 17 million cubic meters of water (more than it had for the 1941 GLOF), no single institution took charge and led a permanent engineering project to partially drain and secure the lake, as the UGRH had done for decades previously. Instead, the institutional instability generated only short-term, unsustainable measures (temporary siphons) to protect downstream populations, despite repeated studies documenting risks relating to Palcacocha (Hegglin and Huggel, 2008;Klimeš et al., 2016;Portocarrero, 2014;Somos-Valenzuela et al., 2016;Vilimek et al., 2005).
In response to political inaction at a regional level, the local governments of Huaraz and Independencia -the two main municipalities affected by GLOF risk from Palcacocha -have collaborated to implement a Palcacocha early warning system. Moreover, in 2016, international experts, in cooperation with local institutions, released a new hazard map, including GLOF hazards and evacuation plans, for the Quillcay catchment (Frey et al., 2018;see Sect. 3 above). International scientific institutions and NGOs primarily took charge of producing the map, in collaboration with (but without leadership of) local, regional or national institutions in Peru. Overall, a combination of effects has contributed to the increase in risk, namely related to decentralization of the national government; institutional instability; conflicting roles and jurisdictions; and waning government support for Palcacocha hazard reduction research, monitoring, and projects. Given the complexities surrounding these processes and dynamics over time, a more detailed indication of their contribution to risk is elusive.

Cultural and emotional components of risk
Cultural factors also influence risk in the valleys below lake Palcacocha. Attachment to place can motivate people to inhabit potential flood zones, while varying local explanations of cause and effect (particularly causation between human behavior and environmental change) can also yield certain understandings of risk that collide with scientific assessments and may lead to inaction in the face of GLOF risks. Research on these cultural dimensions of glaciers is growing both elsewhere (Allison, 2015;Cruikshank, 2005;Sherpa, 2014;Sherry et al., 2018) and in the Peruvian Andes and Cordillera Blanca specifically, where locals often perceive sentient landscapes and maintain spiritual relationships with mountains and glaciers (Bolin, 2009;Carey, 2010;De la Cadena, 2015;Jurt et al., 2015). One key cultural driver of risk along the Quillcay River is the emotional and psychological attachment to place that has historically attracted people to Huaraz, even after the 1941 GLOF and 1970 earthquake devastated the city. A profound sense of place -that is, attachment to homelands, personal identity, heritage, familiarity with landmarks and landscapes, and links to communityfrequently bonds people to particular places, not just in areas prone to GLOFs but in disaster zones worldwide (Hastrup, 2013;Oliver-Smith, 1982;Sherry et al., 2018). These attach-ments to land and community also motivated people to remain living in Huaraz, even after disasters struck or when they had knowledge of GLOF risks (Bode, 1990;Oliver-Smith, 1982, 1986Yauri Montero, 1972). While some survivors emigrated to Lima after the 1941 and 1970 disasters, others remained in their former homeland, connected to their birthplace, close to those who died in the disasters, and part of the same community where they had always lived and experienced trauma.
Another factor influencing risk is the diverse understandings of environmental processes and hazards, particularly where scientific and technical explanations contrast with local beliefs and values. In May 2017, two ice avalanches descended into lake Palcacocha within a 24 h period, causing 3 m high waves that lake workers witnessed. The workers' supervisor maintained that this event occurred because he had not paid tribute to Palcacocha and the surrounding mountains. For workers at Palcacocha and other Quechuaspeaking farmers living nearby, the lake and mountains are beings that require respectful engagement. According to this understanding of glaciers and lakes, spiritual disruptions could trigger a GLOF -such as lake workers' inadequate offerings to mountain beings, rather than only geophysical processes such as glacier and bedrock instability. Some local accounts voiced that past glacier-related disasters such as the 1941 GLOF occurred because people failed to show the landscape entities adequate respect (Yauri Montero, 2000). According to our interviews and focus groups that we conducted in 2017 and 2018, some elderly villagers in areas below Palcacocha corroborate these stories. In one of these local's accounts of the 1941 flood, 2 a deity told a rural woman to perform a ritual offering at Palcacocha. When she failed to do so, the lake became angry and flooded Huaraz. When asked why Cordillera Blanca glaciers are melting, lake workers at Palcacocha pointed to contamination and global industry. While they recognized a global dimension of environmental change, they regularly paid tribute to the lake and mountains in an effort to prevent disaster. As long as the supervisor kept the lake happy with offerings of coca leaves and alcohol, he explained, there would be no GLOF disaster.
