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Climatic and geometric controls on the global distribution of
surge-type glaciers: implications for a unifying model of surging
Heïdi SEVESTRE,
1,2
Douglas I. BENN
1,3
1
Department of Arctic Geology, University Centre in Svalbard, Longyearbyen, Norway
2
Department of Geosciences, University of Oslo, Oslo, Norway
3
Department of Geography, University of St Andrews, St Andrews, UK
Correspondence: Heïdi Sevestre <heidi.sevestre@unis.no; heidi.sevestre@yahoo.fr>
ABSTRACT. Controls on the global distribution of surge-type glaciers hold the keys to a better
understanding of surge mechanisms. We investigate correlations between the distribution of surge-type
glaciers and climatic and glacier geometry variables, using a new global geodatabase of 2317 surge-type
glaciers. The highest densities of surge-type glaciers occur within an optimal climatic envelope bounded
by temperature and precipitation thresholds. Across all regions with both surge-type and normal
glaciers, the former are larger, especially at the cold, dry end of the climatic spectrum. A species
distribution model, Maxent, accurately predicts the major clusters of surge-type glaciers using a series
of climatic and glacier geometry variables, but under-predicts clusters found outside the climatically
optimal surge zone. We interpret the results in terms of a new enthalpy cycle model. Steady states
require a balance between enthalpy gains generated by the balance flux and losses via heat conduction
and meltwater discharge. This condition can be most easily satisfied in cold, dry environments (thin,
low-flux glaciers, efficient conductive heat losses) and warm, humid environments (high meltwater
discharges). Intermediate conditions correspond to the optimal surge zone, where neither heat
conduction nor runoff can effectively discharge enthalpy gains, and dynamic cycling can result.
KEYWORDS: energy balance, glacier surges, ice and climate
INTRODUCTION
Although surging glaciers represent a small percentage of
the world’s glacier population, they are of great importance
in the investigation of glacier processes, flow instabilities
and fast glacier flow (Clarke, 1987; Jiskoot, 1999). Usually
defined as quasi-periodic advances or increases in flow
speeds unrelated to external triggers (Meier and Post, 1969;
Sharp, 1988), glacier surges are widely agreed to occur in
response to internally driven oscillations in basal conditions.
However, surging glaciers exhibit a very wide range of
observed characteristics and behaviors, encompassing land-
terminating and tidewater glaciers, cirque glaciers, valley
glaciers and ice streams, as well as both temperate and
polythermal regimes (Murray, 2003).
The length of the surge cycle is commonly almost
constant for a single glacier (Meier and Post, 1969), and
tends to be proportional to the length of the surge phase
(Dowdeswell and others, 1991). For instance, the well-
documented surge history of Variegated Glacier, Alaska,
USA, is characterized by a short surge cycle (repeating itself
every 13–18 years) and short active phases (1–1.5 years)
with high flow velocities reaching 40–60 m d
–1
(Kamb and
others, 1985; Eisen and others, 2001); in colder regions such
as Svalbard, the surge cycles tend to be relatively longer
(50–500 years), with longer active phases (3–10 years)
(Dowdeswell and others, 1991).
In response to this diversity, a wide variety of potential
surge mechanisms has been proposed, focusing on basal
processes, including cycling of thermal or hydrological
conditions (Kamb and others, 1985; Clarke and others,
1986; Fowler, 1987; Fowler and others, 2001; Van Pelt and
Oerlemans, 2012), or instabilities in a deforming bed
(Clarke and others, 1984; Truffer and others, 2000).
One of the most striking facts about surge-type glaciers is
their tendency to cluster within particular regions (Fig. 1).
Major clusters occur in Alaska–Yukon, Arctic Canada, parts
of West Greenland (Disko Island, Nuusuaq Peninsula) and
parts of East Greenland (Blosseville Kyst and Stauning
Alper), Iceland, Svalbard and Novaya Zemlya (Post, 1969;
Jiskoot and others, 2002, 2003; Copland and others, 2003;
Fischer and others, 2003; Yde and Knudsen, 2007; Citterio
and others, 2009; Grant and others, 2009) and a number of
mountain ranges in central Asia, including the Karakoram,
Pamirs and western Tien Shan (Hewitt, 1969, 1998;
Osipova and others, 1998; Kotlyakov and others, 2008;
Copland and others, 2009, 2011). Outside these major
clusters, surge-type glaciers are rare or absent, although
small clusters or isolated examples also occur in the
Caucasus Mountains, the Andes, New Siberian Islands,
Kamchatka and Tibet (Dolgoushin and Osipova, 1975;
Espizúa, 1986; Zhang, 1992; Kotlyakov, 1996; Dowdeswell
and Williams, 1997; Casassa and others, 1998; Kotlyakov
and others, 2004; Yafeng and others, 2010).
Several statistical studies have been undertaken to
compare surge-type and non-surge-type glaciers within
individual clusters, aiming to identify possible topographic
and geological controls on surging behavior (Post, 1969;
Clarke and others, 1986; Wilbur, 1988; Clarke, 1991;
Hamilton and Dowdeswell, 1996; Jiskoot and others, 1998,
2000, 2003; Björnsson and others, 2003; Barrand and
Murray, 2006; Grant and others, 2009). Such studies have
identified a number of statistically significant correlations
within clusters, indicating that some particular models of
surging are more appropriate in some regions. For example,
work by Jiskoot and others (2000) suggests that a thermal
switch model is more appropriate for the surges in Svalbard,
Journal of Glaciology, Vol. 61, No. 228, 2015 doi: 10.3189/2015JoG14J136646
while a hydrologic switch model appears to operate in
central East Greenland (Jiskoot and others, 2003). Interest-
ingly, in this latter region both Svalbard-type and Alaskan-
type surges were observed (Jiskoot and Juhlin, 2009).
Nonetheless, these studies have not provided definitive
answers as to why glaciers in some regions are prone to
surging whereas others are not.
In this paper, we take a new approach to the problem of
glacier surging, and employ a global geodatabase of all
known surge-type glaciers to investigate climatic and
geometric controls on surge phenomena on global and
regional scales. Although it has long been recognized that
the distribution of surge-type glaciers is non-uniform (Post,
1969; Raymond, 1987), climate has never been statistically
investigated as a possible underlying control on this distri-
bution (Meier and Post, 1969; Post, 1969). Climate has only
been connected to surging as a control on the thermal and
mass-balance regimes of surging glaciers (Jiskoot and others,
2000; Copland and others, 2003; Harrison and Post, 2003),
and the periodicity of surge cycles (Eisen and others, 2005;
Striberger and others, 2011), and climate change has been
invoked as a possible reason for the disappearance of
surging glaciers from regions (Hoinkes, 1969) or a reduction
in their number (Dowdeswell and others, 1995). In this
paper, we investigate the role of climate in the present-day
global distribution of surge-type glaciers using ERA-Interim
(ERA-I) reanalysis data, and consider the role of glacier
geometry as a secondary, local-scale control.
The paper begins with an introduction to the geodatabase
on surge-type glaciers, and a description of the methods
employed in the analysis. We then demonstrate that surge-
type glaciers occupy well-defined subsets of the total
climatic range of the world’s glaciers, defined in terms of
mean precipitation and temperature variables, and also
exhibit strong geometric biases. We go on to model the
global distribution of surge-type glaciers using Maxent, a
species distribution model widely used in the biological
sciences. Finally, we discuss the significance of our results
using the concept of glacier enthalpy balance, and argue
that oscillatory or unstable flow regimes reflect a mismatch
between rates of heat production (balance velocity) and
dissipation (conduction and runoff), both of which have
strong climatic and geometric controls.
