TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-13-325-2019Global glacier volume projections under high-end climate change scenariosGlobal glacier volume projectionsShannonSarahsarah.shannon@bristol.ac.ukSmithRobinhttps://orcid.org/0000-0001-7479-7778WiltshireAndyPayneTonyhttps://orcid.org/0000-0001-8825-8425HussMatthiashttps://orcid.org/0000-0002-2377-6923BettsRichardCaesarJohnhttps://orcid.org/0000-0003-1094-9618KoutroulisArishttps://orcid.org/0000-0002-2999-7575JonesDarrenHarrisonStephanSchool of Geography, University of Exeter, The Queen's Drive,
Exeter, Devon, EX4 4QJ, UKBristol Glaciology Centre, Department of Geographical Science,
University Road, University of Bristol, BS8 1SS, UKNCAS-Climate, Department of Meteorology, University of Reading,
Reading, RG6 6BB, UKMet Office, Fitzroy Road, Exeter, Devon, EX1 3PB, UKDepartment of Geosciences, University of Fribourg, Fribourg,
SwitzerlandLaboratory of Hydraulics, Hydrology and Glaciology, ETH Zurich,
Zurich, SwitzerlandSchool of Environmental Engineering, Technical University of Crete,
Akrotiri, 73100 Chania, GreeceUniversity of Exeter, Penryn Campus, Treliever Road, Penryn, Cornwall,
TR10 9FE, UKSarah Shannon (sarah.shannon@bristol.ac.uk)1February201913132535015February20186March201830November201813December2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://tc.copernicus.org/articles/13/325/2019/tc-13-325-2019.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/13/325/2019/tc-13-325-2019.pdf
The Paris agreement aims to hold global warming to well below 2 ∘C and
to pursue efforts to limit it to 1.5 ∘C relative to the pre-industrial
period. Recent estimates based on population growth and intended carbon
emissions from participant countries suggest global warming may exceed this
ambitious target. Here we present glacier volume projections for the end of
this century, under a range of high-end climate change scenarios, defined as
exceeding +2∘C global average warming relative to the pre-industrial
period. Glacier volume is modelled by developing an elevation-dependent mass
balance model for the Joint UK Land Environment Simulator (JULES). To do
this, we modify JULES to include glaciated and unglaciated surfaces that
can exist at multiple heights within a single grid box. Present-day mass
balance is calibrated by tuning albedo, wind speed, precipitation, and
temperature lapse rates to obtain the best agreement with observed mass
balance profiles. JULES is forced with an ensemble of six Coupled Model
Intercomparison Project Phase 5 (CMIP5) models, which were downscaled using
the high-resolution HadGEM3-A atmosphere-only global climate model. The
CMIP5 models use the RCP8.5 climate change scenario and were selected on the
criteria of passing 2 ∘C global average warming during this century. The
ensemble mean volume loss at the end of the century plus or minus 1 standard
deviation is -64±5 % for all glaciers excluding those on the
peripheral of the Antarctic ice sheet. The uncertainty in the multi-model
mean is rather small and caused by the sensitivity of HadGEM3-A to the
boundary conditions supplied by the CMIP5 models. The regions which lose
more than 75 % of their initial volume by the end of the century are
Alaska, western Canada and the US, Iceland, Scandinavia, the Russian Arctic, central
Europe, Caucasus, high-mountain Asia, low latitudes, southern Andes, and New
Zealand. The ensemble mean ice loss expressed in sea level equivalent
contribution is 215.2±21.3 mm. The largest contributors to sea level
rise are Alaska (44.6±1.1 mm), Arctic Canada north and south (34.9±3.0 mm), the Russian Arctic (33.3±4.8 mm), Greenland (20.1±4.4), high-mountain Asia (combined central Asia, South Asia east and west),
(18.0±0.8 mm), southern Andes (14.4±0.1 mm), and Svalbard (17.0±4.6 mm). Including parametric uncertainty in the calibrated mass
balance parameters gives an upper bound global volume loss of 281.1 mm
of sea level equivalent by the end of the century. Such large ice losses will
have inevitable consequences for sea level rise and for water supply in
glacier-fed river systems.
