Despite their importance for sea-level rise, seasonal water availability, and
as a source of geohazards, mountain glaciers are one of the few remaining
subsystems of the global climate system for which no globally applicable,
open source, community-driven model exists. Here we present the Open Global
Glacier Model (OGGM), developed to provide a modular and open-source
numerical model framework for simulating past and future change of any
glacier in the world. The modeling chain comprises data downloading tools
(glacier outlines, topography, climate, validation data), a preprocessing
module, a mass-balance model, a distributed ice thickness estimation model,
and an ice-flow model. The monthly mass balance is obtained from gridded
climate data and a temperature index melt model. To our knowledge, OGGM is
the first global model to explicitly simulate glacier dynamics: the model
relies on the shallow-ice approximation to compute the depth-integrated flux
of ice along multiple connected flow lines. In this paper, we describe and
illustrate each processing step by applying the model to a selection of
glaciers before running global simulations under idealized climate forcings.
Even without an in-depth calibration, the model shows very realistic
behavior. We are able to reproduce earlier estimates of global glacier volume
by varying the ice dynamical parameters within a range of plausible values.
At the same time, the increased complexity of OGGM compared to other
prevalent global glacier models comes at a reasonable computational cost:
several dozen glaciers can be simulated on a personal computer, whereas
global simulations realized in a supercomputing environment take up to a few
hours per century. Thanks to the modular framework, modules of various
complexity can be added to the code base, which allows for new kinds of model
intercomparison studies in a controlled environment. Future developments will
add new physical processes to the model as well as automated calibration
tools. Extensions or alternative parameterizations can be easily added by the
community thanks to comprehensive documentation. OGGM spans a wide range of
applications, from ice–climate interaction studies at millennial timescales
to estimates of the contribution of glaciers to past and future sea-level
change. It has the potential to become a self-sustained community-driven
model for global and regional glacier evolution.
Introduction
Glaciers constitute natural low-pass filters of atmospheric variability. They
allow people to directly perceive slow changes of the climate system, which
would otherwise be masked by short-term noise in human perception. As
glaciers form prominent features of many landscapes, shrinking glaciers have
become an icon of climate change.
However, impacts of glacier change – whether growth or shrinkage – go far
beyond this sentimental aspect: glaciers are important regulators of water
availability in many regions of the world
, and retreating glaciers can
lead to increased geohazards seefor an overview.
Even though the ice mass stored in glaciers is small compared to the
Greenland and Antarctic ice sheets (<1 %), glacier melt has contributed
significantly to past sea-level rise SLR;
e.g.,. Glaciers have probably
been the biggest single source of observed SLR since 1900 and will
continue to be a major source of SLR in the 21st century
e.g.,.
Therefore, it is a pressing task to improve the knowledge of how glaciers
change when subjected to climate change, both natural and anthropogenic
. The main obstacle to achieving progress in this respect is a severe
undersampling problem: direct glaciological measurements of mass balances
have been performed on ∼ 300 glaciers world wide (≈ 0.1 %
of all glaciers on Earth). The number of glaciers on which these types of
measurements have been carried out for time periods longer than 30 years,
i.e., over periods that potentially allow for the detection of a climate
change signal, is one order of magnitude smaller . Length
variations of glaciers have been observed for substantially longer periods of
time . These variations are, however, much
more difficult to understand, as large glacier length fluctuations may arise
from intrinsic climate variability . Data obtained by
remote sensing allow for gravimetric assessments of ice mass change or volume
change estimates obtained by differencing digital elevation models (DEMs).
Unfortunately, they are only available for the past decade
e.g.,.
During the past few years, great progress has been made in methods to model
glaciers globally
.
While these approaches yield consistent results at the global scale, all of
them suffer from greater uncertainties at the regional and local scales.
These uncertainties stem from the great level of abstraction of the key processes
, from the need to spatially interpolate
model parameters , and from
uncertainties in the boundary and initial conditions. All models lack ice
dynamics, most lack frontal ablation with the exception
of, and all lack modulation of the surface mass balance by
debris cover and snow redistribution (wind and avalanches). Only one model
was able to provide estimates of past glacier volume
changes for the 20th century. None of these models are open-source.
Mountain glaciers are one of the few remaining subsystems of the global
climate system for which no globally applicable, open-source,
community-driven model exists. The ice sheet modeling community is a better
exemplar, with models such as the Parallel Ice Sheet Model
, Elmer/Ice (http://elmerice.elmerfem.org/, last
access: 27 February 2019), Glimmer-CISM
(https://csdms.colorado.edu/wiki/Model:Glimmer-CISM, last access:
27 February 2019), or ISSM (https://issm.jpl.nasa.gov/, last access:
27 February 2019). These models have been applied to mountain glaciers as
well, but cannot be applied globally out-of-the-box. While the atmospheric
modeling community has a long tradition of sharing models (e.g., the Weather
Research and Forecasting model – WRF) or comparing them (e.g., the Coupled
Model Intercomparison Project – CMIP), recent initiatives originating from
the glaciological community show a new willingness to better coordinate
global research efforts following the CMIP example (e.g., the Glacier Model
Intercomparison
Project
http://www.climate-cryosphere.org/activities/targeted/glaciermip
(last access: 27 February 2019)
or the Glacier Ice Thickness Estimation
Working
Group
https://cryosphericsciences.org/activities/ice-thickness
(last access: 27 February 2019)
).
In the recent past, great advances have been made in the global availability
of data and methods relevant for glacier modeling, spanning glacier outlines
, automatized glacier centerline identification
e.g.,, bedrock inversion methods
e.g.,, and global topographic datasets
e.g.,. Taken together, these advances now allow the ice
dynamics of glaciers to be simulated at the global scale, provided that
adequate modeling platforms are available. In this paper, we present the
Open Global Glacier Model (OGGM), developed to provide a modular and
open-source numerical model framework for consistently simulating past and future
global-scale glacier change.
Global not only in the sense of leading to meaningful results for
all glaciers combined, but also for any small ensemble of glaciers, e.g., at
the headwater catchment scale. Modular to allow different approaches
to the representation of ice flow and surface mass balance to be combined and
compared against one another. Open source so that the code can be
read and used by anyone and so that new modules can be added and discussed by
the community, following the principles of open governance.
Consistent between past and future in order to provide uncertainty
measures at all realizable scales.
This paper describes the basic structure and primordial assumptions of the
model (as of version 1.1). We present the results of a series of single
glacier and global simulations demonstrating the model's usage and potential.
This will be followed by a description of the software requirements and the
testing framework. Finally, we will discuss the potential for future
developments that could be conducted by any interested research team.
Fundamental principles
The starting point of OGGM is the Randolph Glacier Inventory
RGI;, and our goal is to simulate the
past and future evolution of all of the 216 502 inventoried glaciers
worldwide (as of RGI V6). This “glacier-centric” approach is the one
followed by most global and regional models to date; its advantages and
disadvantages will be discussed in Sect. . Provided with
the glacier outlines, and topographical and climate data at reasonable resolution
and accuracy, the model should be able to (i) provide a local map of the
glacier including topography and hypsometry, (ii) estimate the glacier's
total ice volume and compute a map of the bedrock topography, (iii) compute
the surface climatic mass balance and (if applicable) at its front via
frontal ablation, (iv) simulate the glacier's dynamical evolution under
various climate forcings, and (v) provide an estimate of the uncertainties
associated with the modeling chain.
For each of these steps, several choices are possible regarding the input
data to be used, the numerical solver, or the parameterizations to be applied.
Any given choice is driven by subjective considerations about data
availability, the estimated accuracy of boundary conditions (such as
topography), and by technical considerations such as the
computational resources available. In this paper we present one way to realize these
steps using OGGM, which, in our opinion, is the best compromise between
model complexity, data availability, and computational effort to date. However, the OGGM
software is built in such a way that future improvements and new
approaches can be implemented, tested, and applied at minimal cost by
ourselves or a larger community.
