We produced a database of GLOFs developed from a collation of regional inventories and reviews (e.g. GAPHAZ¹, WGMS²and GLACIORISK³ databases and the GLOF Database provided under ICL database of glacier and permafrost disasters from the University of Oslo, Reynolds and Richardson, 2000; RGSL, 1997, 2002), regional overviews and reviews (e.g. Clague et al., 1985; Xu, 1987; Costa and Schuster, 1988; Reynolds, 1992; Ding and Liu, 1992; Clague and Evans, 2000; O'Connor et al., 2001; Zapata, 2002; Raymond et al., 2003; Jiang et al., 2004; Carey, 2005; Osti and Egashira, 2009; Narama et al., 2010; Ives et al., 2010; Wang et al., 2011; Carey et al., 2012; Mergili and Schneider, 2011; Fujita et al., 2012; Iribarren et al., 2014, Emmer, 2017) and case studies of individual GLOFs (e.g. Kershaw et al., 2005; Harrison et al., 2006; Worni et al., 2012). A complete list is available in the Supplement. The GLOF database was developed from a collation of regional inventories and reviews (see Supplement). Only GLOFs that could be dated to the year and to moraine failure were included. Past temperature trends from the glacier regions of interest were extracted from three independent global temperature reconstructions (CRUTEM4.2, Jones et al., 2012, NOAA NCDC (National Oceanic and Atmospheric Administration – National Climatic Data Center), Smith et al., 2008, and NASA GISTEMP (Goddard's Institute Surface Temperature Analysis), Hansen et al., 2010). These data sets provided temperature anomaly data relative to a modern baseline beginning in 1850 for CRUTEM4.2 and 1880 for NOAA NCDC and NASA GISTEMP.

2.2 The Earth's recent climate record smoothed along glacier response timescales: development of the GLOF lag hypothesis

A potentially destructive GLOF may elapse after a glacial lake grows to a volume where a sudden release of glacial lake water can exceed a normal year's peak instantaneous discharge. There are timescales associated with the period between a climatic (or other) perturbation and the occurrence of a GLOF. The following thought experiment demonstrates the concept of the lagging responses of GLOF activity to climate change: an initialized stable condition allows glacier–climate equilibrium, where neither the climate nor the glacier has fluctuated much for some lengthy period and where no other strongly perturbing conditions exist; e.g. there are no significant supraglacial or ice-marginal or moraine-dammed lakes, and a steady state exists in the supply and removal of surface debris. We then impose a perturbation (climatic or other) which favours eventual lake development and growth and eventually a GLOF. We describe two successive time periods which must pass before a significant GLOF can occur, and then a third period before a GLOF actually occurs: lake-inception time (τ_i), lake growth time (τ_g) and trigger time (τ_t). The first two sum to the GLOF response time (τ_GLOF) as we define it: ${\mathit{\tau }}_{\text{GLOF}}={\mathit{\tau }}_{\text{i}}+{\mathit{\tau }}_{\text{g}}$. The terms are for illustrative purposes: many supraglacial ponds initially go through a lengthy period where they fluctuate and drain annually and thus do not have a chance to grow beyond one season. Furthermore, lakes can grow to a point where limnological processes take over from climate; hence lake growth becomes detached from climate change. Even so, our set of definitions can be used to explain the lagging responses of glacier lakes and GLOFs to climatic history.

A GLOF does not necessarily occur upon climate step change date +τ_GLOF, which is the timescale over which the metastable system establishes a condition where a significant GLOF could occur. A trigger is needed (e.g. a large ice or rock avalanche into the lake or a moraine collapse as an ice core melts). After a sizeable glacial lake has developed, suitable GLOF triggers may occur with a typical random interval averaging τ_t, which depends on the topographic setting of the glacier lake, valley-side geology, steepness, moraine dam properties and climate. As a result, τ_t could range from years to centuries. Furthermore, as a lake usually continues to grow after τ_GLOF has elapsed, τ_t can in principle change, probably shortening as the lake lengthens and as the damming moraine degrades. The time elapsing between a climatic perturbation and a GLOF then is the sum of three characteristic sequential periods, ${\mathit{\tau }}_{\text{i}}+{\mathit{\tau }}_{\text{g}}+{\mathit{\tau }}_{\text{t}}$.