Introduction
Glaciers act as natural reservoirs by storing water in the winter and
releasing it during dry periods. This is particularly vital for seasonal
water supply in large river systems in South Asia (Immerzeel and Bierkens, 2013; Lutz
et al., 2014; Huss and Hock, 2018) and central Asia (Sorg et al.,
2012) where glacier melting contributes to streamflow and supplies fresh
water to millions of people downstream. Glaciers are also major contributors
to sea level rise, despite their mass being much smaller than the Greenland
and Antarctic ice sheets (Kaser et al., 2006; Meier et al., 2007; Gardner
et al., 2013). Since glaciers are expected to lose mass into the twenty-first century (Radić et al., 2014; Giesen and Oerlemans, 2013; Slangen
et al., 2014; Huss and Hock, 2015), there is an urgent need to understand how
this will affect seasonal water supply and food security. To study this
requires a fully integrated impact model which includes the linkages and
interactions among glacier mass balance, river runoff, irrigation, and crop
production.
The Joint UK Land Environment Simulator (JULES)
(Best et al., 2011) is an
appropriate choice for this task because it models these processes, but it is
currently missing a representation of glacier ice. JULES is the land surface
component of the Met Office global climate model (GCM), which is used for
operational weather forecasting and climate modelling studies. JULES was
originally developed to model vegetation dynamics and snow and soil hydrological
processes within the GCM but now has a crop model to simulate crop yield for
wheat, soybean, maize, and rice (Osborne et al., 2014), an irrigation demand scheme
to extract water from ground and river stores, and two river routing schemes:
Total Runoff Integrating Pathways (Oki et al., 1999) (TRIP) and the RFM kinematic
wave model (Bell et al., 2007). The first objective of this study is to add a
glacier ice scheme to JULES to contribute to the larger goal of developing
a fully integrated impact model.
The second objective is to make projections of glacier volume changes under
high-end climate change scenarios, defined as exceeding 2 ∘C global
average warming relative to the pre-industrial period (Gohar et al., 2017). The Paris
agreement aims to hold global warming to well below 2 ∘C and to
pursue efforts to limit it to 1.5 ∘C relative to the pre-industrial
period; however, there is some evidence that this target may
be exceeded. Revised estimates of population growth suggest there is only a
5 % chance of staying below 2 ∘C and that the likely range of
temperature increase will be 2.0–4.9 ∘C (Raftery et al., 2017). A
global temperature increase of 2.6–3.1 ∘C has been estimated based
on the intended carbon emissions submitted by the participant countries for
2020 (Rogelj et al., 2016). Therefore, in this study we make end-of-the-century glacier volume projections, using a subset of downscaled Coupled
Model Intercomparison Project Phase 5 (CMIP5) models which pass 2 and
4 ∘C global average warming. The CMIP5 models use the Representative
Concentration Pathways (RCP) RCP8.5 climate change scenario for high
greenhouse gas emissions.
The paper is organised as follows: in Sect. 2 we describe the glacier ice
scheme implemented in JULES and the procedure for initialising the model.
Section 3 describes how glacier mass balance is calibrated and validated for
the present day. Section 4 presents future glacier volume projections, a
comparison with other studies, and a discussion on parametric uncertainty in
the calibration procedure. Section 5 discusses the results, model
limitations, and areas for future development. In Sect. 6, we summarise our
findings with some concluding remarks.
Model description
JULES (described in detail by Best et al., 2011) characterises the land
surface in terms of subgrid-scale tiles representing natural vegetation,
crops, urban areas, bare soil, lakes, and ice. Each grid box is comprised of
fractions of these tiles with the total tile fraction summing to 1. The
exception to this is the ice tile, which cannot co-exist with other surface
types in a grid box. A grid box is either completely covered in ice or not.
All tiles can be assigned elevation offsets from the grid box mean, which is
typically set to zero as a default.