DATASETS AND METHODS
Geodatabase of surge-type glaciers
We compiled a global inventory of surge-type glaciers based
on 305 peer-reviewed publications and historical reports,
consisting of either direct observations of a surge or
identification of a glacier as being surge-type from glacio-
logical or geomorphological evidence. The oldest obser-
vations date from 1861 and extend until 2013. No new
observations were made in this study. By compiling such a
large number of references, we faced a patchwork of
interpretations of what a surge is, combined with a wide
spectrum of glacier behaviors interpreted by researchers as a
‘surge’. For inclusion in the geodatabase, every identification
of a surge-type glacier had to conform to the criteria listed in
Table 1. The criteria are consistent with those adopted in
existing inventories (e.g. Copland and others, 2003, 2011;
Grant and others 2009). For glaciers for which a surge phase
was not directly observed, the glacier and/or its proglacial
environment had to display a sufficient combination of
geomorphological/glacial geomorphological features to con-
firm surging (Clarke and others, 1986; Copland and others,
2003; Barrand and Murray, 2006; Grant and others, 2009).
Many existing inventories included in our database assign
a study-specific ‘surge index’ to every glacier listed
(Ommanney, 1980; Clarke and others, 1986; Hamilton and
Dowdeswell, 1996; Jiskoot and others, 2000; Copland and
others, 2003). These indices attempt to quantify the like-
lihood of a particular glacier being of surge type. In the
published literature, a total of 75% of the glaciers of the
geodatabase have been ranked using 11 different surge
Fig. 1. Global distribution of surge-type glaciers (pink dots) based on our geodatabase. Normal glaciers are represented in blue. Glacier
outlines for the normal glaciers are from the Randolph Glacier Inventory (RGI) version 3.2.
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers 647
indices. While single observations were first filtered through
the criteria written in Table 1, we decided to homogenize
and qualitatively reassess every observation by applying our
own harmonized surge index. This ranks every glacier on a
scale from 1 to 3, 3 being a confirmed surge-type glacier, 2 a
very probable surge-type glacier and 1 a possible surge-type
glacier. The details of each of these classes and their
equivalence to other study-specific surge indices are
presented in Tables 1 and 2 and Appendix A (Tables 4 and 5).
The geodatabase incorporates a total of 2317 glaciers and
tributaries, of which 1148 are directly observed and dated
surges, and 186 glaciers have more than one surge
referenced (see Table 2 for numbers of surge-type glaciers
for each region and for categories 1–3). Each glacier is
georeferenced by the latitude/longitude of its center point,
and data on its geometry are provided. Tributaries are added
as separate entries if their behavior differs from that of the
main trunk. To allow comparison of surge-type glaciers with
the total global population of glaciers, the geodatabase was
combined with the Randolph Glacier Inventory (RGI)
version 3.2, released in September 2013 and downloaded
from http://www.glims.org/RGI/ (Arendt and others, 2012).
Combining the geodatabase with the RGI resulted in 1430
individual surge-type glaciers, as the tributaries are merged
with their main trunk.
Climate data
To investigate possible climatic controls on the distribution
of surge-type glaciers we used ERA-I reanalysis datasets
produced and distributed by the European Centre for
Medium-Range Weather Forecasts (ECMWF), downloaded
from http://data-portal.ecmwf.int/data/d/interim_mnth/. Spa-
tial resolution (horizontal and vertical) is 0.75° 0.75° 60
levels (approximately 83 km 28 km in the horizontal at
70° N and S, 83 km 53 km at 50°, and 83 km 72 km at
30°, and 80 km in the vertical) (Dee and others, 2011;Fig. 2).
In this study we use the Synoptic Monthly Means Forecast
surface dataset from January 2000 to December 2009. We
focused our interest on two glaciologically significant
variables: 2 m temperature (parameter 167) and total precipi-
tation (parameter 228). The ERA-I dataset takes into account
the mean topography of each cell. The grids were then
processed in ArcGIS 10.1 to compute annual, seasonal and
decadal averages of the monthly means for the whole world.
Climatic data were spatially extracted for all glaciers in
the RGI based on the location of their center point, whether
they are surge-type or normal glaciers. In total, the 203 975
glaciers composing the RGI v3.2 were assigned temperature
and precipitation data averaged over the decade January
2000–December 2009, over the ERA-I gridcells. We then
split the total glacier population into surge-type and non-
surge-type datasets for analysis.
The mismatch between the time window of the surge
observations (1861–2013) and the ERA-I data (2000–09) is a
potential source of error, because early 21st-century climate
data may not be representative of conditions when a
particular surge took place. However, we do not believe
that this is a serious problem for the initial global-scale
analysis presented here. The ERA-I data represent only an
approximate climatology for individual glaciers, and may be
unrepresentative in cells with very high vertical relief. To
assess which regions could suffer the most from these
vertical differences, we calculated the difference between
the mean elevation of the glaciers’ center point and the
mean elevation of the corresponding ERA-I cell. The surge
clusters most affected are the Caucasus (difference of
2400 m), followed by the Tibetan Plateau (1800 m) and the
Andes (1550 m). Therefore the glaciers found in these
regions are likely to experience colder conditions than
indicated by the ERA-I data. A detailed list of the vertical
differences for each surge cluster is provided in Table 3.
However, we believe that errors introduced by large ERA-I
cell size are offset by the advantages of a homogeneous
global climatic dataset.
Table 1. List of criteria used for inclusion of a glacier in the geodatabase
Criterion Description Source
Periodical changes in flow velocities Observation of a large increase in glacier flow velocities, followed by a
period of abnormally slow flow. Velocities during the active phase
typically reach at least an order of magnitude higher than during the
passive phase. Slower surges have been observed with velocities as
low as 150 m a
–1
.
Meier and Post (1969)
– criteria 1, 2, 5
Terminus advance Advance of the glacier terminus, sometimes sudden and dramatic,
out of synchrony with the behavior of neighboring glaciers.
Meier and Post (1969)
– criterion 6
Glaciological/geomorphological evidence Surge-type glaciers display a combination of features indicative
of oscillations in flow: looped moraines, heavy surface crevassing,
push moraines, eskers, etc.
E.g. Copland and others (2003);
Grant and others (2009)
Table 2. Number of surge-type glaciers included in the geodata-
base, split between regions and surge index categories
Region Category 1 Category 2 Category 3 Total
Alaska–Yukon 1 208 113 322
Arctic Canada 19 11 16 46
Argentina 1 1 8 10
Canada 189 225 36 450
Caucasus 0 4 4 8
Chile 0 0 7 7
China 1 5 3 9
Greenland 3 88 21 112
Iceland 0 2 27 29
Kamchatka 0 0 3 3
Karakoram 22 21 63 106
N. Siberian Islands 2 0 0 2
Novaya Zemlya 15 13 4 32
Pamirs 375 355 90 820
Svalbard 163 48 134 345
Tien Shan 1 1 9 11
Total 794 982 541 2317
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers648
Glacier geometry variables
In addition to climatic data, we investigated differences in
geometry between surge-type and normal glaciers across all
the glacierized regions. Glacier area was measured for all
the glaciers of the RGI using the outlines of the same dataset.
Combining the glacier outlines with the 3 arcsec horizontal
resolution dataset from the ASTER GDEM V2 allowed us to
extract further information on glacier elevation (minimum,
maximum and range) for the same glaciers. The ASTER
GDEM V2 was downloaded from http://gdem.ersdac.
jspacesystems.or.jp/ (ASTER GDEM is a product of the
Ministry of Economy, Trade and Industry, Japan (METI) and
NASA). The absolute vertical accuracy of the GDEM V2 has
been tested against 18 000 geodetic ground control points
from the US National Geodetic Survey. Calculations have
revealed a root-mean-square error of 8.68 m, with a mean
vertical offset from sea level of –0.20 m (Gesch and others,
2012). This dataset has been shown to be suitable for the
compilation of topographic glacier inventory parameters
(Frey and Paul, 2012) and was chosen for its consistency
over all glacierized regions. Other geometrical attributes
(e.g. glacier length, average slope and aspect) were derived
for all the glaciers of the RGI using a global dataset of glacier
center lines from Machguth and Huss (2014). We discov-
ered that in some regions, glacier outlines in the RGI are
erroneously reported as ellipses. Consequently, geometry
data had to be discarded for the following regions:
Kamchatka, parts of Altai, Ural, Gary Byranga, Verkhoyansk
and Kolyma mountain ranges (see Fig. 3).