Example workflow
We illustrate, using an example, how the OGGM workflow is applied to Tasman
Glacier, New Zealand (Fig. ). In the following we briefly describe the
purpose of each processing step, and more details are provided in
Sect. :
Preprocessing. The glacier outlines extracted from the RGI are projected onto a local
gridded map of the glacier (Fig. a). Depending on the
glacier's location, a suitable source for the topographical data is
automatically downloaded (here SRTM) and interpolated to the local grid. The
map's spatial resolution depends on the size of the glacier (here, 150 m).
Flow lines. The glacier centerlines are computed using a geometrical routing algorithm
adapted fromFig. b, filtered and
slightly modified to become glacier flow lines with a fixed grid spacing.
Catchment areas and widths. The geometrical widths along the flow lines are obtained
by intersecting the normals at each grid point with the glacier outlines and
the tributaries' catchment areas (Fig. c). Each tributary
and the main flow line has a catchment area, which is then used to correct the
geometrical widths so that the flow-line representation of the glacier is in
close accordance with the actual altitude–area distribution of the glacier
(Fig. d, note that the normals are now corrected and
centered).
Climate data and mass balance. Gridded climate data (monthly temperature and
precipitation) are interpolated to the glacier location and temperature is
corrected for altitude using a linear gradient. These climate time series are
used to compute the glacier mass balance at each flow line's grid point for
any month in the past.
Ice thickness inversion. Using the mass-balance data computed above and relying
on mass-conservation considerations, an estimate of the ice flux along each
glacier cross section can be computed. By making assumptions about the shape
of the cross section (parabolic or rectangular) and using the physics of ice
flow, the model computes the thickness of the glacier along the flow lines and
the total volume of the glacier (Fig. e).
Glacier evolution. A dynamical flow-line model is used to simulate the advance
and retreat of the glacier as a response of the surface mass-balance forcing.
Here (Fig. f), a 100-year-long random climate sequence
leads to a glacier advance.
Example of the OGGM workflow applied to Tasman Glacier, New Zealand:
(a) topographical data preprocessing; (b) computation of
the flow lines; (c) geometrical glacier width determination (the
colors indicate the different flow lines); (d) width correction
according to catchment areas and altitude–area distribution (see
Fig. and main text for details); (e) ice
thickness inversion; and (f) random 100-year-long glacier evolution run
leading to a glacier advance. See Sect. for details.
Model structure
The OGGM model is built around the notion of tasks, which have to be applied
sequentially to single glacier or a set of glaciers. There are two types of tasks:
Entity tasks are tasks which are applied on single glaciers individually
and do not require information from other glaciers (this encompasses the
majority of the OGGM's tasks). Most often they need to be applied sequentially
(for example, it is not possible to compute the centerlines without having
read the topographical data first).
Global tasks are tasks that are run on a set of glaciers.
This encompasses the calibration and validation routines, which need to
gather data across a number of reference glaciers.
This model structure has several advantages: the same entity task can be run
in parallel on several glaciers at the same time, and they allow a modular
workflow. Indeed, a task can seamlessly be replaced by another similar task,
as long as the required input and output formats are agreed upon beforehand.
The output of each task is made persistent by storage on disk, allowing for
later use by a subsequent task, even in a separate run or on another machine.
For example, the preprocessing tasks store the topography data in a netCDF
file, which is then read by the centerlines task, which itself writes its
output in a vector file format.
In this paper we will refrain from naming the tasks by their function name in
the code, as these are likely to change in the future and are sometimes
organized in a non-trivial way as a result of implementation details. Therefore, the
next section is called “Modules”, where each module can be seen
as a collection of tasks developed towards a certain goal.
Modules
The modules are described in the order in which they are applied for a model
run. When we provide a specific value for a model parameter in the text, we
refer to the model's default parameter value; this value can be changed by the user
at run time.
Preprocessing
The objective of the preprocessing module is to set up the geographical input
data for each glacier (the glacier outlines and the local topography). First,
a Cartesian local map projection is defined: we use a local Transverse
Mercator projection centered on the glacier. Then, a suitable topographical
data source is automatically chosen, depending on the glacier's location.
Currently we use the following:
the Shuttle Radar Topography Mission (SRTM) 90 m Digital Elevation Database v4.1
for all locations in the 60∘ S–60∘ N
range (data acquisition: 2000);
the Greenland Mapping Project (GIMP) digital elevation model
for mountain glaciers in Greenland (data acquisition: 2003 to 2009);
the Radarsat Antarctic Mapping Project (RAMP) digital elevation model, version 2
for mountain glaciers in Antarctica with the exception of some peripheral
islands (data acquisition: 1940 to 1999); and
the Viewfinder Panoramas DEM3 product (http://viewfinderpanoramas.org/dem3.html, last access:
27 February 2019) elsewhere (most notably, North America, Russia, Iceland,
and Svalbard)
All datasets have a comparable spatial resolution (from 30 to 90 m, or
3 arcsec). Using different data sources is problematic but unavoidable as
there is no consistent, gap-free, globally available digital elevation model
(DEM) to date. The Advanced Spaceborne Thermal Emission and Reflection
Radiometer (ASTER) global digital elevation model version 2 (GDEM V2) is
available globally but was quickly eliminated due to large data voids and
artefacts, in particular in the Arctic. These artefacts are often tagged as
valid data and cannot be easily detected automatically. The Viewfinder
Panoramas products rely on the same sources but have been corrected manually
(mostly with topographic maps; Jonathan de Ferranti, personal communication,
2017); thus, this ensures a more realistic void filling. Although they have
nearly global coverage, the DEM3 products are not used in place of as it is
not easy to retrieve the original data sources used to generate them (the
information is scattered around the website, although ASTER and SRTM are the
main data sources in most cases). It must be noted that a number of glaciers
will still suffer from poor topographic information and/or a date of data
acquisition which does not match that of the RGI outlines. Either the errors
are large or obvious (in which case the model will not run), or they are left
unnoticed. The importance of reliable topographic data for global glacier
modeling will be the topic of a follow-up study.
See also
https://rgitools.readthedocs.io/en/latest/dems.html (last access:
27 February 2019) for an ongoing evaluation of further DEM products.
The spatial resolution of the target local grid depends on the size of the
glacier. The default spatial resolution is to use a square relation to the
glacier size (dx=aS12, with a=14 and S the area of
the glacier in km2) clipped to a predefined minimum (10 m) and maximum
(200 m) value. After the interpolation to the target grid, the topography is smoothed using a
Gaussian filter with a radius of 250 m (this value does not change with the
local glacier map resolution because it is meant to be applied to the
original DEM, not the interpolated one). This smoothing is driven by
practical considerations, as the model becomes unstable if the boundary
conditions are too noisy see alsofor a discussion about the
unavoidable trade-off between resolution and accuracy.
Flow lines and catchments
The glacier centerlines are computed following an algorithm developed by
and adapted for our purposes. This algorithm was chosen
because it allows one to compute multiple centerlines and to define a main
branch fed by any number of tributaries. In general we found the method to be
very robust, although some glaciers will obviously not have the optimal
number of centerlines, with either too many (frequent in the case of large
cirque glaciers) or too few (some tributary branches have no centerlines).
However, these errors are assumed to play a relatively minor role compared to
other uncertainties in the model chain.
In the model semantics, the original “centerlines” are then converted to
“flow lines”: the points defining the line geometries are interpolated to be
equidistant from one another (the default spacing along the line is twice that
of the local glacier map, i.e., varying between 20 and 400 m depending on
the glacier size), and the tail of the tributaries are cut before reaching their
descendant (see the differences between Fig. b and c, or
between Fig. a and b). Each grid point's elevation is
obtained from the underlying topography. By construction, upslope
trajectories or sinks along the flow line are rare; however, this can still occur when
the glacier outlines are poorly defined or because of errors in the gridded
topography. In these cases, we interpolate the heights (in the case of a
deepening) or cut the first grid points of the line (in the case of an upslope
trajectory starting from the flow-line's head) until only positive slopes larger than
1.5∘ remain. This is necessary because sinks along a flow line are
incompatible with the forward dynamical model, which will fill them with ice
and create undesirable spin-up issues.