To simulate the mass balance of mountain glaciers more accurately we extend
the tiling scheme to flexibly model the surface exchange in different
elevation classes in each JULES grid box. We have added two new surface types,
glaciated and unglaciated elevated tiles, to JULES (version 4.7) to describe
the areal extent and variation in height of glaciers in a grid box (Fig. 1).
Each of these new types, at each elevation, has its own bedrock subsurface
with a fixed heat capacity. These subsurfaces are impervious to water, and
have no carbon content, so they have no interaction with the complex hydrology or
vegetation found in the rest of JULES. Because glaciated and unglaciated
elevated tiles have their own separate bedrock subsurface they are not
allowed to share a grid box with any other tiles. For instance, grid boxes
cannot contain partial coverage of elevated glacier ice and vegetated tiles.
Schematic of JULES surface types inside a single grid box. The new
elevated glaciated and unglaciated tiles are shown on the left-hand side.
Note that elevated glaciated and unglaciated tiles are not allowed to share a
grid box with the other tiles.
JULES is modified to enable tile heights to be specified in metres above sea
level (m a.s.l.), as opposed to the default option, which is to specify heights as
offsets from the grid box mean. This makes it easier to input glacier
hypsometry into the model and to compare the output to observations for
particular elevation bands. To implement this change, the grid box mean
elevation associated with the forcing data is read in as an additional
ancillary file. Downscaling of the climate data, described in Sect. 2.1, is
calculated using the difference between the elevation band
(zband) and the grid box mean elevation (zgbm).
Δz=zband-zgbm
For the purposes of this study JULES is set up with a spatial resolution of
0.5∘ and 46 elevation bands ranging from 0 to 9000 m in increments of
250 m. The horizontal resolution of 0.5∘ is used because it matches
the forcing data used to drive the model. The vertical resolution of 250 m
was used based on computational cost. The vertical and horizontal resolutions
of the model can be modified for any setup.
Each elevated glacier tile has a snowpack which can gain mass through
accumulation and freezing of water and lose mass through sublimation and
melting. JULES has a full energy balance multilevel snowpack scheme which
splits the snowpack into layers, each having a thickness, temperature,
density, grain size (used to determine albedo), and solid ice and liquid
water contents. The initialisation of the snowpack properties and the
distribution of the glacier tiles as a function of height are described in
Sect. 2.3. Fresh snow accumulates at the surface of the snowpack at a
characteristic low density and compacts towards the bottom of the snowpack
under the force of gravity. When rain falls on the snowpack, water is
percolated through the layers if the pore space is sufficiently large, while
any excess water contributes to the surface runoff. Liquid water below the
melting temperature can refreeze. A full energy balance model is used to
calculate the energy available for melting. If all the mass in a layer is
removed within a model time step then removal takes place in the layer below.
The temperature at each snowpack level is calculated by solving a set of
tridiagonal equations for heat transfer with the surface boundary temperature
set to the air temperature and the bottom boundary temperature set to the
subsurface temperature.
A snowpack may exist on both glaciated and unglaciated elevated tiles if
there is accumulation of snow.
The elevation-dependent mass balance (SMBz,t) is calculated as the
change in the snowpack mass (S) between successive time
steps.
SMBz,t=Sz,t-Sz,t-1
The scheme assumes that the snowpack can grow or shrink at elevation bands
depending on the mass balance, but that tile fraction (derived from the
glacier area) is static with time. The ability to grow or shrink the
snowpack at elevation levels means that the model includes a simple
elevation feedback mechanism. If the snowpack shrinks to zero at an
elevation band, then the terminus of the glacier moves to the next level
above. Conversely, if the snowpack grows at an elevation band it just
continues to grow and there is no process to move the ice from higher
elevations to lower elevations. Typically, in an elevation feedback, when a
glacier grows the surface of the glacier will experience a cooler
temperature; however in this case, the snowpack surface experiences the
temperature of the elevation band.
Downscaling of climate forcing on elevations
Both glaciated and unglaciated elevated tiles are assigned heights in metres
above sea level and the following adjustments are made to the surface
climate in grid boxes in which glaciers are present.