We used an additional set of glacier center lines for
Alaska. This region is home to one of the densest
populations of surge-type glaciers, with a very well-defined
distribution. Surge-type glaciers are notably absent from the
Brooks Range in the north, and gradually disappear south-
wards in the southeastern ranges of the Coast Mountains.
Alaska is therefore a particularly interesting region to
investigate climatic and geometric differences between
normal and surge-type glaciers. Kienholz and others
(2014) have developed an extensive dataset on the geometry
of the Alaskan glaciers, automatically extracting glacier
center lines and a suite of metrics including number of
branches and length of the longest center lines. Here we
employ one of their metrics, glacier ‘branchiness’ measuring
the number of branches composing each glacier.
Maxent: methods
Statistical analysis of the distribution of surge-type glaciers
with respect to climatic and glacier geometry variables was
performed using the species distribution model Maxent
(Phillips and others, 2006). Species distribution models
(SDMs), also referred to as environmental or ecological
niche models, are widely used by biologists to predict the
distribution of a species by correlating known occurrence
localities to a set of environmental variables (Elith and
Graham, 2009). SDMs are traditionally used to estimate the
fundamental niche of a species (i.e. the set of all conditions
that allow for its long-term survival), to define habitat
characteristics and estimate habitat suitability, and to
explain patterns of species distribution (e.g. Corsi and
others, 2000; Peterson and Shaw, 2003). In this study we
challenge an SDM to reproduce the global distribution of
the ‘species’ of surge-type glaciers based on the geodatabase
of surge-type glaciers and the climatic and glacier geometry
information described above.
Maxent is one of the most popular and widely used
methods for environmental niche modelling (Merow and
others, 2013), and is one of the best-performing techniques
for dealing with presence-only data (Elith and others, 2006;
Hernandez and others, 2006; Williams and others, 2009;
Mateo and others, 2010). The popularity of Maxent rides on
the growing interest in presence-only datasets, composed
Fig. 2. Examples of ERA-Interim cells cropped over two glaciated regions: Alaska–Yukon (left) and central Asia (right). The dimensions of the
ERA-I cells vary across the world. Cells with surge-type glaciers are colored based to the number of surge-type glaciers present in each cell.
Table 3. Difference between the elevation of the glaciers’ center
point and the mean elevation of the ERA-I cell they belong to, for all
the main surge clusters. The regions are ranked from the largest to
the smallest difference. The rightmost column indicates the
standard deviation of the mean elevation of the glaciers belonging
to each region
Surge cluster Vertical difference STDEV elevation of glaciers
m
Caucasus 2399.25 363.40
Tibetan Plateau 1811.5 472.16
Andes 1548.93 862.13
Tien Shan 1420.51 309.10
Pamirs 1016.63 359.02
Alaska–Yukon 793.38 568.06
Greenland 582.93 475.46
Karakoram 489.83 443.06
Iceland 420.22 254.63
Arctic Canada 355.98 233.48
Novaya Zemlya 232.54 115.91
Svalbard 230.97 124.397
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers 649
solely of an inventory of the occurrence locations of a
species without any additional information on where the
species is truly absent. It is appropriate to define the
geodatabase on surge-type glaciers as a presence-only
dataset due to the episodic nature of surging and the non-
systematic monitoring of glacier velocity changes. A lack of
observations of surging behavior does not imply that the
glacier has never surged, or will not do so in future.
Maxent computes the probability distribution of a species’
occurrence, constrained by environmental variables that
represent incomplete information about the original un-
known distribution, and assuming that the true distribution
exhibits maximum entropy (i.e. the distribution closest to
uniform) (Phillips and others, 2006). In this case, entropy can
be understood as a measure of uncertainty or ignorance. In
order to estimate the true distribution of surge-type glaciers,
Maxent uses only what we know (i.e. where some surge-type
glaciers are found and in which conditions), without going
beyond these prior stated data. For our study, we utilize
Maxent version 3.3.3k freely available at http://www.cs.
princeton.edu/schapire/maxent/. Phillips and Dudík (2008)
provide a full description of Maxent’s algorithms.
Maxent can only process ASCII grids, which we cropped
to the glacierized regions, meaning that Maxent’s predic-
tions will not cover other land surfaces. Because all climate
data are gridded, we average the glacier geometry values of
all glaciers present in every cell of the canvas. We use as a
canvas the ERA-I grids for the climatic data; the cell size is
therefore 0.75° 0.75°. For runs that included geometry
data, we adopted smaller cells of 0.05° 0.05° in order to
prevent extreme skewing of averaged values (e.g. the
presence of one large glacier surrounded by a thousand
small ones would result in a very low average glacier area
for the cell).
The discriminatory ability of the model output was
quantified using the AUC metric (area under the receiver
operating characteristic curve) (Hanley and McNeil, 1982).
AUC scales from 0 to 1, where 0.5 is no better than random
and 1 denotes perfect discrimination; AUC > 0.9 is con-
sidered an excellent fit (Elith and Graham, 2009). We
performed two types of run of the model, (1) single runs using
75% of the data as a training set and 25% for validation and
(2) series with replicates to evaluate the results with k-fold
cross-validation. The replicate technique performs a series of
random splits of the presence data into training and test sets,
and therefore systematically uses all the data for validation.
At each replication, the model is tested on different training/
testing partitions called ‘folds’. Given the number of
occurrence points, we performed ten replicates, hence
testing 10% of the data at each repetition. K-fold cross-
validation can suffer from spatial correlation between the
training and the testing datasets, which can yield over-
estimates of the model performance and underestimates of
the errors in predictions (Radosavljevic and Anderson,
2014), and we tested for this by comparing the results of
the single and multiple-fold runs. Finally, a jackknife test was
used to assess and rank variable importance (Wu, 1986).
RESULTS
Climatic envelopes
The distribution of surge-type and normal glaciers with
respect to ERA-I mean annual temperature (MAT) and mean
annual precipitation (MAP) is shown in Figure 4a. Surge-
type glaciers are clustered in a well-defined climatic
envelope within which both normal and surge-type glaciers
coexist, whereas outside the envelope only normal glaciers
are found. The climatic envelope for surge-type glaciers can
be divided into two subzones. In the coldest and driest
environments are the surge-type glaciers of Arctic Canada.
Surge-type glaciers are rare in this subzone, accounting for
only 54 of the 11 757 glaciers in the RGI (0.46%). The
second and larger segment of the climatic envelope covers a
broader range of climate, with ERA-I MAT ranging from
–12°C to +8°C, and MAP from 165 to 2155 mm a
–1
. Surge-
type glaciers in this part of the envelope occur within two
superclusters: (1) a broad band extending through the Arctic
and sub-Arctic from Alaska to Novaya Zemlya (the ‘Arctic
Ring’), excluding Arctic Canada, and (2) High Mountain
Asia (Fig. 4a(i)).
Despite their geographical separation, the climatic par-
ameters of the two superclusters almost completely overlap.
The majority of surge-type glaciers in the Arctic Ring and
High Mountain Asia are found below a threshold in MAT,
which rises from –10°C at MAP = 165 mm a
–1
to 0°C at
MAP = 402 mm a
–1
. Above this threshold, surge-type glaciers
are rare, and apart from a few outliers are absent where MAT
exceeds +8°C.
The only exceptions to this pattern are a few surge-type
glaciers in the central Andes, which occur within ERA-I cells
with much higher MAT than any other surge-type glaciers.
Fig. 3. Left: regions where glacier outlines are erroneous are marked in red. Right: example over the Kamchatka region of erroneous outlines
in the shape of ellipses.
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers650
This anomaly can be explained by the large difference
between the elevation of these Andean glaciers and the
mean elevation of the ERA-I cells in which they belong (see
Table 3). Therefore the temperature and precipitation figures
are unrepresentative of the true local climate surrounding
these steep, high-elevation glaciers. More detailed analyses
are required to investigate this issue, and in the present
paper we focus on the general global patterns.