These accounts thus reveal how local people perceive both global and local aspects as drivers of risk, but their perceptions are often not in line with technical and scientific assessments of risk. For instance, many urban and rural residents have referred to enchanted lakes, which, in local understandings, can lure people to their shores and then suck people inside, to the other world, if they do not perform proper rituals or resist approaching these lakes (Carey, 2010;Yauri Montero, 2000). Other residents offer different cultural explanations for natural disasters, such as Catholic residents saying that the 1970 earthquake resulted from sinners' behavior and God's will (Bode, 1990;Oliver-Smith, 1986). Attributing GLOFs to their neighbors' behaviors or to the will of certain deities can ultimately lead to a relinquishment of responsibility and fatalism: why move outside a potential GLOF path if floods are determined by God's will or neighbors' sins? When a resident believes sinning causes floods or coca leaf offerings presented to mountain deities stabilize glacier lakes -as opposed to the scientific conclusions attributing these processes to climate change, glacier shrinkage or bedrock geometry -then development and implementation of risk reduction plans become more difficult, as not everyone agrees about the source of the hazard. In fact, people in Huaraz negotiate cultural and scientific understandings of flood risk on a daily basis and may regard multiple explanations as valid.
These trends in the Cordillera Blanca also exist internationally, and people knowingly inhabit areas exposed to GLOFs in other glacier-fed watersheds. In some cases, they are "forced" into these areas due to cheaper land in the floodplain or nearby job and livelihood opportunities Orlove et al., 2019). In other cases, they select GLOFprone sites to live due to historical and cultural connections to those flood-prone places (Sherry et al., 2018), they utilize other cultural or spiritual techniques to manage glacierrelated risks (Allison, 2015;Gagné, 2019), or they possess different local knowledge about risk that sometimes differs from scientific or institutional assessments of GLOF risks (Drew, 2012;Williams and Golovnev, 2015). Furthermore, in India, for example, there are documented recent major GLOF disasters that are also due to exposure and high vulnerability of a large number of people due to religious and tourismrelated reasons .

Implications for responsibility and justice
So far we have examined physical climate-change-related, socioeconomic, institutional and cultural aspects of Palcacocha GLOF risk. Drawing on that, we now analyze the possible implications for responsibility and ask how concepts of justice can inform these and other similar issues. Responsibility as a concept commonly concerns four aspects that become relevant when analyzing the differentiation and assignment of responsibilities in specific circumstances and at different policy levels (Bayertz, 1995): (i) someone (the agent or subject of responsibility) is responsible for (ii) something (the object of responsibility) and answerable to some (iii) institution according to some (iv) norm. This conceptualization of responsibility encompasses aspects of legal liability or causal responsibility, explaining the link between the subject of responsibility and the object of responsibility that becomes relevant in legal cases like the court case Lliuya vs. RWE. However, this understanding of responsibility is more general, including aspects and concerns that are beyond a more narrow legal understanding of responsibility in the sense of liability.
Responsibility in this wider understanding often concerns different agents and objects (Wallimann-Helmer, 2016). In the case of Palcacocha, a complex network of responsibilities and dependencies exists between different agents of responsibility and institutions. Differentiation and assignment of responsibilities to subjects depends on the perspective of the different drivers of GLOF risk and on whether a forwardor backward-looking concept of responsibility is adopted (Miller, 2007). Backward-looking assignment of responsibilities identifies the agents bearing responsibility for risks and outcomes already materializing and can be adopted to justify corrective duties. Forward-looking ascription of responsibilities concerns remedial duties to prevent negative impacts or minimizing risks (Burns and Osofsky, 2009;Grossman, 2003).
Observed physical risk drivers indicate that, to a large extent, glacier shrinkage and lake growth are due to anthropogenic climate change, which also contributes to GLOF risks. Detection and attribution research is primarily a backward-looking science and may inform the assignment of responsibilities for past emissions causing present climate risks James et al., 2019). Historically, emitters contributing to climate change are primarily highly developed western countries and regions, with large emerging economies strongly increasing their emission footprint over the past couple of decades. Accordingly, detected and attributed physical risk drivers of GLOFs allow us to ascribe some responsibilities for increased risk of GLOFs to these countries and regions. In climate litigation, countries or private companies, typically large corporations as in the case of Lliuya vs. RWE, are sued by plaintiffs, and courts verify the legal responsibilities (liabilities) of these entities.