The flow lines are then sorted according to their Strahler number a
measure of branching complexity defined byand commonly used in hydrological
applications, from the lowest (line without tributaries but
with possible descendants) to the highest (the main – and longest –
centerline). This order is important for the mass flow routing;
each flow line contains a reference to its descendant, and this reference is
used by the inversion and dynamical models to transfer mass from the
tributaries towards the main flow line.
The width of each grid point along the flow line is computed in four steps.
First, the catchment area of each flow line is computed using a routing
algorithm similar to that used to compute the centerlines
(Fig. a). Then the geometrical widths are computed by
intersecting the flow-line's normal to the boundaries of either the individual
catchments or the glacier itself (Fig. b). These
geometrical widths are then corrected by a factor specific for each
altitudinal bin (Fig. c), so that the true altitude area
distribution of the glacier is approximately preserved
(Fig. d). Finally, these widths are multiplied by a
single factor ensuring that the total area of the glacier is the exact same
as the one provided by the RGI, ensuring consistency with future model
intercomparisons.
At this stage, it is important to note that the map representation of the
flow-line glacier presented in Fig. c is purely
artificial. The fact that the glacier cross sections are overlapping is
irrelevant. The role of the flow lines is to represent the actual flow of ice
as accurately as possible while conserving the fundamental aspects of the
real glacier: slope, altitude, area, and geometry. The flow-line approximation
will work better for valley glaciers (like Tasman Glacier shown above)
than for cirque glaciers (such as the Upper Grindelwald glacier). For ice caps, the
flow-line representation is likely to work poorly, as discussed in
Sect. . From Fig. c one can see that
future improvements of the mass-balance model based on, e.g., topographical
shading or snow redistribution are made possible by knowledge about the
flow-lines' location.
Example of the flow-lines' width determination algorithm applied to
the Upper Grindelwald glacier, Switzerland: (a) determination of
each flow-line's catchment area; (b) geometrical widths;
(c) widths corrected for the altitude–area distribution – the bold
lines represent the grid points where the cross section touches a
neighboring catchment; and (d) the frequency distribution of the glacier
area per altitude bin, as represented by OGGM and by the SRTM topography.
Climate data and mass balance
The mass-balance model implemented in OGGM is an extended version of the
temperature index melt model presented by . The monthly
mass balance mi at an elevation z is computed as follows:
mi(z)=pfPiSolid(z)-μ*maxTi(z)-TMelt,0+ε,
where PiSolid is the monthly solid precipitation, pf is a
global precipitation correction factor (defaults to 2.5, see
Appendix ), μ* is the glacier's temperature sensitivity,
Ti is the monthly air temperature, TMelt is the monthly air
temperature above which ice melt is assumed to occur (default:
-1∘C, chosen because melting days can occur even if the monthly
average temperature is below 0 ∘C), and ε is a residual (or
bias correction) term. Solid precipitation is computed as a fraction of the
total precipitation: 100 % solid if Ti<=TSolid (default:
0 ∘C); 0 % if Ti>=TLiquid (default: 2 ∘C); and linearly interpolated in between.
The parameter μ* indicates the temperature sensitivity of the glacier
and needs to be calibrated. For this paper, the temperature and precipitation
time series (1901–2016) are obtained from gridded observations CRU
TS4.01;see Appendix . The temperature lapse rate
is set to a constant value (default: 6.5 K km-1) or it can be
time-dependant and computed from a linear fit of the nine surrounding
grid points.
For the calibration of the temperature sensitivity parameter μ* we use
the method described by and successfully applied many
times since then e.g.,.
Although the general procedure did not change, its peculiarity justifies
describing it here. We will start by noting that μ* depends on many
factors, most of them glacier-specific (e.g., avalanches, topographical
shading, cloudiness), and others that are related to systematic biases in the
input data (e.g., climate, topography). As a result, μ* can vary
greatly between neighboring glaciers without obvious physical reasons. The
calibration procedure implemented in OGGM makes use of these apparent
handicaps by turning them into assets.
The procedure begins with glaciers for which we have direct observations of
specific mass balance (N=254, see Appendix ). For each of
these glaciers, annual sensitivities μ(t) are computed from
Eq. () by requiring that the glacier specific mass balance
m‾(t) is equal to zero.
Note that this is not valid for
water-terminating glaciers where mass loss occurs at the glacier front and
the equilibrium surface mass-balance budget does not have to be closed. See
Sect. for more details.
m‾(t) is the
glacier integrated mass balance computed for a 31-year period centered around
the year t and for a constant glacier geometry fixed at the RGI
outline's date (e.g., 2003 in the Alps). The process is illustrated in
Fig. c (blue line): around 1920 the climate was cold and wet
(Fig. a and b), and as a consequence the hypothetical temperature
sensitivity required to maintain the 2003 glacier geometry needs to be high.
Inversely, the more recent climate is warmer and the temperature sensitivity
needs to become smaller for the glacier to remain stable.
Calibration procedure for μ* applied to the Hintereisferner
Glacier, Austria. (a, b) Annual and 31-year average of temperature
and precipitation obtained from the nearest CRU grid point (altitude
2700 m a.s.l.). (c) Time series of the μ candidates
(mm yr-1 K-1) and their associated mass-balance bias
(mm w.e. yr-1, right axis) in comparison to observations. The vertical
dashed line marks the time where the bias is closest to zero (t*).
These hypothetical, time-dependent μ(t) are called “candidates”, as it is
likely (but not certain) that at least one of them is the correct μ*.
To determine which of the candidates is suitable, we then compute the
mass-balance time series for each of the μ(t) and compute their bias
ε with respect to observations (red line in Fig. c).
Note that the period over which the observations are taken is not relevant
for the bias computation, and each μ candidate can produce a mass balance for
any year, as per Eq. (). In comparison to observations, μ(t=2000) is too low and produces mass balances with a positive bias.
Inversely, μ(t=1920) is too high and leads to a negative bias. For 3 years,
the bias is close to or crossing the zero line and μ(t) is
therefore very close to the ideal μ*. These dates represent the center
of a 31-year-long climate period where today's glacier would be in
equilibrium and maintain its current geometry. From these three
candidates, we pick the date with the smallest bias and call it t*. This
t* is an actual date but is mostly an abstract concept: we make use of it in the next step.
For the vast majority of the glaciers, μ* and t* are unknown. For
these we could interpolate the μ* (probably the most obvious
solution), or we could interpolate t*; indeed, the procedure above can be
reversed and t* can be used to retrieve μ*, again by requiring that
m‾(t*) is equal to zero (Eq. ). We interpolate t*
to all glaciers without observations using inverse distance interpolation
from the 10 closest locations (which can be quite far away, see
Appendix and ). The residual bias ε
for glaciers with observations can be close to zero (the case for
Hintereisferner Glacier in Fig. , where the bias curve crosses the zero
line) but can also be higher (indicating that no 31-year period in the last
century would sustain the current glacier geometry). When no perfect t*
is found, the date with the smallest absolute bias is chosen. This residual
ε is also interpolated between locations and added to the
modeled mass balance. This residual may be significant at certain locations
(up to 1.5 m yr-1, median of 6 cm yr-1) and would benefit from
further calibration, e.g., with regional geodetic mass-balance estimates. The
benefit of this approach is best shown by cross-validation
(Fig. ), where one can see that the error increases considerably
when using μ* interpolation instead of the proposed method. This is
due to several factors, including the following:
The equilibrium constraint applied on μ(t) implies that the sensitivity
cannot vary much during the last century. In fact, μ(t) at one glacier often
varies less in one century than between neighboring glaciers, because of the local
driving factors mentioned earlier. In particular, it will vary comparatively little
around a given year t: errors in t* (even large) will result in relatively small errors in μ*.