Figure 4a(ii) shows the number of glaciers per ERA-I cell,
and highlights the optimal climatic envelope for surge-type
glaciers. While cells containing high densities of normal
glaciers are scattered throughout a wide range of climatic
conditions, high densities of surge-type glaciers are clearly
grouped in a band located in the central part of the surge-
type climatic envelope, with MAT of –10°C to 0°C, and
MAP from 30 to 2250 mm a
–1
. Surge-type glaciers are
uncommon in colder, drier environments (i.e. Arctic Can-
ada), and become increasingly rare when MAT exceeds 0°C.
Seasonal climatic data highlight further patterns in glacier
distributions (Fig. 4b and c). Surge-type glaciers occur over a
very wide range of mean winter (October–April for the
Northern Hemisphere, June–September for the Southern
Hemisphere) temperatures (MWT) and precipitation (MWP),
although they are absent from warm, wet regions. The
thresholds delineating the climatic envelope for surge-type
glaciers can be described by a linear relation between
temperature and precipitation. In this case, surge-type
glaciers occur very seldom in regions where MWT > 0.007
MWP – 4.7 (MWT in °C, MWP in mm a
–1
). However, the
majority of surge-type glaciers occupy a much tighter winter
climatic envelope (Fig. 4b(ii)), with MWT = –16°C to
–6°C, and MWP = 200–1130 mm a
–1
. Surge-type glaciers
are strongly restricted by an upper limit in mean
summer (May–September for the Northern Hemisphere,
October–May for the Southern Hemisphere) temperature
(MST), and almost entirely absent where MST = 0.0025MSP +
6.5 (MST in °C; MSP: mean summer precipitation in mm a
–1
).
Only four cells with surge-type glaciers in the Caucasus
Mountains and four cells with surge-type glaciers in the
Andes occur above this threshold. Again, we expected these
regions to be affected by the unrepresentativeness of ERA-I
climatic averages in steep, isolated mountain massifs. Surge-
type glaciers are also uncommon above a summer precipi-
tation threshold, with only a few in the Pamirs and the
Tibetan Plateau occurring where MSP > 1100 mm a
–1
.
Thresholds bounding the optimal surge zone appear even
clearer when plotting MST against MWP (Fig. 5). Surge-type
glaciers are absent above MST = 0.001MWP + 8.4, and
below MST = 0.0014MWP – 0.97. A clear threshold in
Fig. 4. Climatic distribution of the populations of normal and surge-type glaciers. (a(i)) Mean annual precipitation against mean annual
temperature; (a(ii)) completes the same plot with additional information on the number of glaciers present in every ERA-I cell. (b(i)) Mean
winter precipitation against mean winter temperature; (b(ii)) completes the same plot with additional information on the number of glaciers
present in every ERA-I cell. (c(i)) Mean summer precipitation against mean summer temperature; (c(ii)) completes the same plot with
additional information on the number of glaciers present in every ERA-I cell. Note that all horizontal axes are in log scale, and that the size
of the ellipses representing number of glaciers per cell differs between surge-type and normal glaciers.
Fig. 5. Climatic distribution of the populations of normal and surge-
type glaciers, in a combination of mean winter precipitation against
mean summer temperature. Regions so far not known among the
clusters of surge-type glaciers but overlapping the optimal surge
zone are delineated. Note that the horizontal axis is in log scale.
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers 651
precipitation provides the lower boundary for the optimal
surge envelope with MST = 0.015MWP – 28.23.
Delineation of these climatic envelopes allows identifica-
tion of other potentially suitable regions where surge-type
glaciers may occur, but which have not been reported.
These regions belong to the same climatic envelope as the
Arctic Ring and High Mountain Asia superclusters, and
include the glaciers of Siberia and Franz Josef Land.
Interestingly, the entire Antarctic Peninsula falls within the
optimal surge climatic envelope (see Fig. 5).
Glacier geometry
Previous analyses have identified a number of glacier
geometry variables that show statistically significant correla-
tions with surging behavior, including glacier length, width
and surface slope (Clarke and others, 1986; Clarke, 1991;
Hamilton and Dowdeswell, 1996; Jiskoot and others, 1998,
2000, 2003; Björnsson and others, 2003; Barrand and
Murray, 2006; Grant and others, 2006). Until now, only four
regions have been covered by these investigations:
Alaska–Yukon, Iceland, Karakoram and Svalbard. Using
the outlines of the RGI combined with the global dataset of
center lines from Machguth and Huss (2014), we investi-
gated differences in area, length, range, slope and aspect
between surge-type and normal glaciers both on global and
regional scales. In addition, and similarly to Clarke and
others (1986), Hamilton and Dowdeswell (1996), Jiskoot
and others (2003) and Grant and others (2009), we explored
the importance of glacier complexity and number of
tributaries composing a glacier system by using the
branchiness index of Kienholz and others (2014) in Alaska.
Figure 6 shows the results for every geometry attribute for
the main surge clusters. New Siberian Islands and Kamchat-
ka were excluded from the analysis for having respectively
three and two surge-type glaciers, according to our
geodatabase. In every cluster where both surge-type and
normal glaciers coexist, the former are larger. A ttest denoted
statistically significant differences between the means of both
populations for all clusters. The largest surge-type glaciers
are found in Arctic Canada, with an average area of 627 km
2
,
compared with 9.5 km
2
for normal glaciers. This region also
displays the largest difference in size between the two
populations in the world. Most of these glaciers are outlets
from ice caps. Very large differences between the areas of
surge-type and normal glaciers are also found in Iceland and
Novaya Zemlya. The smallest differences in size between
surge-type and normal glaciers are found in the Caucasus
and High Mountain Asia. There, surge-type glaciers are still
larger than normal glaciers but the average difference in size
between the two is <14 km
2
.
Glacier length and slope appear as the two next most
important variables in differentiating surge-type from normal
glaciers across the main surge clusters. Since glacier length
and glacier area are not independent, it is unsurprising that
length follows a similar pattern. Surge-type glaciers are
significantly longer than normal glaciers, with the largest
difference being in Arctic Canada. Slope also significantly
differs between the two populations, but this time with an
inverse relationship where surge-type glaciers have shal-
lower slopes than normal glaciers, as already observed in
Jiskoot and others (2000). The largest differences occur in
Greenland and Iceland. Glacier elevation range shows some
difference between the two populations, although this is
likely to be the result of a correlation between elevation
range and glacier length. Arctic Canada and Alaska display
the largest differences between the two populations. On the
other hand, aspect does not appear to be significantly
different between surge-type and normal glaciers across our
studied clusters. If anything, surge-type glaciers cover a
slightly narrower span of orientations.
Differences in geometry between surge-type and normal
glaciers exhibit a clear climatic bias, as shown in Figure 7.
Whereas normal glaciers display little systematic variation in
area on the MAT–MAP plot, surge-type glaciers show much
greater variation in area with climate. In the optimal climatic
envelope for surge-type glaciers (where there are high
numbers of surge-type glaciers per ERA-I cell; Fig. 4a(ii)),
surge-type and normal glaciers are relatively similar in area.
In contrast, at the ‘cold-dry’ extreme of the distribution
(Arctic Canada and Tibetan Plateau) surge-type glaciers
have much larger areas and greater lengths than normal
glaciers in the majority of cells. At the ‘warm-humid’ end of
Fig. 6. Difference in glacier geometry between normal and surge-
type glaciers across the main surge clusters. Surge-type glaciers are
represented in pink, with normal glaciers in gray. ‘Area’ denotes
glacier area, ‘Range’ stands for elevation range, ‘Length’ is the
length of the center line, ‘Aspect’ is measured clockwise from the
true north, and ‘Slope’ is averaged along the glacier’s center line.
Note that the vertical axes for area and length are in log scale.
Significant statistical differences between the two groups are noted
with a * (p= 0.05), while comparisons between groups containing
<30 samples are shaded in gray. In each box, the central line
represents the median, and the lower and upper edges of the box
are the 25th and 75th percentiles. Whiskers extend from the most
extreme values (continuous line) to the outliers (dashed line).