Attribution research has only limited explanatory value for assigning forward-looking responsibilities, which also depends on the extent to which specific future risks are controlled by past emissions and related environmental changes. For instance, lake Palcacocha has formed as a result of climate and glacier change of the past decades but is likely to persist for decades or even centuries into the future. Assignment of forward-looking responsibilities in case of climaterelated loss and damage commonly implies remedying negative impacts or minimizing the risk of their occurrence, i.e., in case of Huaraz minimizing risks of GLOFs and their impacts . Investigating the different risk drivers can be useful to identify what risk reduction measures need to be taken, but it cannot identify the appropriate responsibility bearers or whether remedial responsibilities should concern monetary payments, help in building the required infrastructure and protection measures, assistance in governance, or capacity building (O'Neill, 2017;Page and Heyward, 2016).
It seems plausible that the industrialized countries and regions contributing most to anthropogenic climate change could foster the development of appropriate infrastructure and capacity in order for the affected people to be able to govern local climate risk themselves (Wallimann-Helmer, 2016). In cases like Huaraz, this is particularly important for two reasons. Firstly, many locals moved to Huaraz and to Nueva Florida especially for social and economic reasons. As we have seen, relocation out of the GLOF hazard zone means to many a risk of losing social status and achieved assets, exacerbated by a lack of trust in the government to compensate people so that they can retain their achieved status. Capacity building here demands building trust in governmental institutions and, if necessary, providing financial resources. Secondly, due to the socioeconomic opportunities provided by moving to Huaraz from rural areas, as well as due to cultural beliefs, perceptions of GLOF risk are diverse and not necessarily congruent with technical and scientific findings. This makes the sharing and exchange of comprehensive information and education to inhabitants of Huaraz and especially to those living in the flood hazard zone another key factor of capacity building. Otherwise, there is a risk of decisions being made by locals on the basis of insufficient information. Local or international experts may provide information on what can happen in case of a GLOF (e.g., flood height and extent in Huaraz). However, for reasons of efficiency, effectiveness, and local appropriation and acceptance of measures, it is sensible to leave decisions about what constitutes an acceptable or tolerable risk and how risk governance is implemented to those people who are most directly affected (Kaswan, 2016). In fact, locals' perspectives (e.g., in terms of cultural and spiritual understandings) should be taken seriously, suggesting a dialogue between differing knowledges about GLOF risk and environmental change more broadly, rather than a hierarchical knowledge exchange.
Governmental institutions and legal regulations define whether or not and to what extent individuals must bear responsibility for their own decisions with regard to settlements in risk zones like Nueva Florida. Institutions regulate behavior and demand justification if their regulations are not followed. However, institutions themselves are most often also responsibility bearers. The policy level at issue thereby defines the agent to take on responsibilities and the object of the responsibilities to be taken on (Wallimann-Helmer, 2019). Institutions are answerable to other, higher-level institutions and depend in their functioning on these institutions. For instance, the Glacier and Lake Evaluation Unit in Huaraz depends on finance and decisions from the central government in Lima through the National Water Authority (ANA), and, according to available resources, this office can take on more or less ambitious responsibilities. Since responsible agents are always answerable towards some institution, the institutional inconsistencies and instabilities at Palcacocha tend to foster lax implementation of regulations on the side of the agents that should take on responsibility. Who bears the responsibilities to help establish, strengthen and maintain functioning institutions depends on the governance level and capacities of relevant responsibility bearers. Socioeconomically disadvantaged locals might not be able to strengthen institutions, but wealthy locals and government officials may have this power. In the case of Palcacocha, some technical and governmental institutions in conjunction with international assistance and cooperation may be best suited to do so, including the Ancash Regional Government and possibly the municipal government of Huaraz.
These considerations in relation to the Palcacocha case suggest that there may be at least two different perspectives of responsibility corresponding to two different approaches to fairness and justice, which, however, we consider neither competing nor mutually exclusive. One of them aligns with the "ability to pay" principle (Caney, 2005;Page, 2008) that proposes that capacity is the most important criterion for fairly differentiating responsibilities in the context of climate risk governance. One may argue that efficiency and effectiveness in risk governance is achieved if those agents and institutions with the greatest capacity take on responsibility. This perspective would then also call for capacity-building efforts where capacity is lacking. The other responsibility perspective is more guided by the "polluter pays" principle (Gardiner, 2004;Hayward, 2012), implying that other responsibility bearers would have to carry heavier burdens. This leads to a more backward-looking approach to justice.