The equilibrium constraint will also imply that systematic biases in
temperature and precipitation (no matter how large) will automatically be
compensated for by all μ(t), and therefore also by μ*. In that sense,
the calibration procedure can be seen as an empirically driven downscaling
strategy: if a glacier is located there, then the local climate (or the
glacier temperature sensitivity) must allow a glacier to be there.
For example, the effect of avalanches or a negative bias in precipitation
input will have the same impact on calibration, and the value of μ* should
be lowered to take these effects into account, even though they are not
resolved by the mass-balance model.
The most important drawback of this calibration method is that it assumes
that two neighboring glaciers should have a similar t*. This is not
necessarily the case, as factors other than climate (such as the glacier
size) will also influence t*. However, our results (and the arguments listed above)
show that this is an approximation we can cope with.
Finally, it is important to mention that μ* and t* should
not be over-interpreted in terms of real temperature sensitivity or the response
time of the glacier. This procedure is primarily a calibration method, and as
such it can be statistically scrutinized (for example with cross-validation).
It can also be noted that the mass-balance observations play a relatively
minor role in the calibration, and they could be entirely avoided by fixing a
t* for all glaciers in a region (or even worldwide) without much
performance loss. However, the observations play a major role in the
assessment of model uncertainty (Fig. ). For more information
about the climate data and the calibration procedure, refer to
Appendix .
Benefit of spatially interpolating t* instead of μ* as
shown by leave-one-out cross-validation (N=254). (a) Error
distribution of the computed mass balance if determined by the interpolated
t*. (b) Error distribution of the mass balance if determined by
interpolation of μ*. The vertical lines indicate the mean, median, and
5 % and 95 % percentiles. See
https://cluster.klima.uni-bremen.de/~github/crossval (last access:
27 February 2019) for an online visualization of model performance for each
glacier.
Ice thickness
Measuring ice thickness is a labor-intensive and complex task; therefore,
only a fraction of the world's glaciers is monitored and direct measurements
are sparse. A physical or statistical approach is necessary for modeling
glacier evolution at the global scale. For a recent review of available
techniques for ice thickness modeling, see . OGGM
implements a new ice thickness inversion procedure, physically consistent
with the flow-line representation of glaciers and taking advantage of the
mass-balance calibration procedure presented in the previous section. It is a
mass-conservation approach largely inspired by , but
with distinct characteristics.
The principle is quite simple. The flux of ice q (m3 s-1) through
a glacier flux-gate (cross section) of area S (m2) reads as follows:
q=uS,
where u is the average velocity (m s-1). Using an estimate for u and
q obtained from the physics of ice flow and the mass-balance field, S and
the local ice thickness h (m) can be computed relying on some assumptions
about the bed geometry. We compute the depth-integrated ice velocity using
the well known shallow-ice approximation :
u=2An+2hτn,
where A is the ice creep parameter (s-1 Pa-3), n is the exponent of
Glen's flow law (n=3), and τ is the basal shear stress; τ is computed as follows:
τ=ρghα,
where ρ is the ice density (900 kg m-3), g is the gravitational
acceleration (9.81 m s-2), and α is the surface slope computed
numerically along the flow line. Optionally, a sliding velocity us
can be added to the deformation velocity to account for basal sliding. We use
the same parameterization as , who relied on
:
us=fsτnh,
where fs a sliding parameter (default: 5.7×10-20 s-1 Pa-3). If we consider a point on the flow line and
the catchment area Ω upstream of this point, mass conservation
implies
q=∫Ωm˙-ρ∂h∂tdA=∫Ωm̃dA,
where m˙ is the mass balance (kg m-2 s-1), and
m̃=m˙-ρ∂h/∂t is the “apparent
mass balance” following . If the glacier is in steady
state, the apparent mass balance is equivalent to the actual (and observable)
mass balance. In the non-steady-state case, ∂h/∂t is
unknown, and so is the time integrated (and delayed) mass balance
∫Ωm˙ responsible for the flux of ice through a section of
the glacier at a certain time. and
deal with the issue by prescribing an apparent mass-balance
profile as a parameterized linear gradient which is, arguably, more a
semantic than a physical way to deal with the transience of the problem.
Like , OGGM cannot deal with the transient problem yet; therefore, we
deliberately assume steady state and set m̃=m˙.
This has the strong advantage that we can make direct use of the equilibrium
mass-balance m‾(t*) computed earlier, which satisfies ∫m‾=0 by construction. q is then obtained by integrating the
equilibrium mass-balance m‾ along the flow line(s). The
tributaries will have a positive flux at their last grid point, and this mass
surplus is then transferred to the downstream line, normally distributed
around the nine grid points centered at the flow-lines' junction. By construction,
q starts at zero and increases along the major flow line, reaches its
maximum at the equilibrium line altitude (ELA), and decreases towards zero at
the tongue (for glaciers without frontal ablation).
Equation () turns out to be a degree 5 polynomial in h with
only one root in R+, easily computable for each grid point.
Singularities due to flat areas are avoided as the constructed flow lines are
not allowed to have a local slope α below a certain threshold
(default: 1.5∘, see Sect. ). The equation varies
by a factor of approx. 2/3 if one assumes
a parabolic (S=23hw, with w the glacier width) or
rectangular (S=hw) bed shape. The default in OGGM is to use a parabolic
bed shape, unless the section touches a neighboring catchment (see
Fig. c), neighboring glacier (ice divides, computed from
the RGI), or at the terminus of a calving glacier. In these cases the bed
shape is rectangular. Optionally, OGGM can also compute the effect of lateral
bed stresses following a parameterization and tabular
correction factors developed by .
Idealized inversion experiments: we compute the bed topography from
the surface elevation obtained from a flow-line model applied to a
predefined bed topography. (a–c) Glacier grown to equilibrium with
different bed topographies (flat, cliff, random). (d) Transient
experiment with a shrinking glacier. The same mass-balance profile is used
for all experiments (linear gradient of 3 mm w.e. m-1, ELA altitude
of 2600 m a.s.l.). For (d), the glacier is first grown to
equilibrium then shrunk for 60 years after an ELA shift of +200 m.
Figure displays some examples taken from the OGGM test suite,
where the automated inversion procedure is applied on idealized glaciers
generated with OGGM's flow-line model (see Sect. ). In the
equilibrium cases (Fig. a–c), the inverted topography is nearly
perfect. Differences arise at strong surface gradients, mostly because of
numerical differences (the inversion method uses a second-order central
difference which tends to smooth the slope). The transient case
(Fig. d) illustrates the consequences of the steady-state
assumption: although the glacier is retreating, the constraint ∫m̃=0 leads to a lowered ELA and, even with a perfectly known
mass-balance gradient, results in an overestimated ice thickness (in this case,
25 %). This effect is visible everywhere, but is strongest at the tongue.
The importance of the steady-state assumption on ice thickness estimates has
been studied using numerical experiments e.g., and is
often compensated for by calibration in real-world applications.
Total volume of the Hintereisferner Glacier computed with
(a) varying factors for the default creep parameter A, and
(b) varying precipitation factors. The dotted and dashed black lines
display the total volume estimated with volume–area scaling
VAS, and based on point observations
. For (a), additional sensitivities are computed
with an additional sliding velocity following Oerlemans (1997) using his sliding parameter
fs. For (b), additional sensitivities are computed with a varying creep
parameter A.
The sensitivity of the inversion procedure to various parameters is
illustrated using the Hintereisferner Glacier as an example
(Fig. ). The total volume (and the local thickness) is very
sensitive to the choice of the creep parameter A, varied from a factor
1/10 to 10 times the default value of 2.4×10-24 s-1 Pa-3. With a smaller A, the
ice is stiffer and the glacier gets thicker (A is expected to get smaller
by one or more orders of magnitude with colder ice temperatures). Inversely,
softer ice leads to a thinner glacier. The shape of the curve is proportional
to the fifth root of the fraction 1/A, explaining why the volume gets very
sensitive to small values of A. Adding sliding reduces the original
thickness significantly for the same reasons as an increasing A, as both
sliding and ice rheology (A) have a strong influence on the computed ice
flux q. Inversely, adding lateral bed stresses reduces ice velocity and
increases the computed ice volume. Changing from a rectangular to a parabolic
bed shape yields a volume loss of approximately one-third, which is expected from geometrical considerations. The
mixed parabolic/rectangular bed shape model implemented by default therefore
lies in between.