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers652
the distribution, surge-type and normal glaciers tend to be
similar in area and length, except for a few cells where the
former are much larger. These anomalies appear to reflect
random effects of glacier sampling in ERA-I cells, rather than
a systematic size distribution. Both slope and range vary
greatly across the whole climatic spectrum without follow-
ing a distinctive pattern. At most, a narrow core of smaller
elevation ranges can be seen for the population of surge-
type glaciers in a small part of the optimal surge zone.
To test whether the complexity of glacier systems shows
any correlation with surging behavior (cf. Clarke and others,
1986; Hamilton and Dowdeswell, 1996; Jiskoot and others,
2003; Barrand and Murray, 2006; Grant and others, 2009),
we compared the ‘branchiness’ of glaciers in the Alaskan
cluster, for which high-quality geometry data are available.
The branchiness index is defined as the number of branches
required to reach 85% of the total glacier length (Kienholz
and others, 2013). It is therefore not the total number of
tributaries forming the glacier system, but an index of glacier
complexity ignoring tributaries of negligible size (e.g. minor
embayments or niches). Surge-type glaciers are, on average,
branchier than normal glaciers (on average, five branches
against one for normal glaciers across all length classes;
Fig. 8).
Maxent: results
We ran Maxent with a wide range of climatic and glacier
geometry variables, including mean annual temperature,
mean summer temperature, mean winter temperature, mean
annual precipitation, mean summer precipitation, mean
winter precipitation, glacier area, length of the center line,
elevation range, slope and aspect. To test for collinearity, we
calculated correlation coefficients between variables at the
individual glacier level (for geometry variables) and ERA-I
cells (for climate variables). The results (Tables 6–8,
Appendix B) show that glacier length has a strong positive
correlation with area and elevation range. Initial runs
Fig. 7. ‘Normal glaciers’ column: climatic distribution of normal glaciers plotted in mean annual temperature against mean annual
precipitation. The size of the ellipses represents the average geometry of all glaciers present in every cell. ‘Surge-type glaciers’ column:
climatic distribution of surge-type glaciers plotted in mean annual temperature against mean annual precipitation. The size of the ellipses
represents the average geometry of all glaciers present in every cell. ‘Difference’ column: absolute difference in geometry between surge-
type and normal glaciers, averaged per gridcell, across the climatic spectrum. The size and color of the ellipses represent the average value
for surge-type glaciers ‘minus’ the average value for normal glaciers. Please note that only cells containing both surge-type and normal
glaciers are represented in the three columns. Horizontal axes are in log scale.
Fig. 8. Comparison of the average number of branches between
surge-type glaciers (in pink) and normal glaciers (in gray) across the
Alaska Range, over different classes of glacier length. Significant
statistical differences between the two groups are noted with a *,
while comparisons between groups containing <30 samples are
shaded in gray. On each box, the central line represents the
median; the lower and upper edges of the box are the 25th and
75th percentiles. Whiskers extend to the most extreme values.
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers 653
demonstrated that glacier aspect made an insignificant
contribution to the model. Regarding the climate variables,
mean annual precipitation is strongly correlated with mean
winter and summer precipitation, while mean annual
temperature is strongly correlated with mean winter and
summer temperature. Based on these results, we conducted
Maxent runs with a limited set of climatic and glacier
geometry variables. Mean annual precipitation and mean
annual temperature were chosen as the fundamental
climatic variables, while length and slope were adopted as
the two most significant glacier geometry variables.
When run with all the glaciers of the geodatabase and the
limited set of climatic and glacier geometry variables, the
output of Maxent reproduces with great accuracy the known
distribution of surge-type glaciers across the glacierized
regions (Fig. 9). Excellent model performance is indicated by
training AUC = 0.919 and testing AUC = 0.902 (Elith and
Graham, 2009). The model converged after 1600 iterations.
The results of the cross-correlation replications are perfectly
spatially correlated with single run (correlation matrix
>0.99). Regions with missing data are excluded from
Maxent’s final map output (cf. Fig. 3).
Major clusters such as Alaska–Yukon, East and West
Greenland, Svalbard, Novaya Zemlya and High Mountain
Asia clearly stand out as highly suitable areas for surge-type
glaciers. The northern, western and eastern boundaries of
the Alaskan–Yukon cluster are accurately depicted by the
model, which shows low probabilities for the Brooks Range
(short glaciers, low MAT and limited MAP) and the Coast
Mountains (short glaciers, high MAT). In Iceland, only the
interior of the island shows high probabilities of presence
due to climatic factors and long glaciers. In contrast, cells in
the north and west of the island, where glaciers are smaller,
display lower probabilities. The model represents Svalbard
as one of the strongest potential clusters, and Novaya
Zemlya is equally accurately depicted as a highly suitable
region, with lower probabilities towards the north and east
of the island, where glaciers are shorter, and MAT and MAP
are lower.
Maxent accurately predicts high probabilities of occur-
rence of surge-type glaciers in the Pamirs, the Karakoram
and the central Tien Shan. Outside these optimal regions,
probabilities decline sharply in all directions, largely for
climatic reasons (e.g. rising temperature or decreasing
precipitation).The Tibetan Plateau, mostly characterized
by short glaciers and low MAP, is clearly represented with
low probabilities of surge-type glacier presence. In the
eastern Himalaya, where precipitation is higher, the model
again accurately predicts higher probabilities of presence.
However, Maxent apparently over-predicts the occurrence
of surging glaciers in Nepal, Bhutan and neighboring areas
of China. Both main surge clusters of Greenland stand out
with low probabilities of presence north of these regions.
Relatively high probabilities are also predicted for southern
Baffin Island, where no surges have been reported. Else-
where in Arctic Canada, however, the model under-predicts
the occurrence of surge-type glaciers.
Low probabilities of occurrence are accurately predicted
in many regions with high mean annual temperature,
including mainland Scandinavia, the European Alps,
Pyrenees and New Zealand. Low probabilities are also
predicted for areas of low mean annual precipitation and
very low mean annual temperature, such as the New
Siberian Islands. The model seems to under-predict the
small clusters of the Andes, but further analysis shows that
the number of small cells (0.05° 0.05°) with high
probability of presence was too small compared to the
number of small cells with low probability of presence.
Averaging the results over the larger ERA-I cells (0.75°
0.75°) generated large cells with low probabilities of
presence. The same bias also occurs with the Antarctic
Peninsula and in the Caucasus.
Fig. 9. Maxent’s final logistic output, displaying the probabilities of presence of the population of surge-type glaciers across all glaciated
regions. The model was trained with 75% of the population of surge-type glaciers and tested with the remaining 25%. Four variables were
used for this model: MAT, MAP, length and slope.
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers654
Maxent’s outputs also include detailed response curves,
which show how each climate and glacier geometry
variable influences the predictions (see Fig. 11, Appendix
B). Predicted suitability is positively correlated with glacier
length and slope, but the response for the climatic variables
is more complex, reflecting the upper and lower thresholds
in precipitation and temperature that bound the optimal
surge zone.
Mean annual precipitation generates the highest prob-
abilities of presence between 340 and 2140 mm a
–1
, and
rapidly decreases above this threshold. Mean annual
temperature generates high probabilities of presence be-
tween –8°C and –0.5°C.
A jackknife test allows us to rank the variables by
importance. The permutation importance is determined by
randomly permutating the values of a variable among the
training locations, and measuring the decrease in training
AUC. Mean annual precipitation is the most important
variable in building the model (by 30.9%), followed by slope
(24.6%), which is almost as important as length (23.2%).
Finally, mean annual temperature contributes 21.3% to the
model. In total, the cumulative permutation importance of
the climatic layers is higher than that of the glacier geometry
variables (respectively 52.2% and 47.8%). Based on these
results, we hypothesize that climatic variables exert the
primary control on the location of the main surge clusters,
while glacier geometry variables influence which glaciers
within clusters are prone to surging.
To test this idea we performed additional runs using
different sets of variables, and different surge categories. On
the one hand these analyses would allow us to investigate
the importance of the variables in contributing to Maxent’s
predictions, and on the other hand we could assess the
representativeness of the three categories of the surge index.