The lake inception time τ_i might be approximated by the glacier response time, which has been defined parametrically (Jóhannesson et al., 1989; Bahr et al., 1998) but in general describes a period of adjustment toward a new equilibrium following a perturbation. We take a simple parameterization (Jóhannesson et al., 1989) and equate ${\mathit{\tau }}_{\text{l}}=h/b$, where h is the glacier thickness of the tongue near the terminus and b is the annual balance rate magnitude. The glacier response time approximating the lake inception time may be many decades for most temperate valley glaciers, but it can range between a few years and a few centuries. The glacier response time is a climate-change-forgetting timescale. After a few response times have elapsed, a glacier's state and dynamics no longer remember the climate change that induced the response to a new equilibrium. For illustration, we adopt τ_l=60 years, a value typical of many temperate valley glaciers.

Figure 1Reconciliation of GLOF and climate records. (a) Blue curve: composite record of Northern Hemisphere land surface temperature (merged from multi-proxy data and instrumental records, as described in the main text), plus a model of land surface temperature during the period 2015–2100. Red, grey and black curves: moving historical averages of the blue curve, as described in the text, using τ_GLOF=20, 40 and 80 years. (b, c) Close-up of the more recent periods covered in (a). (d) Warming rate extracted from the moving historical averages using τ_GLOF=20, 40 and 80 years. Periods of cooling and warming are shown with blue and red tints, respectively, using the τ_GLOF=80 years curve. (e) Close-up of (d) to a more recent period. (f) Comparison of a smoothed GLOF frequency curve (red line, GLOFs/year historical moving average) with the moving historical average Northern Hemisphere temperature (black curve) using τ_GLOF=80 years and shifted +45 years, where the 45-year shift is considered to be reflective of τ, the GLOF trigger timescale. See supplement text for more description and explanation.

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A supraglacial pond may drain and redevelop annually (posing no significant GLOF risk), but at some point, if there is a sustained long-term negative mass balance, supraglacial ponds commonly grow, coalesce and form a water body big enough that rapid partial drainage can result in a significant GLOF. That lake growth period is defined here as τ_g, for which we adopt 20 years, a value typical of many temperate glacier lakes of the 20th century (e.g. Wilson et al., 2018; Emmer et al., 2015) Hence, ${\mathit{\tau }}_{\text{GLOF}}={\mathit{\tau }}_{\text{i}}+{\mathit{\tau }}_{\text{g}}\approx$ 80 years for the favoured values. Hence, a significant GLOF may occur at any time from 80 years following a large climatic perturbation: what the GLOF waits on is τ_t, which could be years or a century. This concept can be extended to the lagging response of a whole population of glaciers following a perturbation in regional climate (Fig. 1).

We distinguish between climate change, which may establish conditions needed for a GLOF to happen, and weather, which sometimes may be involved in a GLOF trigger. GLOF triggers are diverse; e.g. protracted warm summer weather may trigger an ice avalanche into the lake or moraine melt-through, or heavy winter snow may trigger an ice avalanche into the lake.

However, the relevant controlling climate in this example is that of the prior climatic history and the conditioning period defined by τ_GLOF and the typical trigger interval τ_t. Hence, τ_GLOF is closely connected to climate, whereas τ_t can be connected to weather for certain types of triggers.

The assessment above is for a single step-function climate change. Considering that climate changes continuously and glacier characteristics vary, populations of glaciers must have full distributions of τ_i, τ_g and τ_GLOF. Even while glaciers are still adjusting to any big recent historical climate change, more climate change accrues; glacier and lake dynamics take all that into account, either increasing the likelihood and perhaps size of a GLOF or decreasing or delaying it. Hence, the overall GLOF frequency record cannot be synchronous with climatic fluctuations, and it also should not simply trace past climate change with a time lag; rather, the GLOF frequency record for any large population of glaciers should be definitely but complexly related to the recent climatic history.