The total precipitation amount, by acting on the mass-balance gradient and
therefore on the ice flux q will also play a non-negligible role for the
ice thickness (Fig. b). The effect is small in comparison to
the influence of A, but it is noticeable: glaciers located in maritime
climates (with high values of accumulation) will be thicker on average than
similar glaciers in drier conditions.
This example shows that one can always find an optimum (and nonunique) set of
parameters leading to the correct total volume. In practice, however,
calibrating the model for accurate global glacier volume estimates is a major
challenge for global glaciological models and will be the topic of a separate
study. The IACS Working Group on Glacier Ice Thickness
Estimation
http://www.cryosphericsciences.org/wg_glacierIceThickEst.html
(last access: 27 February 2019)
is working towards this goal: OGGM
participated in the first Ice Thickness Models Intercomparison eXperiment
ITMIX,, ranking amongst the best models with limited
data requirements.
Ice dynamics
At this stage of the processing workflow, the ice-dynamics module is
straightforward to implement. Provided with the mass balance, slope, width
w, and bed topography along the flow line, we solve
∂S∂t=wm˙-∇⋅uS
numerically with a forward finite difference approximation scheme on a
staggered grid. Numerical stability is ensured by the use of an adaptive time
stepping scheme following the Courant–Friedrichs–Lewy (CFL) condition
Δt=γΔxmax(u) with γ as the
dimensionless Courant number chosen between zero and one. Unlike many solvers
of the shallow-ice equation, we do not transform Eq. () to
become a diffusivity equation in h, but solve it as it is formulated here.
This has the advantage that the numerical solver is the same regardless of
the shape of the bed (parabolic, trapezoidal, or rectangular). The new
section S at time t+Δt allows for the computation of h(t+Δt) according to the local bed geometry. Therefore, it is possible to
have changing bed geometries along a single flow line using the same
numerical solver. The drawback of our approach is that we cannot take
advantage of the diffusivity equation solvers already available elsewhere. We
tested our solution against the robust and mass-conservative solver presented
by . Our model yields accurate (and faster) results in
most cases, but fails to ensure mass-conservation for very steep slopes like
most other solvers to date. While a flow-line version of the solver presented
by is available in OGGM, it is not used operationally as
it cannot yet handle varying bed shapes and multiple flow lines – it will
become the default solver when these elements are implemented.
At a junction between a tributary and its downstream line, an artificial grid
point is added to the tributary line. This grid point has the same section
area S and thickness h as the previous one, but the surface slope is
computed from the difference in elevation between the tributary and descendant
flow line. This is necessary to ensure a dynamical connection between the two
lines: when the main flow line is at a higher elevation than its tributary, no
mass exchange occurs and the tributary will build up mass until enough ice is
available. At a junction point, Eq. () therefore contains an
additional mass flux term from the tributary.
Before the actual run, a final task merges the output of all preprocessing
steps and initializes the flow-line glacier for the model. For the glaciers to
be allowed to grow, a downstream flow line is computed using a least cost
routing algorithm leading the glacier towards the domain boundaries (this
algorithm is similar to the algorithm used to compute the glacier
centerlines). The bed geometries along the downstream line are computed by
fitting a parabola to the actual topography profile. In the case of bad fit, the
values are interpolated or a default parabola is used. Along the glacier,
where the bed geometries are unknown before the inversion, the bed geometries
are either rectangular (ice divides and junctions) or parabolic. Very flat
parabolic shapes can occasionally occur, for wide sections with a shallow
ice thickness. These geometries are unrealistically sensitive to changes in
h. They create a strong positive feedback (the thickening of ice leading to
a highly widening glacier) and are therefore prevented: when the parabola
parameter falls below a certain threshold, the geometry is assumed to be
trapezoidal instead.
The coupling between the mass balance and ice dynamics modules is a user
choice. The spatially distributed mass balance used by the dynamical model
can be updated (i) at each time step of the dynamical model's computation,
(ii) each month, (iii) each mass-balance year (the default), or (iv) only
once (for testing and feedback sensitivity investigations). In practice, this
does not make much difference for the yearly averages of glacier change
(except for option iv), and the choice of a yearly update is mostly driven by
performance considerations. Note that the mass-balance model can compute the
mass balance at shorter time intervals if required by the physical
parameterizations, as the interface between the model elements simply
requires the mass-balance model to integrate the mass balance over a year
before giving it to the dynamical model.
Evolution of the
Hintereisferner Glacier under two random forcing scenarios and for the default
parameter set. For each scenario, the “climate years” during a 31-year
period are shuffled randomly, creating a realistic climate
representative for a given period. (a) The glacier volume evolution
for each scenario (the black line marks the initial computed glacier volume).
(b, c) The glacier shape at the end of the 800-year simulation for
each case.
The results of two idealized simulations with an advancing and a shrinking
scenario are shown in Fig. . When put under the cold and
wet climate of the beginning of the 20th century, Hintereisferner Glacier would grow
about two-thirds larger than it is today. Inversely, the glacier is in strong
disequilibrium with today's climate, and it would lose about two-thirds of its volume
if the climate remained as it was over the past 31 years. The response time
of the glacier is approximately twice as fast in the shrinking case, and the
natural random variations of the glacier are much smaller than for a large
glacier with more inertia and a longer response time.
Evolution of volume (a) and length (b) of
Hintereisferner Glacier under a random climate forcing generated by shuffling
the “climate years” representative for the 31-year period centered on t*.
The glacier is reset to zero for each simulation, and the bed topography is
obtained using the default parameters. The sensitivity to the addition of a
sliding velocity or to a halving of the creep parameter A are also shown.
The noisy patterns of the length time series are due to the fact that the
length of a glacier on a discrete grid is sensitive to small interannual
variations.
The previous results were obtained with the default setup of OGGM. In
Fig. we assess the sensitivity of the dynamical model to
changes in the creep parameters A and to the addition of lateral drag and
basal sliding velocity. As expected, these dynamical parameters affect the
equilibrium volume and the response time of the glacier (faster ice leading
to a thinner glacier, and visa versa). Due to the mass-balance–elevation
feedback, the stiffer and therefore thicker glacier is also larger and
longer, but its response to climate variability is smaller in amplitude than
that of the fast moving sliding glacier.
A and fs depend on many factors such as ice temperature or basal
characteristics and they cannot be assumed to be globally constant. They are
considered as calibration parameters in OGGM, and will be tuned towards
observations of ice thickness or glacier length changes. In this study we
only calibrate the mass-balance model while the ice dynamics parameters are
set to their default values (A=2.4×10-24 s-1 Pa-3,
fs=0, no lateral drag). Nevertheless, we discuss the model
sensitivity to these dynamical parameters for individual glaciers
(Fig. ) or global runs (Fig. ).
Special cases and model limitations
The previous experiments demonstrate that the OGGM model is capable of
simulating the dynamics of glaciers in a fully automated manner. In this
section we describe the implications of the flow-line approximation in the
special cases of water-terminating glaciers and ice caps, and discuss some
examples of glaciers with a less trivial geometry.
Water-terminating glaciers
Glaciers are defined as “water-terminating” in OGGM when their RGI terminus
attribute is either flagged as marine-terminating or lake-terminating. The
major difference between a water-terminating glacier and a valley glacier is
the additional mass loss that occurs at the glacier front (frontal ablation).
This has implications for the bed thickness inversion, which currently
assumes that the mass flux at the front is zero (by setting ∫m̃=0, see Sect. ), and for the dynamics of
the glacier. The current treatment of water-terminating glaciers in OGGM is very simple but
explicit. We do not take frontal ablation into account for the bed inversion
(i.e., the original glacier front has a thickness of zero), but we do have a
basic parameterization in the ice dynamics module. We add a grid point behind
the glacier front which is reset to zero ice thickness at each time step: the
ice mass suppressed this way is the frontal ablation flux, which we store.