We focus our results on the North Atlantic region (Fig. 10).
The figure is divided into rows (for the different sets of
variables), while columns indicate the different surge index
categories. The runs including ‘all variables’ (MAT, MAP,
length and slope) show that the model performs increasingly
well as we move from category 1 to category 3. When
trained with glaciers from category 3 only, the large surge
clusters such as Alaska–Yukon, East and West Greenland,
Iceland and Svalbard are well delineated. Under-predictions
are noticeable in Arctic Canada. The middle row displays
the results of runs performed with climatic layers only (MAT
and MAP). Interestingly, results are very similar (or improved
in the case of category 1). Contrasts between surge cluster
and non-surge cluster regions are clear, and their distri-
bution mirrors the results from the top row. Finally,
predictions made using glacier geometry variables only are
presented in the bottom row. Evidently, the model picks out
all cells where the average glacier length or slope is
important: most of Alaska, the majority of Arctic Canada,
the periphery of Greenland and cells in Svalbard and
mainland Norway. To assess the performance of the three
surge categories, we evaluate the results by averaging the
probabilities of presence using the results from the top row
(all variables) over the entire population of cells with surge-
type glaciers. Category 3 (‘confirmed surge-type’) yields the
highest average probability of presence for all surge-type
glaciers, 0.54, followed by category 2 with 0.51, and
category 1 with 0.46.
These results allow three important conclusions to be
made. First, data on mean annual precipitation and mean
annual temperature are enough to delineate the main surge
clusters, confirming that climate is the primary control on
the distribution of surge-type glaciers on a global scale.
Second, although glacier length clearly influences the
tendency of glaciers to surge, geometry variables alone
cannot predict the location of clusters. Finally, glaciers from
category 3 are the most representative for the whole
population of surge-type glaciers.
DISCUSSION
Our results show that the global distribution of surge-type
glaciers can be predicted with a high degree of confidence
from a limited set of climatic and glacier geometry variables.
This fact strongly suggests that some hitherto unrecognized
principle may underlie all surging behavior, irrespective of
thermal regime or other local factors. So why should certain
climatic and geometric conditions encourage surging? To
address this issue, we begin by inverting the question and
ask, ‘why are some conditions not conducive to surging?’
Expressed more fully, we ask: what conditions must be
satisfied for a glacier to maintain a dynamic equilibrium or
steady state, and flow at speeds closely matching its
balance velocity? It is then meaningful to ask, in which
Fig. 10. Maxent’s predictions based on different sets of training points (columns) represented by glaciers from the three surge index categories,
and on different sets of variables (rows). Models from top row, ‘All variables’, are based on MAT, MAP, length and slope. Models from middle
row, ‘Climate’, are based on MAT and MAP only. Models from bottom row, ‘Geometry’, are based on glacier length and slope only.
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers 655
circumstances do these conditions break down, producing
unsteady or oscillatory behavior? Therefore, we bypass the
particular details and quirks of individual surges, and seek
explanations for the patterns emerging from our analysis in
the general principles of glacier dynamics.
To maintain a steady state (i.e. to have constant geom-
etry, and velocity and temperature distributions in equi-
librium with a hypothetical static climate), a glacier must
simultaneously meet two conditions. First, mass flux through
the system must be in equilibrium with surface mass
balance. That is, on annual and longer timescales, ice
discharge through any cross section must evacuate exactly
the net mass gains up-glacier (this steady-state discharge
divided by cross-sectional area is the balance velocity
(Clarke, 1987). Second, energy fluxes into and out of the
system must balance to maintain constant enthalpy. In a
glaciological context, enthalpy is defined as the internal
energy of the glacier system, a function of ice temperature
and water content (Aschwanden and others, 2012). Changes
in enthalpy result from (1) energy exchanges at the glacier
surface (radiative and turbulent fluxes, runoff) and the bed
(geothermal heat flux, runoff); and (2) frictional heating
associated with ice flow. As the glacier flows downslope,
gravitational potential energy is converted into sensible or
latent heat, warming and melting ice, respectively. If
equilibrium is to be maintained, these enthalpy gains must
be dissipated from the glacier by heat conduction through
the ice to the surface, heat advection with flowing ice, and/
or runoff of meltwater. At the bed of a temperate glacier, the
heat conduction and advection terms are zero, and enthalpy
dissipation from the bed can only occur by the evacuation of
basal meltwater.
The mass- and enthalpy-balance problems are tightly
coupled, because flow speeds are dependent on both ice
temperature and water storage, and vice versa. If the glacier
is to remain close to steady state, there must be a broad
equality between rates of build-up of gravitational potential
energy (snow accumulation), conversion of potential energy
into enthalpy by ice flow, and loss of enthalpy by the
dissipation of heat and meltwater. If strain heating near the
bed increases ice temperature and/or creates basal melt-
water faster than enthalpy can be dissipated from the
glacier, positive feedbacks between ice flow processes
(creep and sliding) and warming/melting will cause the
glacier to accelerate above the balance velocity, evacuating
mass faster than it can be replaced. Conversely, if heat is lost
more rapidly than generated by ice flow and geothermal
heating, the glacier will decelerate and ice will accumulate
within the system. Thus, if simultaneous solutions to
the mass- and enthalpy-balance problems cannot be found,
the glacier will deviate from steady state, introducing the
possibility of oscillatory or other unstable behavior. These
concepts echo and build upon ideas proposed by Post
(1969), Budd (1975), Dolgoushin and Osipova (1975) and
Van Pelt and Oerlemans (2012). We now apply these
concepts to the interpretation of our results, and outline the
implications for a general, unified theory of glacier surging.
The scarcity of surge-type glaciers at the cold, dry end of
the climatic spectrum (Fig. 4) can be explained by low basal
enthalpy production and efficient heat losses by conduction.
For small glaciers in cold, arid environments, balance fluxes
and frictional heating are low, increasing the likelihood that
enthalpy production can be balanced by conductive losses.
In contrast, longer and larger glaciers, especially those
where flow is focused from multiple tributaries into narrow
outlets, will have higher balance velocities and therefore
higher steady-state basal enthalpy production. Larger gla-
ciers will also tend to be thicker, reducing conductive heat
losses to the atmosphere. Therefore, in cold, dry environ-
ments larger glaciers (e.g. the surge-type glaciers of Arctic
Canada) are less likely to find a balance between enthalpy
production and dissipation than small glaciers.
Surge-type glaciers are also essentially absent at the warm
end of the climatic spectrum (Fig. 4). In this zone, glaciers
are likely entirely temperate due to high summer air
temperatures, warming of the snowpack by melting and
refreezing, and high mass turnover. Conductive losses are
zero in the temperate case, so enthalpy dissipation can only
occur via runoff of meltwater. We hypothesize that high
runoff will be encouraged by (1) high basal melt rates
maintaining efficient drainage systems and (2) seasonal
development of efficient basal drainage systems in response
to high surface melt and rainfall, and surface-to-bed
drainage via crevasses and moulins. Therefore, although
enthalpy production is high in high-turnover glaciers, it may
be easy for glaciers within the warm–temperate zone to
evacuate excess energy by high water discharge.
Most surge-type glaciers occupy a climatic envelope
between the cold-dry and warm–temperate extremes, the
highest densities occurring in the ‘optimal surge zone’
(Fig. 4). We suggest that glaciers in this climatic environ-
ment are prone to surging because neither heat conduction
nor subglacial drainage systems are efficient enough to
evacuate the enthalpy gains associated with their balance
velocities, creating the possibility of heating–velocity feed-
backs at the bed. In temperate glaciers, this may manifest as
increasing storage of basally produced water in inefficient,
distributed drainage systems, and in polythermal glaciers as
warming of cold basal ice to the pressure-melting point,
followed by increasing water storage. Failing to find an
equilibrium solution to the enthalpy budget, the system is
forced to oscillate between fast and slow states to evacuate
excess energy.