The functional dependence on climate history is not known for any glacier or population of glaciers, but to explore the concept of a lagged GLOF response to accrued climate changes, we assert that the integration function will tend to weight recent climatic shifts more strongly than progressively older climatic shifts, the memory of which is gradually lost as the glacier population adjusts. That is, because of glacier dynamics and the responses of a population of glaciers to climatic changes, the population eventually loses memory of sufficiently older climatic changes and adjusts asymptotically toward a new equilibrium. This should be true for any climate-sensitive glacier dynamics (Oerlemans, 2005). Though we do not know the functional form of the glacier responses (either for an individual glacier or a population), we nonetheless wish to illustrate our point while not driving fully quantitative conclusions. We propose that the integration of climate information into ongoing glacier dynamical adjustments occurs with exponentially declining weighting going backward in time from any given year. The exponential time-weighting constant may be similar to τ_GLOF. We have computed a moving time-average Northern Hemisphere temperature with the weighting of the average specified by an assumed τ_GLOF= 80 years; the computed moving average pulls data, for any year, over the preceding period of τ_GLOF; i.e. it includes temperature information up to 240 years prior to any given year. The weighting of earlier years' temperatures within that τ_GLOF is less than that of later years, according to the exponential. The cut-off at τ_GLOF is arbitrary and was done for computational expediency, seeing that any climate fluctuation occurring before τ_GLOF years earlier is inconsequential due to the exponential memory loss.

We combined the Mann et al. (2008) multi-proxy Northern Hemisphere temperature anomaly from 501 AD to 1849, the Jones et al. (2012)⁴ Northern Hemisphere land instrumental temperature record from 1850 to 2014 and a model of expected warming from 2015 to 2100. It is the recent climate history at each glacier lake or region that is strictly relevant, but lacking such records and needing here to only establish the concept, we settle for the treatment described above involving the Northern Hemisphere temperature anomaly.

The model is a constant 2.7 ^∘C century⁻¹ warming; noise was added from a naturally noisy but overall non-trending instrumental record from 1850 to 1899, with some years repeated to append the 2015–2100 period (Fig.  1). The Mann et al. (2008) and Jones et al. (2012) data sets were brought into congruence in 1850. Then we smoothed the composite record and model results using the τ_GLOF exponentially weighted filter, as described above, where the natural logarithmic “forgetting” timescale τ_GLOF= 20, 40 or 80 years for three illustrative cases. Smoothing was computed for τ_GLOF, i.e. 240 years if τ_GLOF= 80 years. Our favoured value τ_GLOF= 80 years is based on large Himalayan and other temperate glacier lakes. The shorter response times would likely apply to small glaciers or those occurring in steep valleys.

Regardless of the functional form of the glacier response and lake dynamics, GLOF frequency in any given region or worldwide must lag the climate record. The historically filtered/smoothed temperature record and model incorporating τ_GLOF= 20, 40 and 80 years is shown in Fig. 1a–c together with the unsmoothed actual record and model temperature series. The temperature anomalies are plotted in panels (a), (b) and (c); and the warming rate in panels (d) and (e). The historically averaged/smoothed temperature record lags fluctuations in the unsmoothed record. The lag is most easily seen where temperatures start to rise rapidly in the 20th and 21st centuries. The high-frequency temperature anomaly fluctuations also show concordantly but in damped form in the smoothed moving average curves because the curves are historical moving averages with the heaviest weighting toward the more recent years. The lagging responses are also seen at several times when the running average curves variously show warming and cooling for the same year depending on the value of τ_GLOF .

We posit that the historically filtered warming rate (more than the temperature anomaly) drives GLOF frequency. In Fig. 1 we show GLOF frequency (smoothed over 10-year moving averages) together with the warming rate extracted from the historically filtered temperature and model temperature time series. To get a better match with the temperature treated as such, we applied a further 45-year shift. From a glacier and lake dynamics perspective, this shift might relate to the trigger timescale, τ_t. Singular values ofτ_GLOF andτ_t should not pertain globally to all glaciers but should span wide ranges. The adopted values τ_GLOF= 80 years and τ_t= 45 years nonetheless make for a plausible match between the GLOF and climate records. These numbers make sense in terms of glacier and lake dynamics timescales, but we reiterate that our purpose with this climate–GLOF fitting exercise is illustrative. In sum, a notable shift in GLOF frequency does not connote a concordant shift in climate, though prior climate change may still underlie the cause.