This parameterization has the advantage of preventing water-terminating
glaciers from advancing while still allowing them to retreat (in which case
they stop calving). We are working on a more advanced frontal ablation
parameterization for both the ice dynamics and the ice thickness inversion
.
Ice caps and ice fields
Ice caps and ice fields in the RGI are divided into single dynamical entities
separated by their ice divide (Fig. ). However, the entities
that belong to an ice cap are classified as such in the RGI; currently, the
only special treatment for these entities in OGGM is that only one major
flow line is computed (without tributaries). Indeed, the geometry of ice caps
is often non-trivial, and it is not clear whether tributaries would really
improve the model results. An example of an ice cap is shown in
Fig. . While the general behavior of this ice cap is
reasonably simulated by the flow-line model (e.g., at the outlet glaciers),
other features appear to be unrealistic (e.g., close to the ice divides).
Moreover, the mass-conservation inversion method probably underestimates
the real ice thickness at the location of the ice divide, where other
processes related to the past history of the ice cap are at play. A possible
way forward would be to run a distributed shallow-ice model instead of the
flow-line representation, and it is part of our long-terms plans to do so.
The OGGM inversion workflow
applied to the RGI entities of the Eyjafjallajökull ice cap, Iceland.
(a) Outlines and topography. (b) Glacier thickness.
Glacier complexes
Single glaciers can be defined as the smallest dynamically independent
entity, i.e., the boundaries between two glaciers should approximately follow
the ice divides or hydrological basin boundaries. The flow-line assumption
strongly relies on this condition being true, and indeed most of the RGI
glaciers are properly outlined. Unfortunately there are notable exceptions,
for three main reasons:
Human decision: some well known glaciers have historical boundaries that
the inventory provider wanted to keep, although the glacier is now
divided in smaller entities. A good example is the Hintereisferner Glacier (Fig. ), which
should have three outlines instead of one.
Uncertainties in the topography: the inventories are often generated using
both automated processes and manual editing. There is no guarantee that we use
the same DEM as the original inventory, and therefore OGGM and RGI might disagree
on the ideal position of an ice divide.
Unavailable data: some remote glaciers and ice caps are outlined in the RGI,
but not divided at all. These are the most problematic cases, and should be a
matter of concern for all RGI users. For example, the largest glacier in RGI
(an ice cap in northeastern Greenland with the ID RGI60-05.10315 and an
area of 7537 km2) is wrongly outlined and should be separated into at least a dozen
smaller entities.
Most of the small errors are filtered out by OGGM with algorithms based on
surface slope thresholds (see Sect. ), but the latter
group of glaciers should be handled upstream. We have developed an
open-source tool to automatically compute glacier divides
https://github.com/OGGM/partitioning, last access:
27 February 2019, based on, but do not use it here. This
issue is a large source of uncertainty for ice thickness estimates and
dynamical modeling of glaciers in general, and could be the subject of a
dedicated study.
Glacier centric modeling
Like most global glacier models, OGGM simulates each glacier individually.
This has evident practical advantages, and is also a strong asset for our
mass-balance model calibration algorithm. However, this has two major
drawbacks: (i) neighboring glaciers will not merge although they grow
together, and (ii) we can only simulate glaciers which are already
inventoried, whereas uncharted glaciers are simply ignored. Both errors are a
source of uncertainty for long or past simulations but less so for short-term
projections in a warming world. The most obvious way to deal with this issue
is to use distributed models e.g.,, with their own
drawbacks (e.g., computational costs and the need for distributed
mass-balance fields). Another way would be to allow the dynamical merging of
neighbor flow-line glaciers at run time. While both are viable options for
the OGGM workflow, they represent a considerable increase in complexity and
are not available yet. Like other fundamental issues described in this paper
(such as missing topographical data or wrongly outlined glaciers), this
problem will also affect other glacier models. We hope that some of the tools
we introduce here will help to solve some of these issues upstream, and that
the community will soon be able to put pressure on commercial data providers
for better data availability.
Global simulations
Thanks to its automated workflow, OGGM is able to apply all of the processes
described in the previous section to all glaciers globally with the exception
of Antarctica, where no CRU data are available (see Appendix
for an overview of the RGI regions). No special model setup is needed, and we
use all model default settings without any calibration (this is not strictly
true for the μ* calibration, which is an automated process and cannot
be tuned or turned off). In the following analyses the focus is placed on the
model behavior and not on the quantitative results. However, in the following
we show that our results are close to expectations even without calibration,
indicating realistic model behavior.
Hardware requirements and performance
Thanks to the computational efficiency of the flow-line model, OGGM runs
quickly enough to be used on a personal computer for up to
several dozen glaciers. At the global scale a high performance computing environment is required. For these global
simulations we used a small cluster comprising two nodes with 16 quad-core
processors each, resulting in 128 parallel threads. With this configuration,
the model preprocessing chain (including the ice thickness inversion) takes
about 7 h to complete (without data download). The total size of the
(compressed) preprocessed output is 122G, which can be reduced by deleting
intermediate computing steps. The amount of required storage increases with
each dynamical run; here again it is possible to reduce the amount of data by
only storing diagnostic variables, such as volume, area, length, and ELA,
instead of the full model output. The dynamical runs are the most expensive
computations: running five 300-year-long global runs takes about 24 h on our
small cluster, which is a very satisfying performance. It is interesting to
note that because of the adaptive time step, glacier shrinkage scenarios run
faster than growing ones.
Invalid glaciers
Due to uncertainties in the input data (topography, outlines, climate), a
certain number of glaciers fail to be modeled by OGGM. The statistics of
these invalid glaciers are summarized in Table . The
largest number of errors (2.6 % of the total area) are due to invalid climate series.
Errors mostly occur when the climate
is too cold for melt to occur or, inversely, too warm or too dry for
accumulation to take place. While some of these errors are directly due to
incorrect climate data, some can also be attributed to missing processes in
the OGGM mass-balance model, such as sublimation and frontal ablation, which
both lead to mass loss even at cold temperatures. The least problematic source of error
(0.2 % of the total area) is due to failures during the actual dynamical
run. The large majority of dynamical failures (751 out of 772) happen because
the glacier exceeded the domain boundaries at run time. Some of these errors
could be mitigated by increasing the domain size (at the cost of
computational efficiency). Only 21 glaciers fail due to numerical
instabilities. Finally, there are a number of other errors (0.3 % of the
total area) occurring at other stages of the model chain. Examples include
errors in processing the geometries or failures in computing certain
topographical properties due to invalid DEMs. In total, 7084 glaciers
(3.1 % of the total area) cannot be modeled by the OGGM. There are strong
regional differences, with remote high and low latitude regions accounting
for most of the errors.
Statistics of the model errors for each RGI region. The column names
indicate which processing step produces an error, the value is the number of
invalid glaciers and (in parentheses) the percentage of regional area they
represent.
A summary of the volume inversion results is presented in
Fig. . As expected from theory ,
our glacier volume estimates approximately follow a power law relationship
with the glacier area (V=cSγ). The coefficients obtained by a
linear fit in log space are close, but not equal to the coefficients computed
by . In particular, the OGGM fit is slightly flatter than the
theoretical value (Fig. a), in accordance with empirical
coefficients e.g.,. This is an encouraging
result, especially because it was reached using the OGGM default settings and
without calibration.