Glacier geometry variables exert a second-order control
on glacier enthalpy balance. First, glaciers that are long,
branchy and with high areas (i.e. probably both long and
branchy) will have higher balance velocities than small,
simple glaciers, and therefore will have greater enthalpy
production at the bed. Second, glacier length and branchi-
ness will influence subglacial water balance. Where rates of
basal meltwater production are low, it may be possible to
evacuate all meltwater from small glaciers via inefficient,
distributed drainage systems (e.g. pore-water flow in till,
water films or linked cavities). On larger glaciers, however,
such systems may be unable to evacuate the cumulative
discharge, leading to increased water storage and velocity–
strain heating feedbacks. Thus, at the cold-dry end of the
climatic spectrum, long, branchy glaciers may be more
susceptible to dynamic instabilities as a result of inefficient
basal drainage. Third, large glaciers will also tend to be
thick, leading to inefficient heat conduction from the bed to
the surface. Geological factors (not examined in this study)
could also affect basal water balance, and tendency to
surging in some regions (e.g. Hamilton and Dowdeswell,
1996; Jiskoot and others, 2000, 2003).
Maxent’s results further highlight the importance of
climatic and glacier geometry attributes in modelling the
global distribution of surge-type glaciers, although the
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers656
model might suffer from collinearity between variables.
When run with climatic layers only, the model accurately
delineates the main surge clusters, which is not the case
when run with glacier geometry variables only. We
conclude that, of our two categories of potential controls,
climate is the first-order global control on the distribution of
the surge clusters, while glacier geometry is a second-order
regional control.
The great diversity of surging glaciers suggests that many
processes are involved, which may differ substantially from
glacier to glacier depending on thermal regime, bed
materials, drainage system type and other factors. However,
we believe that the enthalpy cycle model provides a
powerful new unifying concept, with which all surging
behaviors (and ‘normal’ glaciers) can be understood within
a single framework. In this study, we have taken a very
‘broad brush’ approach to analyzing the relationship
between glaciers and their environments. Now that the
global patterns have been established, more detailed
regional studies are needed to further explore and refine
our conclusions. The enthalpy cycle concept can generate
testable hypotheses, and inspire future field and remote-
sensing observation programs. Experiments with energy-
conserving enthalpy models (Aschwanden and others, 2012)
could potentially identify the precise combinations of
balance velocity, surface climatology and basal boundary
conditions that give rise to oscillatory behavior. To date,
most model studies of oscillatory behavior have focused on
basal conditions (e.g. Van Pelt and Oerlemans, 2012).
Interestingly, however, Calov and others (2010), using a
range of thermomechanically coupled models of the
Laurentide ice sheet, found that oscillations were encour-
aged by low surface temperatures and low snowfall, and did
not occur for high surface temperatures and accumulation
rates. It might be expected that the influence of climate is
much stronger in simulations of thinner, smaller ice masses,
representative of the valley glaciers and ice-cap outlets
making up our geodatabase.
It is also interesting to speculate on the effect that climate
change may have on the distribution of surge-type glaciers.
The existence of climatic envelopes conducive to surging
implies that glaciers may change from ‘normal’ to surge-type
and vice versa under cooling or warming climates. Indeed,
there are some indications that this has occurred over the
Little Ice Age climatic cycle of the last millennium (e.g.
Hoinkes, 1969; Benn and Evans, 2010; Striberger and
others, 2011). Identification of palaeosurges in the geo-
morphological record will allow further testing of this
intriguing possibility.
SUMMARY AND CONCLUSIONS
A geodatabase of surge-type glaciers compiled from 305
publications and combined with the RGI has enabled
investigation of the spatial distribution of surge-type glaciers
at a global, regional and individual glacier level.
Analysis of ERA-I data indicates that surge-type glaciers
occur within a well-defined climatic envelope, which can
be divided into two subzones. The highest densities of
surge-type glaciers occur within an optimal climatic
envelope bounded both by temperature and precipitation.
Surge-type glaciers are absent above a threshold MST =
0.001MWP + 8.4 (MST: mean summer temperature in °C;
MWP: mean winter precipitation in mm a
–1
), and below
MST = 0.0014MWP – 0.97. A clear threshold in precipitation
provides the lower boundary for the optimal surge envelope
with MST = 0.015MWP – 28.4. Surge-type glaciers in this
zone belong to two superclusters: (1) the Arctic Ring,
extending from Alaska–Yukon to Novaya Zemlya (but
excluding Arctic Canada) and (2) High Mountain Asia,
particularly the Pamirs, Karakoram and Tien Shan. Much
lower densities of surge-type glaciers are found in the
colder, drier climates of Arctic Canada.
In all clusters, surge-type glaciers have larger areas and
are longer than normal glaciers, and a more detailed study
of the Alaska–Yukon cluster shows that surge-type glaciers
are more complex (more branches) over all size classes.
These results agree with the findings of Clarke and others
(1986), Hamilton and Dowdeswell (1996), Jiskoot and
others (2000) and Barrand and Murray (2006). The size
and length differential is greatest at the cold and dry end of
the climatic spectrum, while less pronounced but still
significant throughout the optimal surge zone. A tendency
for surge-type glaciers to have lower slopes appears to be a
by-product of the inverse relationship between slope and
glacier length, as argued by Clarke (1991). The same applies
to glacier elevation range: the longer the glacier, the larger
the range. Multivariate tools are more performant when it
comes to disentangling correlations between variables (see
Atkinson and others, 1998; Jiskoot and others, 2000, 2003).
Glacier aspect did not contribute in distinguishing normal
from surge-type glaciers.
The species distribution model Maxent was used to
model the distribution of surge-type glaciers based on
geometry (length and slope) and climatic variables (mean
annual temperature and mean annual precipitation). The
model was able to accurately reproduce the distribution of
surge-type glaciers in many regions. It performed best for the
major clusters (e.g. Alaska–Yukon, Iceland and Svalbard),
but performed less well in marginal regions (e.g. Arctic
Canada, the Andes and the Caucasus).
Our analysis highlighted a number of regions where
surge-type glaciers have not been reported, but are
predicted by the Maxent model, including parts of the
Antarctic Peninsula, the Russian Arctic and parts of Siberia.
These are all regions where observations of glacier dynam-
ics are sparse, and focused studies of these regions may
expand the known population of surge-type glaciers.
We interpret our results in terms of a new conceptual
framework, the enthalpy cycle model. According to this
model, steady-state conditions can only occur if the
enthalpy gains (sensible and latent heating) generated by
the glacier flux can be dissipated by heat conduction and
meltwater discharge. This condition can be most easily
satisfied in cold, dry environments (thin, low-flux glaciers,
efficient conductive heat losses) and warm, humid environ-
ments (high mass flux and meltwater discharges). Inter-
mediate conditions correspond to the optimal surge zone,
where neither heat conduction nor runoff can effectively
discharge heat gains for many glaciers. Glacier size and
branchiness affect susceptibility to surging through their
influence on balance velocity, thermal insulation of the bed,
and subglacial water balance.
In summary, the climatic and topographic environment of
a glacier imposes constraints on its dynamic behavior.
Surges are not anomalous phenomena requiring special
explanation, but arise naturally as a consequence of the
ways in which all glaciers interact with their environments.
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers 657
ACKNOWLEDGEMENTS
We gratefully acknowledge Horst Machguth and Matthias
Huss for providing the global dataset of glacier center lines,
and Christian Kienholz for the center lines of the Alaskan
glaciers. We thank Hester Jiskoot and Nick Hulton for
valuable discussions throughout this research. A special
thank you is extended to the contributors to the geodatabase
for their valuable observations and time: Shad O’Neel,
William D. Harrison, Sam Herreid, Garry Clarke, Jacob C.