Figure 2(a–f) Left: temporal distribution of regional GLOF frequency and magnitude. At all locations, the cumulative sum of events (black line) indicates an upsurge in the number of events per year. The timing of this upsurge differs by location and likely reflects an increase in reporting, especially in the early part of the record, rather than a change in GLOFs, at least until the 1970s–1990s after which the GLOF rate reduces. Right: global time series climate data from the five regions using CRUTEM 4.2, NOAA NCDC and NASA GISTEMP. Grey columns represent the baseline against which temperature is measured.

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Figure 3(a) Record of all precisely dated GLOFs from 1860 to 2011. (b) Wavelet power spectrum of global GLOF record, significant at 5 %. (c) Frequency-integrated wavelet power spectrum.

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Our global analysis identifies 165 moraine-dam GLOFs, recorded since the beginning of the 19th century (Fig. 2a). The vast majority of these GLOFs (n=160; 97 %) occurred since the beginning of the 20th century, at a time of climate warming and increasing glacier recession (Figs. 2 and 5). None of these GLOFs were associated with repeat events from the same lake. Around 65 % of GLOFs occurred between 1930 and 1990. Thirty-six GLOFs occurred in the mountains of western North America between 1929 and 2002 (Table S1 in the Supplement). Fifteen of these occurred in western Canada, 15 in the Cascade Range of the USA and four in Alaska. One occurred in Mexico and 1 in the Sierra Nevada. In the South American Andes we identified 40 GLOFs. Eleven occurred in Chile between 1913 and 2009 (including the large one in Patagonia at Laguna del Cerro Largo in 1989); one in Colombia in 1995 and 28 in Peru between 1702 and 1998. Fourteen GLOFs are listed from the European Alps. Three are from Austria between 1890 and 1940, five from Switzerland between 1958 and 1993 one from France in 1944 and five from Italy between 1870 and 1993. In the Pamir and Tien Shan mountains in central Asia, we identified 20 GLOFs, with most of these dating from the late 1960s to the early 1980s. The largest number of GLOFs (55) is reported from the Hindu Kush Himalaya (HKH) including the mountains of Bhutan and Tibet, dated from the 20th and 21st century. Thirty are from Tibet (between 1902 and 2009), 12 from Nepal between 1964 and 2011(and one is reported to have occurred in 1543) and five in Pakistan between 1878 and 1974. There is uncertainty in reporting some of these GLOFs and we discuss this further in the Supplement.

From around 1930 to about 1950, GLOFs occurred with regularity but a low frequency (Fig. 3). In other words, floods occurred with relatively long period variability (50–60 years). Starting around 1960, the frequency of these events increased (period decreased to approximately 20 years), remaining relatively high until about 1975, after which the statistically significant periodicities end, though GLOFs continue to occur.

While incomplete data restrict a full analysis of GLOF triggers, precise date, magnitude and initiation at a global scale, many GLOFS triggered by ice avalanches and rockfalls occur during summer (see Fig. 4). The characteristics of GLOFs that could be influenced by climate change include changes in magnitude, frequency, timing (either changes in seasonality or changes over longer timescales) and trigger mechanisms. In addition, many rock avalanches into lakes triggering a GLOF may represent a paraglacial response to deglaciation from the LIA or earlier times (Knight and Harrison, 2013; Schaub et al., 2013) and this delayed response demonstrates the need to account for lags between changes in forcing and responses in attribution studies.

From this analysis, we highlight three key observations: (1) GLOFs became more common around 1930 but then their incidence was maintained at a quasi-steady level for a few decades thereafter; (2) since about 1975, GLOF periodicity has decreased globally; and (3) the periodicities of GLOF occurrence have changed throughout the 20th century. These observations are discussed below.