Air temperature and specific humidity
Temperature is adjusted for elevation using a dry and moist adiabatic lapse
rate depending on the dew point temperature. First the elevated temperature
follows the dry adiabat:
Tz=T0-γdryΔz,
where T0 is the surface temperature, γdry is the dry
adiabatic temperature lapse rate (∘C m-1), and Δz is the
height difference between tile elevation and the grid box mean elevation
associated with the forcing data.
If Tz is less than the dew point temperature Tdew then
the temperature adjustment follows the moist adiabat. A moist adiabatic lapse
rate is calculated using the surface specific humidity from the forcing data.
γmoist=g(1+lc⋅q0)r⋅Tv(1-q0)Cp+lc⋅2⋅q0⋅Rr⋅Tv2(1-q0)q0 is the surface
specific humidity, lc is the latent heat of fusion of water at
0 ∘C (2.501×106 J kg-1), g is the acceleration
due to gravity (9.8 m s-2), r is the gas constant for dry air
(287.05 kg K-1), R is the ratio of molecular weights of water and dry
air (0.62198), and Tv (K) is the virtual dew point temperature.
Tv=Tdew(1+1R-1.0q0)
The height at which the air becomes saturated z is
z=T0-Tdewγdry.
The elevated temperature following the moist adiabat is then
Tz=Tdew-Δz-zγmoist.
Additionally, when Tz<Tdew, the specific humidity is
adjusted for height. The adjustment is made using the elevated air
temperature and surface pressure from the forcing data using a lookup table
based on the Goff–Gratch formula (Bakan and Hinzpeter, 1987). The adjusted humidity
is then used in the surface exchange calculation.
Longwave radiation
Downward longwave radiation is adjusted by assuming the atmosphere behaves as
a black body using Stefan–Boltzmann's law. The radiative air temperature at
the surface Trad,0 is calculated using the downward longwave
radiation provided by the forcing data LW↓z0Trad,0=LW↓z0σ14,
where σ is the Stefan–Boltzmann constant (5.67×10-8 W m-2 K-4). The radiative temperature at height is then
adjusted:
Trad,z=Trad,0+Tz-T0,
where T0 is the grid box mean temperature from the forcing data and
Tz is the elevated air temperature. This is used to calculate the
downward longwave radiation LW↓z at height
LW↓z=σTrad,z4.
An additional correction is made to ensure that the grid box mean downward
longwave radiation is preserved:
LW↓z=LW↓z-∑z=1nLW↓z⋅fraczLW↓z∑i=1zLW↓z⋅fracz,
where frac is the tile fraction.
Precipitation
To account for orographic precipitation, large-scale and convective rainfall
and snowfall are adjusted for elevation using an annual mean precipitation
gradient (%/100 m):
Pz=P0+P0γprecipz-z0,
where P0 is the surface precipitation, γprecip is the
precipitation gradient, and z0 is the grid box mean elevation. Rainfall
is also converted to snowfall when the elevated air temperature Tz is
less than the melting temperature (0 ∘C). The adjusted precipitation
fields are input into the snowpack scheme and the hydrology subroutine. When
calibrating the present-day mass balance, we needed to lapse rate correct the
precipitation to obtain sufficient accumulation in the mass balance compared to
observations. The consequence of this is that the grid box mean precipitation
is no longer conserved. We tested scaling the precipitation in a way that
conserves the grid box mean by reducing the precipitation near the surface and
increasing it at height, but this did not yield enough precipitation to obtain a
good agreement with the mass balance observations. If the model is being used
to simulate river discharge in glaciated catchments, then the precipitation
lapse rate could be used as a parameter to calibrate the discharge.
Wind speed
A component of the energy available to melt ice comes from the sensible
heat flux, which is related to the temperature difference between the surface
and the elevation level and the wind speed. Glaciers often have katabatic
(downslope) winds which enhance the sensible heat flux and increase melting
(Oerlemans and Grisogono, 2002). It is important to represent the
effects of katabatic winds on the mass balance when trying to model glacier
melt, particularly at lower elevations where the katabatic wind speed is
highest.