Yde, Gordon Hamilton, Luke Copland, Sveinn Brynjólfsson,
Skafti Brynjólfsson, Twila Moon, Wanqin Guo, Gabriel
Alberto Cabrera, Kay Helfricht, Michael Kuhn, Torborg
Heid, Nicolai Osokin, Takatoshi Yasuda, Evan Burgess,
Ólafur Ingólfsson, Andrey Glazovsky, Wesley van Wychen,
Robert McNabb, Melanie Rankl. We also thank Ruth
Mottram and Fredrik Boberg from the Danish Meteoro-
logical Institute for patiently answering questions regarding
climatic data processing. Finally we thank Luke Copland
and Hester Jiskoot for constructive comments and the
scientific editor, Ralf Greve, for handling the paper.
Financial support was provided by the ConocoPhillips
Lundin Northern Area Program project CRIOS.
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APPENDIX A
Table 5. Equivalence to other surge indices
Confirmed surge-type glacier (index 3)
Barrand (2002): index 3 Glaciers with an observed surge, or with strong indirect evidence of a surge event.
Barrand and Murray (2006): index 3 Glaciers with a previously observed or reported surge.
Clarke (1991): index 5 Definite surge characteristics: current, historical or corroborative evidence exists.
Clarke and others (1986): index 5 Definite surge characteristics: current, historical or corroborative evidence exists.
Copland and others (2003): index 1 Active phase observed, many distinct surge features (e.g. fast flow velocities measured, terminus advance,
observed surge, looped moraine, sheared margins).
Copland and others (2011): index 1 Confirmed: rapid terminus advance is observed (out of phase with surrounding glaciers), with many distinct
surge features (e.g. looped moraines).
Grant and others (2009): index 1 Active surge phase observed and three or more distinct surge features.
Hamilton (1992): index 3 Most likely to be of surge type (contemporary observation).
Osipova and others (1998):
indices 1a, 1b
1a: surge and advance, based on aerial photos and satellite scenes, and 3 or more distinct surge features.
1b: surge observed but no advance. Glaciers with large internal motions expressed in sharp, significant
redistribution of mass and increased flow velocities, all within the glacier’s boundaries, or into the dead ice
forming the tongue.
Weidick and others (1992): index 7 Known surge.
Yde and Knudsen (2007): index 7 Observed surge event: chaotic surface, looped moraine, fast and large advance, potholes.
Very probably surge-type glacier (index 2)
Barrand (2002) Show a likely surge-type glacier (e.g. presence of contorted moraines).
Barrand and Murray (2006) Likely surge-type glacier.
Clarke (1991): indices 3, 4 3: probable surge characteristics.
4: very probable surge characteristics.
Clarke and others (1986): indices 3, 4 3: possible surge characteristics (several features).
4: very probable surge characteristics (strong surface evidence).
Copland and others (2003): index 2 Likely to have surged: many distinct surge features but active phase is not observed (e.g. looped moraines,
sheared margins, extensive surface folding and looping, digitate terminus, small advance).
Copland and others (2011): index 2 Likely. Rapid terminus advance is not observed (or difficult to identify), but several surge features are
present (e.g. looped moraines, distortion of medial moraines, small and slow terminus advance, old
reported advance, large and short-lived terminus advance).
Grant and others (2009): index 2 Likely to have surged: 3 or more distinct features, but active phase not observed (can have all other features
but no advance)
Hamilton (1992) Probably surge type (>2 features, and historical report of surging).
Osipova and others (1998):
indices 2a, 2b, 2c, 2d
2a: glaciers with fixed internal advance. Limited part of the glaciers undergoes displacement. Internal mass
shifts can be caused by significant and fast-moving front activation within the glacier.
2b: glaciers with traces of recent movements (fresh paws on the slopes, looped moraines) with the ability to
specify (presumably) the years of movement.
2c: glaciers with relatively slow advances with alternating retreats of the front, and other signs of pulsations.
2d: glaciers with signs of activation of their upper parts, displacement of the front, disintegration of the
lower part.
Weidick and others (1992): index 6 Possible surge.
Yde and Knudsen (2007): index 6 Significant surge diagnostic characteristics: potholes, undulating surface, looped moraines, old glacier
advance, steep front.
Possible surger (index 1)
Barrand (2002): index 1 Represents a possible surge-type glacier.
Barrand and Murray (2006): index 1 Ambiguous morphological evidence.
Clarke (1991): indices 1, 2 1: uncertain surge.
2: possible surge.
Table 4. Harmonized surge index used in the geodatabase
Surge index Surge likelihood Description
1 Confirmed surge-type glacier (direct evidence) Active phase directly observed with or without advance of the front.
Significant and large displacement of mass, within the glacier boundaries or
yielding an advance. High flow speeds measured, sheared margins, stranded
ice, chaotically crevassed surface, deformation of medial moraines into loops.
The observation of the active phase can be current, historical or corroborative.
2 Very probably surge-type glacier (indirect evidence) Three or more well-preserved surge features. Short-lived and small-scale
movements or pulsations are observed.
3 Possible surge-type glacier (indirect evidence) One or two surge-features observed. Signs of past dynamics, rapid terminus
retreat.
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers660
APPENDIX B
Fig. 11. Maxent’s logistic response curves corresponding to the run displayed in Figure 9.
Table 5. (Continued)
Clarke and others (1986): indices 1, 2 1: uncertain surge characteristics.
2: Possible surge characteristics (1 or 2 surge features).
Copland and others (2003): index 3 Possible: a few surge features are present, but active phase not observed (e.g. terminus advance, some
folding and cross-cutting crevasses; or suggested surging from looped moraines/folds close to the terminus).
Copland and others (2011): index 3 Possible: a few surge features are present, but active phase not observed (e.g. mainly folding and looping of
terminal moraines; rapid terminus retreat; asynchronous behavior compared to neighboring glaciers).
Grant and others (2009): index 3 Possibly surged: <3 features are present, active phase not observed.
Hamilton (1992): index 1 Possible surge (1–2 features present).
Table 6. Correlation matrix among the glacier geometry variables
for three glacier populations: ‘all glaciers’ for all the glaciers in the
world, ‘normal glaciers’ for non-surge-type and surge-type glaciers
All glaciers Area Range Slope Length
Area 1 0.241675 –0.11593 0.718212
Range 0.241675 1 0.043657 0.622939
Slope –0.11593 0.043657 1 –0.27999
Length 0.718212 0.622939 –0.27999 1
Normal glaciers Area Range Slope Length
Area 1 0.25673 –0.11976 0.730302
Range 0.25673 1 0.04913 0.631388
Slope –0.11976 0.04913 1 –0.28212
Length 0.730302 0.631388 –0.28212 1
Table 6. Correlation matrix among the glacier geometry variables
for three glacier populations: ‘all glaciers’ for all the glaciers in the
world, ‘normal glaciers’ for non-surge-type and
Surge-type glaciers Area Range Slope Length
Area 1 0.23809 –0.33992 0.790505
Range 0.23809 1 0.058926 0.502652
Slope –0.33992 0.058926 1 –0.51577
Length 0.790505 0.502652 –0.51577 1
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers 661
Table 7. Correlation matrix among the climatic variables
MAP MSP MWP MAT MST MWT
MAP 1 0.84044 0.92042 0.65093 0.53261 0.66871
MSP 0.84044 1 0.56172 0.50307 0.43437 0.5084
MWP 0.92042 0.56172 1 0.63101 0.49994 0.65431
MAT 0.65093 0.50307 0.63101 1 0.90494 0.98902
MST 0.53261 0.43437 0.49994 0.90494 1 0.83782
MWT 0.66871 0.5084 0.65431 0.98902 0.83782 1
Table 8. Correlations between glacier geometry and climatic variables
Area Range Length Slope Aspect
MWP –0.01775 –0.05714 –0.0736 0.02257 –0.00461
MSP –0.0592 –0.02783 0.018091 0.00188 –0.00189
MAP –0.02543 –0.01335 –0.03953 0.015948 –0.00403
MWT –0.04318 –0.06012 –0.04686 0.032932 –0.00117
MST –0.03521 –0.06042 –0.072 0.045651 –0.00066
MAT –0.04178 –0.06536 –0.05651 0.037332 –0.00106
MS received 19 July 2014 and accepted in revised form 20 April 2015
Sevestre and Benn: Climatic and geometric controls on surge-type glaciers662