The global volume estimates are particularly sensitive to the choice of the
ice dynamics parameters, as shown in Fig. b. As for
individual glaciers, the total volume follows an inverse polynomial curve as
expected from the equations of ice flow. Changing from a rectangular to a
parabolic bed shape yields a volume loss of exactly one-third (see
Sect. ). Adding lateral drag yields a volume very close
to the rectangular case, and, although this is fortuitous (individual
glaciers can show different results, see Fig. ), it matches
the original purpose of the parameterization nicely, which is to compute a
more realistic ice flow for parabolic bed shapes. The three independent
estimates plotted as straight dotted lines
VAS; illustrate that A is a relatively
straightforward parameter to act upon in order to fit the model to
observations. The effect of A, however, is going to be the same on all
glaciers and therefore will be a poor measure of performance see
alsoSect. 8.11. In fact, the added value of OGGM is more likely
to be found in the deviations from the scaling law
(Fig. b). The deviations are the result of a range of
possible factors such as slope, total accumulation, or altitude area
distribution. With accurate boundary conditions, OGGM should be able to
provide more accurate estimates, within the limits of the assumptions and
simplifications behind the model equations. The calibration and validation of
the OGGM inversion model will be the topic of a subsequent
study.
Global glacier volume
modeling. (a) Binned scatterplot of volume versus area for all valid
glaciers (N= 207 438) using the default OGGM setup. Color shading
indicates the number of glaciers in each bin. Note the logarithmic scale of
the axes and the irregular color scale levels. The dashed lines indicate the
volume–area scaling relationship with either the theoretical parameters from
(V=0.034S1.375) or fitted on our own data (V=0.042S1.313). (b) Global volume estimates as a function of
the multiplication factor applied to the ice creep parameter A, with five
different setups: defaults, with sliding velocity, with lateral drag, and
with rectangular and parabolic bed shapes only (instead of the default mixed
parabolic/rectangular). In addition, we plotted the estimates from standard
volume–area scaling (VAS, V=0.034S1.375), (HF2012) and
(G2013). The latter two estimates are provided for indication only as they
are based on a different glacier inventory.
Dynamical runs
We test the model behavior by running several 300-year-long global
simulations under various climate “scenarios”. In the first simulations
(Fig. ), we run the model under the climate of the past
31 years. In order to keep the forcing realistic, we create a pseudo-random
climate by shuffling the years infinitely. We also run two additional
simulations with a 0.5 ∘C positive and negative bias. The unbiased
simulation illustrates the committed glacier mass loss, i.e., the ice mass
which is not sustainable under the current climate.
Figure shows that all regions will continue to lose ice
even if the climate remains constant. The regions with the largest committed
mass loss relative to the initial volume are western Canada and US (02),
Svalbard (07), and the three “High Mountain Asia” regions (13, 14, and 15). Conversely, the Arctic Canada
south (04), Greenland (05), and Iceland (06) regions are least affected. The
reasons for these regional differences are complex; they are due to the
climate itself of course, but also to glacier properties such as size, slope,
and continentality. The regions that are far from equilibrium also tend to be
less sensitive to the temperature bias experiments, although this should not
be overinterpreted (indeed, the range of the y axes can hide differences
which appear small in comparison to the large regional glacier loss).
In general, the model behavior looks reasonable and the regional differences
are in qualitative agreement with other global studies e.g.,where the
regions with a stronger response to 21st century climate change are the same
as those listed above. Furthermore, our global estimate of the
committed mass loss (approx. 33 % at the end of the 300-year simulation,
probably more at equilibrium) is in agreement with other studies
27±5 %, 38±16 %, and 36±8 %
forrespectively.
Regional glacier volume change under the 1985–2015 climate
(randomized) with three temperature biases (-0.5∘, 0∘, and
+0.5∘). Note the units of the y axes (103 km3) and the
marked regional differences.
A further model test is presented in Fig. . Here, we apply a
new climate scenario: the climate at t* which, for each glacier
individually, represents a theoretical equilibrium climate. In addition to
the global response to these scenarios, we separate between the majority
group of smaller glaciers and the much smaller group of very large glaciers.
Both groups are selected so that they sum up to one-quarter of the total
glacier volume. A striking feature of the runs is that the glaciers tend to
grow under the artificial t* climate. The growth is slow at first and
accelerates with time, hinting towards a positive feedback. This feedback is
driven by two factors: first, a higher surface elevation leads to a positive
change in mass balance (mass-balance–elevation feedback); and second, due to
the parabolic and trapezoidal bed shapes, a larger ice thickness leads to a
wider accumulation area above the ELA and to a wider ablation area below the
ELA. It appears that the positive width–accumulation feedback is stronger
than the negative width–ablation feedback. This can be explained by the
larger accumulation area of glaciers in an equilibrium climate: the average
accumulation area ratio at t* in OGGM is 51 %. In order to test
which of these feedbacks is stronger, we run a simulation with rectangular
bed shapes exclusively (dotted light purple line in Fig. ),
thereby eliminating the width–accumulation but keeping the mass-balance–elevation feedback.
The results show that for the vast majority of
glaciers the feedback almost disappears, whereas the very large glaciers still
show a weak and delayed altitude feedback.
It is unclear whether this is a bug or a feature. On the one hand, this
behavior is not really desirable as one would expect glaciers to remain
constant under a theoretical equilibrium climate. On the other hand, t* is
just a vehicle to calibrate the model and was not supposed to yield a
particular insight (for example, many glaciers can only have an equilibrium
t* climate after the application of a bias to the operational mass-balance
model). There are many reasons why small initial perturbations such as
numerical noise or the differences between the bed inversion and forward
model numerical schemes might lead to a different equilibrium. It must also
be noted that this feedback is slow to appear, and will only have a notable
influence on the largest glaciers for long-term simulations in a cooler
climate (the global volume change after 100 years due to the feedback is
2.4 % for the default and 1 % for the all rectangular cases). The
very simple definition of an “equilibrium climate” for these very large
glaciers is problematic anyway: large glaciers have a very slow but
potentially large response to the smallest changes in climate. At the global
scale, most of the 300-year volume loss is due to the small glaciers, which
respond faster and stronger than larger ones.
(a) Global glacier volume change under various climate
scenarios (1985–2015 climate with three temperature biases and climate at
t* which, for each glacier individually, represents a theoretical
equilibrium climate) and model configurations (rectangular bed instead of the
mixed default), plotted as a fraction of the initial volume.
(b, c) Volume changes of all glaciers making up for the first and
last quartile of the sorted cumulative total volume.
Conclusions
We present a new model of global glacier evolution, the Open Global Glacier
Model (OGGM, v1.1). The panoply of tools available to compute past and future
glacier change range from simple box models e.g., to
more complex, geometry aware models to cite the most recent in
date. OGGM undoubtedly belongs to the complex side of this scale.
Different model complexities are justified by different problem settings,
taking the model-specific merits and drawbacks into account. Instead of
endorsing one approach over the other, OGGM aims to provide a framework which
allows one to switch between models and allows objective intercomparisons. In
fact, the ice dynamics module represents only a small fraction of the OGGM
code base: a huge amount of work has been invested to provide a series of
tools which will help others in their own modeling endeavors. Any
interested person can download, install, and run these tools at no cost. This
includes the automated download of topographic and climate data for any
location on the globe, the collation of glacier attributes, the automated
computation of glacier centerlines, or the delineation of glacier dynamical
entities. While some of these tools have been described elsewhere, the added
value of OGGM is that they are now centralized, documented, and available for
public review via the open-source model.
In the future, we will continue to encourage external contributions in
several ways. First, it must be as easy as possible for a new user to detect
where and how a contribution can be implemented; hence, documentation is key.
Then, the model must be able to cope with different ways of simulating a
considered process: every single task in the OGGM workflow can be replaced or
enhanced, as long as the format of the input and output files is agreed upon
beforehand. Perfect modularity will be hard to achieve, but the recent
implementation of alternative numerical solvers show that modularity is
possible. Finally, we need to ensure attribution to the original contribution
(e.g., a scientific publication) in order to engage the wider community. For
this purpose, we developed a template repository for external OGGM modules:
https://github.com/OGGM/oggmcontrib (last access: 27 February 2019).
This development model will ensure that users importing OGGM extensions will
be aware of the source of each module they are using and will be able to
refer to the original contribution appropriately. We hope that this
development model will foster new collaborations.