To explicitly model katabatic winds would require knowledge of the grid box
mean slope at elevation bands, so instead a simple scaling of the surface
wind speed is used to represent katabatic winds. Over glaciated grid boxes
the wind speed is
uz=u0γwind,
where γwind is a wind speed scale factor and u0 is the
surface wind speed. The simple scaling increases the wind speed relative to
the surface forcing data and assumes that the scaling is constant for all
heights.
Although our approach is rather crude, we found that scaling the wind speed
was necessary to obtain reasonable values for the sensible heat flux. This is
seen when we compare the modelled energy balance components to observations
from the Pasterze glacier in the Alps (Greuell and Smeets, 2001). The
measurements consist of incoming and outgoing short- and longwave radiation,
albedo, temperature, wind speed, and roughness length at five heights between
2205 and 3325 m a.s.l. on the glacier. Table S6 in the
Supplement lists the observed and modelled energy balance components and
meteorological data, for experiments with and without wind speed scaling. The
comparison shows that JULES underestimates the sensible heat flux by at least
1 order of magnitude and the modelled wind speed is 4 times lower than
the observations. When we increase the wind speed to match the observations
there is a better agreement with the observed sensible heat flux. The surface
exchange coefficient, which is used to calculate the sensible heat flux, is a
function of the wind speed in the model.
Glacier ice albedo scheme
The existing spectral albedo scheme in JULES simulates the darkening of fresh
snow as it undergoes the process of aging (Warren and Wiscombe, 1980). In this scheme the change in albedo
as snow ages is related to the growth of the snow grain size, which is a function of the snowpack temperature. The snow aging scheme does not reproduce the low albedo values
typically observed on glacier ice; therefore a new albedo scheme is used. The
new scheme is a density-dependent parameterisation which was developed for implementation in the Surface Mass Balance and Related Sub-surface
processes (SOMARS) model (Greuell and Konzelmann, 1994). The scheme linearly
scales the albedo from the value of fresh snow to the value of ice, based on
the density of the snowpack surface. The new scheme is used when the surface
density of the top 10 cm of the snowpack (ρsurface) is
greater than the firn density (550 kg m-3) and the original snow aging
scheme is used when (ρsurface) is less than the firn density.
αλ=αλ,ice+ρsurface-ρiceαλ,snow-αλ,iceρsnow-ρiceαλ,snow is the maximum albedo of fresh snow,
αλ,ice is the albedo of melting ice,
ρsnow is the density of fresh snow (250 kg m-3), and
ρice is the density of ice (917 kg m-3). The albedo
scaling is calculated separately in two radiation bands: visible (VIS) wavelengths
λ=0.3–0.7 µm and near-infrared (NIR) wavelengths
λ=0.7–5.0 µm. The parameters, αvis,ice, αvis,snow, αnir,ice, αnir,snow, γtemp, γprecip, and
γwind are tuned to obtain the best agreement between
simulated and observed surface mass balance profiles for the present day (see
Sect. 3).
Initialisation
The model requires initial conditions for (1) the snowpack properties and
(2) glaciated and unglaciated elevated tile fractions within a grid box. The
location of glacier grid points, the initial tile fraction, and the
present-day ice mass are set using data from the Randolph Glacier Inventory
version 6 (RGI6) (RGI Consortium, 2017). This dataset contains information on
glacier hypsometry and is intended to capture the state of the world's
glaciers at the beginning of the twenty-first century. A new feature of the RGI6 is
0.5∘ gridded glacier volume and area datasets, produced at 50 m
elevation bands. Volume was constructed for individual glaciers using an
inversion technique to estimate ice thickness created using glacier outlines,
a digital elevation model, and a technique based on the principles of ice flow
mechanics (Farinotti et al., 2009; Huss and Farinotti, 2012). The area and
volume of individual glaciers have been aggregated onto 0.5∘ grid
boxes. We bin the 50 m area and volume into elevations bands varying from 0
to 9000 m in increments of 250 m to match the elevation bands prescribed in
JULES.