In global climate policy, the underlying premise has generally been that it is the industrialized countries (Annex I countries) that have heavily contributed to anthropogenic emissions and are thus assigned heavier burdens. Applying the logic and mechanisms of global climate policy to the Palcacocha case would foresee global emitters nourishing international climate funds (such as the Green Climate Fund) used to implement local adaptation and risk management measures. However, we also have seen that a substantial, yet hardly quantifiable fraction of increased GLOF risk in Huaraz is due to socioeconomic, institutional and cultural factors with a complex network of agents and responsibilities. How the different components and drivers of risk are weighted (e.g., as major or minor risk drivers) is eventually a societal or political process from which we abstain here. Notwithstanding, our analysis suggests that while global emitters bear responsibility for their contribution to locally materializing risks, local governments are not exempted from their responsibilities to address and effectively reduce the risk of negative GLOF impacts.
Defining the legal responsibilities for private company (or other) emitters (such as RWE in this case) needs to be determined by the court based on the respective laws and available evidence. In principle, the contribution of single or corporate emitters (being countries or private companies) to specified components and drivers of GLOF hazard can be quantified (Stuart-Smith et al., 2020), as has also been suggested for other climatic extreme events (Otto et al., 2017), and it is reasonable to indicate an associated uncertainty margin.
Palcacocha is in many aspects representative for the interlinkages of global and local drivers of climate risks and potential or actual loss and damage. The case shows that risks develop and loss and damage occur in a local context and over a certain period of time. Comprehensively understanding the different contributors to risk is challenging and has only been addressed by research in a limited way so far. Risk (and associated loss and damage) is a multifaceted construction, and the question of causality can often not be fully solved, at least not in a quantitative way.
Here we have seen that an anthropogenic signal (related to greenhouse gas emissions) is traceable through an impact chain of temperature, glacier change and associated lake growth that has increased GLOF hazard in Huaraz over the past few decades. Long-term climate, glacier, and lake observation modeling; geotechnical and geomorphological analyses; and flood modeling are needed to develop an understanding of the impact cascade. In contrast, the current conditions of exposure and vulnerability of people and values in Huaraz to GLOF hazard can only be understood with a historical perspective of social, economic, political and cultural dynamics.
Questions of responsibility, more broadly speaking, are difficult to address in cases where global, national and local drivers build a complex interlinked network. Courts, as in the case of Luciano Lliuya vs. RWE, operate under specific rules of (national) law that we have not further analyzed here. For questions of responsibility, we have sketched how the Palcacocha case could be embedded in a normative framework where we distinguish between perspectives of efficiency (with respect to risk management) and backwardlooking contributor-pays principles. Rather than promoting one or the other principle, we suggest a more differentiated and blended perspective on responsibility, implying that global emitters commit to support strengthening capacities in affected regions and localities, and local institutions and societies engage in local risk reduction measures and policies. In the case of Palcacocha and Huaraz, a suite of measures are suggested, some of them having been implemented over the past few years. Structural measures such as flood protection dams and lake drainage can effectively reduce flood hazard levels, and a GLOF early warning system can help save lives, increase awareness, and strengthen institutional prevention and response capacities. More rigorous land-use planning would be a highly effective risk reduction measures, but we have seen the significant associated social, economic, political and institutional barriers, in particular when communities are not directly and meaningfully involved in such policymaking. Comprehensive efforts for a dialogue between risk knowledges could have positive, long-term risk reduction effects.
After all, and beyond the case of Palcacocha and GLOF's in general, we believe that an improved understanding of drivers of risk and explicit differentiation of responsibilities can contribute to more effectively addressing climate risk and loss and damage.
Data availability. The socioeconomic and population data can be accessed from the National Statistical Institute of Peru, INEI: http:// sige.inei.gob.pe/sige/ (INEI, 2020). Satellite data are available from Google Earth. Historical aerial imagery, results of hazard modeling runs and lake volume data can be requested from the corresponding author.
Author contributions. CH developed and led the study, wrote and edited the text, analyzed the climate change attribution, did the socioeconomic data analysis, and produced the figures. AE contributed the sections and data relating to lake development, HF performed the the GLOF modeling and hazard assessments, and both contributed figures. MC and NWC contributed to and wrote the sections on socioeconomic, institutional and cultural aspects of risks. IWH led the section on justice and responsibility. All authors revised and edited the manuscript.
Competing interests. Two authors had paid and unpaid working relations with Germanwatch, the non-governmental organization that supports Saúl Lliuya in the court case Lliuya vs. RWE. Specifically, Noah Walker-Crawford had an internship with Germanwatch (2 months, 2014), followed by short-term consultancies (2014 to 2020) and employment in 2016. Adam Emmer prepared scientific material for Germanwatch on a short-term paid basis, and Christian Huggel made an expert statement for the Lliuya party of the court case on an unpaid basis.
Review statement. This paper was edited by Heidi Kreibich and reviewed by Dmitry Petrakov and Marcus Nüsser.