We cannot (and do not want to) demonstrate that OGGM will provide more
accurate estimates of future sea-level rise than earlier attempts. However,
OGGM allows new studies which were not previously possible. The dynamical
representation of glacier advance and retreat enables studies of glacier
evolution at long (paleo-) timescales, where ice dynamics and geometrical
attributes such as the accumulation area ratio play an important role
e.g.,. The first OGGM simulations over the last
millennium show very promising results . The modular framework allows one to
compare the performance of various parameterizations such as the mass balance
and downscaling algorithms. It may be argued that the amount of available
data is not sufficient to constrain modeling studies such as ours at the
global scale. The OGGM can now be used to test this argument by allowing
simpler modules to be added to the code base and test the added value of
increased complexity.
Planned and envisioned future developments for the model follow the general
guidelines of modularity and extendability. While some of the authors are
working on adding even more complexity to the model (for example by improving
the frontal ablation and mass-balance parameterizations or by implementing a
distributed ice dynamics module), it is part of our plans to implement
simpler approaches, such as the original model or the
approach to ice thickness estimation. A considerable amount
of work will be needed to correctly assess the uncertainties associated with
the model chain; therefore, Monte Carlo and Bayesian approaches might be the best courses of action.
The non-linear dynamical behavior of glaciers raises a wide range of very
interesting inverse problems. For example, how to deal with the transient
climate issue in the ice thickness inversion algorithm? How much information
about past climate can be extracted from moraine proxies and today's glacier
extent? What are the uncertainties associated with global sea-level rise
estimates, and where do they originate? How much complexity is appropriate?
These are all questions that the authors hope will be easier to address through
the publication of the OGGM.
Code availability, testing, and software requirements
The OGGM software is coded in the Python language and licensed under the
GPLv3 free software license. The latest version of the code is available on
GitHub (https://github.com/OGGM/oggm, last access: 27 February 2019),
the documentation is hosted on Read the Docs (http://docs.oggm.org,
last access: 27 February 2019), and the project website for communication and
dissemination can be found at http://oggm.org (last access:
27 February 2019). The OGGM version used for this study is version 1.1
. Past and future OGGM versions will be available from a
permanent DOI repository (https://zenodo.org/badge/latestdoi/43965645,
last access: 27 February 2019). The software ships with an extensive test
suite which can be used by the users to test their configuration. The tests
are triggered automatically at each new code addition, reducing the risk of
introducing new bugs (https://travis-ci.org/OGGM/oggm, last access:
27 February 2019). The suite contains unit tests (for example for the
numerical core) and integration tests based on sets of real glaciers. At the
time of writing, 85 % of all relevant lines of code are covered by the
tests (i.e., called at least once by the test suite). The remaining 15 %
are challenging to monitor because they mostly concern the automated
downloading tools which are used in production and cannot be tested
automatically.
The following open-source libraries have to be installed in order to run
OGGM: numpy/scipy,
scikit-image, shapely, rasterio, pandas, geopandas, xarray,
pyproj, matplotlib, and salem. OGGM runs on all major platforms (Windows, Mac, and
Linux) but we recommend using Linux as this is the platform it is most tested
on. The code and data used to generate all figures and analyses in this paper
can be found at .
Climate data
The default climate dataset used by OGGM is the Climatic Research Unit (CRU)
TS v4.01 dataset released 20 September 2017. It is a
gridded dataset at 0.5∘ resolution covering the period from 1901 to 2016.
The dataset is obtained by interpolating station measurements; therefore, it
does not cover the oceans and Antarctica. The TS dataset is further
downscaled to the resolution of 10′ by applying the 1961–1990 anomalies to
the CRU CL v2.0 gridded climatology . This step is necessary
because the TS datasets do not contain altitude information, which is
needed to compute the temperature at a given height on the glacier. To
compute the annual mass balances we use the hydrological year convention (the
year 2001 being October 2000 to September 2001 in the Northern Hemisphere and
April 2000 to March 2001 in the Southern Hemisphere).
For each glacier, the monthly temperature and precipitation time series are
extracted from the nearest CRU CL v2.0 grid point and then converted to the
local temperature according to a temperature gradient (default:
6.5 K km-1). No vertical gradient is applied to precipitation, but we
apply a correction factor pf=2.5 to the original CRU time series
similar to. This correction factor can be seen as a
global correction for orographic precipitation, avalanches, and wind-blown
snow. It must be noted that this factor has little (if any) impact on the
mass-balance model performance in terms of bias. This is due to the automated
calibration algorithm, which will adapt to a new factor by acting on the
temperature sensitivity μ*. To verify that the chosen precipitation
factor is realistic, we use another metric – the standard deviation of the
mass-balance time series. Comparisons between model and observations show
that the model underestimates variability by about 10 %. We could tune
the precipitation factor towards higher values to reduce this discrepancy but
refrain to do so, as we do not want to add an additional free parameter in
the model.
WGMS glaciers
To calibrate and validate the mass-balance model, OGGM relies on mass-balance
observations provided by the World Glacier Monitoring Service
. The Fluctuations of Glaciers (FoG) database contains annual
mass-balance values for several hundreds of glaciers worldwide. We exclude
water-terminating glaciers and the time series with less than 5 years of
data. Not all of the remaining glaciers can be used by OGGM; we also need a
corresponding RGI outline. Indeed, the WGMS and RGI databases have distinct
glacier identifiers and it is not guaranteed that the glacier outline
provided by the RGI fits the outline used by the local data providers to
compute the specific mass balance. Since 2017, the WGMS has provided a lookup
table linking the two databases. We updated this list for version 6 of
the RGI, leaving us with 254 mass-balance time series.
These data are not equally distributed over the glaciated regions see
e.g.,and Fig. , and their quality is highly
variable. In the absence of a better data basis (at least for the 20th
century), we have to rely on them for the calibration and validation of our
model. Fortunately, these data play a relatively minor role in the model
calibration as explained in Sect. . For future studies it might
be advisable to use independent, regional geodetic mass-balance estimates for
validation as well.
RGI Regions
A map of the RGI regions and some basic statistics are presented in
Fig. .
(a) Map of the RGI regions: the red dots indicate the
glacier locations and the blue circles the location of the 254 reference WGMS
glaciers used by the OGGM calibration. (b) Region names and basic
statistics of the database (number of glaciers per region, regional
contribution to the global area in percent, and the percentage of the regional
area which cannot be modeled by OGGM).
Author contributions
BM and FM are the initiators of the OGGM project. FM is the main
OGGM developer and wrote most of the paper. AB developed the downstream bed shape
estimation algorithm. NC wrote parts of the documentation. MD wrote the cross-validation
monitoring website. JE developed the glacier partitioning tool. KF wrote parts of the bed
inversion and dynamical cores. PG wrote the lateral drag parameterization. AJ provided a
robust implementation of the dynamical core used for testing and contributed to the development
of the operational scheme. JL provided the WGMS to RGI lookup table and contributed to the
topographical data download tool. FO contributed to the AWS deployment tool. BR developed the
frontal ablation parameterization tool. TR developed the download and parallelisation tools and
is largely responsible for the successful deployment of the OGGM on supercomputing environments.
AV contributed to the climate and mass-balance tools. CW provided the first implementation
of the centerline determination algorithm. All authors continuously discussed the model
development and the results together.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
Ben Marzeion, Johannes Landmann, and Christian T. Wild were supported by the
Austrian Science Fund (FWF), grant no. P25362. Ben Marzeion, Anton Butenko, and
Julia Eis were supported by the German Research Foundation, grant no. MA6966/1-1.
Anouk Vlug and Beatriz Recinos were supported by the DFG through
the International Research Training Group IRTG 1904 ArcTrain.
Kévin Fourteau was supported by the ENS Paris-Saclay. Nicolas Champollion
was funded by the German Federal Ministry of Education and Research (grant
no 01LS1602A). The computations were partially realized on resources provided by
Amazon Web Services Cloud Computing (sponsored by Amazon) and on the
computing facilities of the Institute of Geography, University of
Bremen. Edited by: Didier Roche
Reviewed by: David Rounce and one anonymous referee
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