Initial tile fraction
The elevated glaciated fraction is
fracice(n)=RGI_area(n)gridbox_area(n),
where RGI_area is the area (km2) at height from the RGI6, n is the
tile elevation, and gridbox_area (km2) is the area of the grid box. In
this configuration of the model, any area that is not glaciated is set to a
single unglaciated tile fraction (fracrock) with a grid box mean
elevation. It is possible to have an unglaciated tile fraction at every
elevation band, but since the glaciated tile fractions do not grow or
shrink, we reduce our computation cost by simply putting any unglaciated area
into a single tile fraction.
fracrock=1-∑n=1n=nBandsfracice(n)nBands =37 is the number of elevation bands.
Initial snowpack properties
The snowpack is divided into 10 levels in which the top nine levels consist
of 5 m of firn snow with depths of 0.05, 0.1, 0.15, 0.2, 0.25, 0.5, 0.75, 1,
and
2 m and the bottom level has a variable depth. For each snowpack level the
following properties must be set: density (kg m-3), ice content
(kg m-2), liquid water content (kg m-2), grain size
(µm),
and temperature (K). We assume there is no liquid content in the snowpack by
setting this to zero. The density at each level is linearly scaled with
depth, between the value for fresh snow at the surface (250 kg m-3) and the value for ice at the bottom level (917 kg m-3).
For the future simulations the thickness and ice mass at the bottom of the
snowpack come from thickness and volume data in the RGI6. The data are based
on thickness inversion calculations from Huss and Farinotti (2012) for
individual glaciers which are consolidated onto 0.5∘ grid boxes. The
ice mass is calculated from the RGI6 volume assuming an ice density of
917 kg m-3. For the other layers the ice mass is calculated by
multiplying the density by the layer thickness, which is prescribed above. For
the calibration period, the ice mass at the start of the run (1979) is
unknown. In the absence of any information about this, a constant depth of
1000 m is used, which is selected to ensure that the snowpack never
completely depletes over the calibration period. This consists of 995 m of
ice at the bottom level of the snowpack and 5 m of firn in the layers above.
The ice content of the bottom level is the depth (995 m) multiplied by the
density of ice.
The snow grain size used to calculate spectral albedo (see Sect. 2.2) is
linearly scaled with depth and varies between 50 µm at the surface
for fresh snow and 2000 µm at the base for ice. The snowpack
temperature profile is calculated by spinning the model up for 10 years for
the calibration period and 1 year for the future simulations. The temperature
at the top layer of the snowpack is set to the January mean temperature and
the bottom layer and subsurface temperature are set to the annual mean
temperature. For the calibration period the monthly and annual temperature
comes from the last year of the spin-up. Setting the snowpack temperature
this way gives a profile of warming towards the bottom of the snowpack
representative of geothermal warming from the underlying soil. The initial
temperature of the bedrock before the spin-up is set to 0 ∘C but
this adjusts to the climate as the model spins up. We use these prescribed
snowpack properties as the initial state for the calibration and future runs.
Mass balance calibration and validationModel calibration
Elevation-dependent mass balance is calibrated for the present day by tuning
seven model parameters and comparing the output to elevation-band specific
mass balance observations from the WGMS (2017).
Calibrating mass balance against in situ observations is a technique which
has been used by other glacier modelling studies (Radić and Hock, 2011;
Giesen and Oerlemans, 2013; Marzeion et al., 2012). For the calibration,
annual elevation-band mass balance observations are used because there are
data available for 16 of the 18 RGI6 regions. For validation,
winter and summer elevation-band mass balance is used because there are fewer
data available.
The tuneable parameters for mass balance are VIS snow albedo (αvis,snow), VIS melting ice albedo (αvis,ice), NIR snow albedo (αnir,snow),
NIR melting ice albedo (αnir,ice), orographic
precipitation gradient (γprecip), temperature lapse rate
(γtemp), and wind speed scaling factor
(γwind).