Figure 4Seasonal variation in the occurrence of GLOF associated with the failure of moraine dams. Only a proportion of the GLOFs have seasonal data on timings.

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Figure 5Temperature anomalies in the CRUTEM4.2 data set for each mountain region. For each region we extract all the grid points that contain a glacier as defined in the World Glacier Inventory – Extended Format (WGI-XF) and these are shown as black crosses.

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Our first main observation is that GLOF frequency increased dramatically and significantly around 1930 globally and between 1930 and 1960 regionally (Figs. 1 and 2). We find no obvious reason for an abrupt improvement of GLOF reporting in 1930. While acknowledging that incompleteness of the record must be a pervasive factor throughout the early period covered by the database, we discount reporting variations as the cause of the abrupt shift. For instance, this pattern is observed in the European Alps, a region with a long history of mountaineering, glacier research and valley-floor habitation and infrastructure development. Given that we record individual GLOFs in the 19th and early 20th centuries we argue that the increase in GLOF frequency in the 1930s represents a real increase rather than an observational artefact. Following the increase around 1930, we observe a similar rate of GLOFs for the subsequent years, typically 1 per year in the following decade, increasing to 2–3 per year during the 1940s (e.g. Figs. 1a, 2a). Again, there is no evidence that incompleteness of data is a main cause of the observed pattern. We therefore conclude that the incidence of global GLOFs has remained generally constant between about 1940 and about 1960. In the 1960s and early 1970s, several years saw more than five GLOFs. We argue below that the trend between 1940 and 1960 hides a more complex spatial and temporal pattern (Clague and Evans, 2000; Schneider et al., 2014).

Our second main observation is that, while there is considerable variability between regions, GLOF incidence rates have decreased since about 1975 globally (Fig. 2). There are both more and larger GLOFs during the 1970s and early 1980s in the Pamir and Tien Shan, in the 1960s in the HKH and in the 1990s in Alaska, the Coast Mountains and Canadian Rockies; and then decreases in both magnitude and frequency follow these periods. In the Andes however, GLOF incidence decreased after the early 1950s. The latter observation may be at least partly attributable to considerable GLOF mitigation measures in Peru, such as engineering-based lake drainage or dam stabilization (Carey et al., 2012; Portocarreo-Rodriguez, 2014). Carrivick and Tweed (2014) propose several reasons why “glacial floods” may have decreased in frequency in recent decades. These include successful efforts to stabilize moraine dams and changes in the ability of fluvial systems to transmit floods over time. We argue, conversely, that this reduction may represent a “lagged” response to glacier perturbations following climate change. More research is clearly needed on this question, and we believe that our analysis, along with that of Carrivick and Tweed's, will stimulate further work and discussion.

Our third main observation is that for several decades in the 20th century, GLOF occurrence has been periodic, but that periodicity has varied. Since about 1975, and especially since 1990, the periodic nature of GLOF occurrence has diminished, even though GLOFs have continued. In other words, GLOFs since 1975 have become more irregular. We suspect that the switch to less periodic outburst floods in recent decades is related to an underlying mechanism such as topographic constraints and glacier hypsometries, with glaciers retreating into steeper slopes, implying a reduced rate of moraine-dammed lake formation – a phenomenon observed, for example, in the European Alps (Emmer et al., 2015).

The statistics of small numbers affect these regional, time-resolved records, but the overall validity of a similar mid-20th century increase and then decrease in the frequency of GLOFs can be further detected in the global record and is statistically significant (Fig. 3). We argue that the reduction in global GLOF frequency after the 1970s (especially in central Asia, HKH and North America) is real, because the contemporary reporting is likely to be nearly complete given the scientific and policy interest in glacier hazards from the late 20th century. Hence, our conclusion is that globally and regionally there have been interdecadal variations in the frequency of GLOFs, and in general the most recent couple of decades have seen fewer GLOFs than the early 1950s to early 1990s. The record's (in)completeness is not able to explain a decreasing incidence rate. This temporal variation in GLOF frequency and recent decrease is therefore a robust and surprising result and has occurred despite the clear trend of continued glacier recession and glacier lake development in recent decades.