Random parameter combinations are selected using Latin hypercube sampling
(McKay et al., 1979) among plausible ranges which have been
derived from various sources outlined below. This technique randomly selects
parameter values; however, reflectance in the VIS wavelength is always higher
than in the NIR. To ensure the random sampling does not select NIR albedo
values that are higher or unrealistically close to the VIS albedo values, we
calculate the ratio of VIS to NIR albedo using values compiled by
Roesch et al. (2002). The ratio VIS / NIR is calculated as 1.2 so any albedo
values that exceed this ratio are excluded from the analysis. This reduces
the sample size from 1000 to 198 parameter sets.
In the VIS wavelength the fresh snow albedo is tuned between 0.99 and 0.7 for
which an
upper bound value comes from observations of very clean snow with few
impurities in the Antarctic (Hudson et al., 2006). The lower bound represents
contaminated fresh snow and comes from taking approximate values from a study
based on laboratory experiments of snow, with a large grain size
(110 µm) containing 1680 parts per billion of black carbon (Hadley
and Kirchstetter, 2012). VIS snow albedos of approximately 0.7 have also
been observed on glaciers with black carbon and mineral dust contaminants in
the Tibetan Plateau (Zhang et al., 2017). In the NIR wavelength the fresh
snow albedo is tuned between 0.85 and 0.5 for which the upper bound comes from
spectral albedo observations made in Antarctica (Reijmer et al., 2001). We
use a very low minimum albedo for ice in the VIS and NIR
wavelengths (0.1), in order to capture the low reflectance of melting ice.
Tuneable parameters for mass balance calculation and their ranges
from the literature.
The temperature lapse rate is tuned between values of
4.0 and 10 ∘C km-1 for which the upper limit is determined from
physically realistic bounds and the lower limit is from observations based at
glaciers in the Alps (Singh, 2001). The temperature lapse rate in JULES is
constant throughout the year and assumes that temperature always decreases
with height.
The wind speed scaling factor γwind is tuned within the
range of 1–4 to account for an increase in wind speed with height and for the
presence of katabatic winds. The upper bound is estimated using wind
observations made along the profile of the Pasterze glacier in the Alps
during a field campaign (Greuell and Smeets, 2001). Table S6 in the
Supplement contains the wind speed observations on the Pasterze glacier. The
maximum observed wind speed was 4.6 m s-1 (at 2420 m a.s.l.)
while the WATCH–ERA Interim dataset (WFDEI) (Weedon et al., 2014) surface
wind speed for the same time period was 1.1 m s-1, indicating a scaling
factor of approximately 4.
The orographic precipitation gradient γprecip is tuned
between 5 and 25 % per 100 m. This parameter is poorly constrained by
observations; therefore a large tuneable range is sampled. Tawde et
al. (2016)
estimated a precipitation gradient of 19 % per 100 m for 12 glaciers in the
western Himalayas using a combination of remote sensing and in situ
meteorological observations of precipitation. Observations show that the
precipitation gradient can be as high as 25 % per 100 m for glaciers in
Svalbard
(Bruland and Hagen, 2002) while glacier–hydrological
modelling studies have used much smaller values of 4.3 % per 100 m (Sorg et al.,
2014) and 3 % per 100 m (Marzeion et al. (2012). The tuneable parameters and
their minimum and maximum ranges are listed in Table 1.
The model is forced with daily surface pressure, air temperature, downward
longwave and shortwave surface radiation, specific humidity, rainfall,
snowfall, and wind speed from the WFDEI dataset
(Weedon et al., 2014). To reduce the computation time, only grid
points at which glacier ice is present are modelled. An ensemble of 198
calibration experiments are run. For each simulation the model is spun up for
10 years and the elevation-dependent mass balance is compared to observations
at 149 field sites over the years 1979–2014.
The elevation-dependent mass balance observations come from stake
measurements taken every year at different heights along the glaciers. Many
of the mass balance observations in the World Glacier Monitoring Service (WGMS, 2017) are supplied without
observational dates. In this case, we assume the mass balance year starts on 1 October and ends on 30 September with the summer commencing on
1 May. Dates in the Southern Hemisphere are shifted by 6 months. The
observations are grouped according to standardised regions defined by the
RGI6 (Fig. 2). The best regional parameter sets are identified by finding the
minimum root-mean-square error between the modelled mass balance and the
observations.