Our data allow us to test and refine the widespread assumption that GLOFs are a consequence of recent climate change (Bajracharya and Mool, 2009; Riaz et al., 2014). This is an important assumption because it implies that GLOF frequency will increase as the global climate continues to warm with potential major impacts for downstream regions.

The global increase in GLOF frequency after 1930 must be a response to a global forcing, considering global glacier retreat (Zemp et al., 2015), and physical process understanding suggests that this is a lagged response to the warming marking the end of the LIA (Clague and Evans, 2000). Although the global response appears sudden, in 1930 the region-by-region assessment shows that the response was asynchronous regionally and temporally over three decades (Fig. 2). This is consistent with the fact that the end of the LIA was not globally synchronous (Mann et al., 2009) and we also argue that this reflects regional variations in glacier response times.

We argue that as a climate shift occurs, after some period related to the glacier response time, previously stable or advancing glaciers start to thin and recede; after a further limnological response time proglacial ponds start to grow, coalesce and deepen into substantial moraine-dammed lakes. GLOFs typically occur after some additional period of time (the GLOF response timescale), but this time can be brief in glaciers with short response times, such as in the tropical Andes (Fig. 1).

In the HKH and central Asia the near-concordant formation of many Himalayan glacier lakes and the abrupt increase in GLOF rates in the 1950s and 1960s suggest that the GLOF response time is much smaller than the limnological response time. The moraine evidence here indicates that a shift from mainly glacier advance to recession and/or thinning occurred widely, though regionally asynchronously, between 1860 and 1910. The HKH underwent this shift by around 1860 (Owen, 2009; Solomina et al., 2015) in response to warming following the regional LIA. The limnological response time in the Himalayan–Karakoram region is thus around 100 years, i.e. substantially longer than in the tropical Andes.

We have arrived at a plausible explanation for the post-1930 (1930–1960) increases in GLOF rates. They are most likely heterogeneous, lagging responses to the termination of the LIA, with limnological response times of the order of decades to 100 years, depending on the region (e.g. Emmer et al., 2015). The limnological response times may be of a similar order to the glacier dynamical response times (Jóhannesson et al., 1989; Raper and Braithwaite, 2009) but are appended to them. Thus, measured from a climatic shift to increased GLOFs, the combined glaciological and limnological response times (plus GLOF response times, which may be the shortest of the three response times) may sum to roughly 45–200 years (Fig. 1). It cannot be much more than this, because then we would not see the multi-decadal oscillations in GLOF rates in some regions or globally.

Some individual glaciers may have faster response times than estimated above (Roe et al., 2017), but taken on a broader statistical basis we infer that the most recent GLOFs are a delayed response to the end of the LIA. A fundamental implication is that anthropogenic climatic warming to date will likely manifest in increasing GLOFs in some regions of the world starting early this century and continuing into the 22nd century. In all the mountain regions considered here the available evidence indicates a warming trend over the last century around 0.1 ^∘C decade⁻¹ (Figs. 2 and 5). The trend varies between data set and region, with the highest rates in the Pamir Tien Shan region and the lowest in the HKH. The most uncertain region is the Andes, where the sparseness of data prevents any meaningful assessment. The trends are consistent with the global mean land temperature trend 0.95 ± 0.02 to 0.11 ± 0.02 ^∘C for 1901–2012, implying these regions have warmed at approximately the same rate as the global land surface.

The baseline behaviour of glacial lake systems in the absence of climate change is not known in detail, but the low rate of GLOFs prior to 1930 may indicate that without warming the frequency would be low. The difficulty of attributing individual GLOF behaviour to climate change relates to the presence of non-climatic factors affecting GLOF behaviour, such as moraine dam geometry and sedimentology, climate-independent GLOF triggers (e.g. earthquakes) and the timescales related to destabilization of mountain slopes, producing mass movements into lakes (Haeberli et al., 2017). This represents the period of paraglaciation (e.g. Ballantyne, 2002; Holm et al., 2004; Knight and Harrison, 2013). These system characteristics may vary regionally and temporally within the evolutionary stage of a receding mountain glacier, and non-climatic factors such as lake mitigation measures additionally influence GLOF frequency and magnitude (Clague and Evans, 2000; Portocarreo-Rodriguez, 2014). We argue that while the original driver of lake development is likely to involve climate change (resulting in glacier downwasting and slowed meltwater flux through glaciers systems as glacier surfaces reduce in gradient) other mechanical and thermodynamic processes likely assume more importance as the lakes evolve, and these includes small-scale calving and insolation-induced melting of ice cliffs (e.g. Watson et al., 2017).

We also recognize that contemporary mountain glaciers are dissimilar to those that existed in the LIA. They are, in the main, shorter, thinner and with prominent moraines. Assumptions that climate processes acted on similar glacial systems over time are therefore likely to be simplistic.

Based on the analysis of our global GLOF database we have shown that a clear trend is detectable globally and regionally diversified in the 20th century with a sharp increase in GLOF occurrence around 1930. This trend is attributable to the observed climate trend, namely the warming since the end of the LIA. The delayed response of GLOF occurrence is an exemplar for the complexities of how natural systems respond to climate change, underlining the challenges of attribution of climate change impacts. We have shown here that attribution of GLOFs to climate change is possible, although the suite of factors influencing GLOF occurrence cannot be fully quantified.

In addition, lake outbursts following moraine failures are likely to be quite different in different regions. This reflects differences in a number of factors including ground thermal conditions, presence or absence of ground ice and permafrost, influence of extreme weather and seismic processes, topography and glacial history. To assess these we would need to better understand the geomorphological timescales involved in lake evolution and failure to design a more robust statistical analysis and to understand each region's GLOF history. We thus recommend close attention by the Earth surface processes science community to various process timescales using field studies, satellite remote sensing and theoretical modelling.

Our inventory and the global pattern of GLOFs that is derived from it lacks in many cases precise data on the processes responsible for GLOFs. This is a consequence of incomplete reporting of GLOFs in remote mountain regions, especially before the advent and wide use of remote sensing. In many cases the record is of a large flood being observed and then some time afterwards a collapsed moraine dam is seen and the flood is attributed to this collapse. Clearly the precise details of how the collapse occurred is not always available, and this uncertainty bedevils all similar detection and attribution studies, especially on those events associated with rapid geomorphological change. This intrinsic incompleteness in the record is problematic but should not prevent reasonable assertions on GLOF triggers to be made, especially if global-scale and consistent patterns in GLOF behaviour are observed.

Future research should therefore more systematically study the factors influencing GLOF frequency and magnitude and lake formation where a distinction between GLOF conditioning and triggering factors will be helpful (e.g. Gardelle et al., 2011).

If climate (such as temperature time series) influences GLOFs, as surely must be the case, long lag times are necessarily implied by the empirical data sets. With such lags as we have modelled, this brings the increase of GLOFs following 1930 into line with temperature increases at the end of the Little Ice Age. Subsequent changes in the GLOF rate (including a several-decades-long fall in GLOF rates) can similarly be attributed to fluctuations in global warming. If these conclusions are broadly correct, a further implication is that an acceleration in GLOF rates will probably occur in the 21st century, perhaps starting rather soon. Even though the actual global warming rate for the 21st century may be nearly constant, as modelled, the fitted warming rate as plotted in Fig. 1f accelerates because of the memory of a post-LIA, pre-anthropogenic quasi-stable climate. We are entering a stage where anthropogenic warming will increasingly dominate GLOF activity and attribution of GLOFs to anthropogenic global warming will be confirmed.  For now, this remains a hypothetical projection or expectation and is not yet borne out in the GLOF record.

The database of GLOFs analysed in this paper is attached as a supplement.

The supplement related to this article is available online at: https://doi.org/10.5194/tc-12-1195-2018-supplement.

The project was designed by SH following discussions with JK, CH and JR. Climate model data were provided by AW and RAB. Data analysis was carried out by SH, JK, DHS, LR and UH. JR, VV and AE provided inventory data. All authors helped to write and review the text.

The authors declare that they have no conflict of interest.