The location of mass balance profile observation glaciers from the
World Glacier Monitoring Service and the Randolph Glacier Inventory regions
(version 6.0).
Modelled annual elevation-dependent specific mass balance against
observations from the WGMS. The modelled mass balance is simulated on a
0.5∘ grid resolution at 250 m elevation bands and the observations
are for individual glaciers at elevation levels specific to each glacier. The
observed mass balance is interpolated onto the JULES elevation bands. If only
a single observation exists, then mass balance for the nearest JULES
elevation band is used. The number of glaciers is shown in the top left-hand
corner and the number of observation points in brackets. In central Europe
mass balance for the Maladeta glacier in the Pyrenees is shown in black
circles.
Figure 3 shows the modelled mass balance profiles plotted against the
observations using the best parameter set for each region. The best regional
parameter sets are listed in Table 2 and the root-mean-square error,
correlation coefficient, Nash–Sutcliffe efficiency coefficient, and mean bias
are listed in Table 3. Nine out of the 16 regions have a negative bias
in the annual mass balance. Notably Svalbard, southern Andes, and New Zealand
underestimate mass balance by 1 m w.e. yr-1. The negative bias is also seen in the summer
and winter mass balance and discussed in Sect. 3.2. The model performs
particularly poorly for the low-latitude region, which has a large RMSE
(3.02 m w.e. yr-1). This region contains relatively small tropical
glaciers in Colombia, Peru, Ecuador, Bolivia, and Kenya. Marzeion et
al. (2012) found a poor correlation with observations in the low-latitude
region when they calibrated their glacier model using Climatic Research Unit (CRU) data (Mitchell and Jones, 2005). They
attributed that to the fact that sublimation was not included in their model,
a process which is important for the mass balance of tropical glaciers. Our
mass balance model includes sublimation, so it is possible the WFDEI data
over tropical glaciers are too warm. The WFDEI data are based on the ERA-Interim
reanalysis in which air temperature has been constrained using CRU data. The CRU
data comprise temperature observations which are sparse in regions where
tropical glaciers are located. Furthermore, the quality of the WFDEI data
will depend on the performance of the underlying ECMWF model. In central
Europe some of the poor correlations with observations are caused by the
Maladeta glacier in the Pyrenees (Fig. 3), which is a small glacier with an
area of 0.52 km2 (WGMS, 2017). When this glacier is excluded from the
analysis the correlation coefficient increases from 0.26 to 0.35 and the RMSE
decreases from 2.03 to 1.73 m of water equivalent per year.
Best parameter sets for each RGI6 region. The regions are ranked from
the lowest to the highest RMSE. There are no observed profiles for Iceland
and the Russian Arctic, so the global mean parameter values are used (bold) for
the future simulations.
Regionαvis,snowαnir,snowαvis,iceαnir,iceγtempγprecipγwindK km-1% per 100 mArctic Canada south0.940.770.680.538.3162.15Arctic Canada north0.960.700.490.124.271.10Greenland0.950.720.410.198.0151.07Alaska0.880.650.560.278.2161.32South Asia east0.910.730.670.565.391.55South Asia west0.990.730.600.304.0241.69Western Canada and the US0.970.640.450.269.382.29Central Asia0.940.740.690.508.1191.40North Asia0.940.740.690.508.1191.40Central Europe0.830.630.590.355.871.83Svalbard0.950.760.540.359.0141.02Caucasus and the Middle East0.900.710.530.288.353.32Scandinavia0.950.760.540.359.0141.02New Zealand0.940.740.690.508.1191.40Low latitudes0.940.740.690.508.1191.40Southern Andes0.950.760.540.359.0141.02Mean0.930.720.580.377.55141.56
Root-mean-square error (RMSE), correlation coefficient (r),
Nash–Sutcliffe efficiency coefficient (NS), mean bias (Bias), and the number
of elevation-band mass balance observations (No. of obs) for RGI6 regions. The
regions are ranked from the lowest to the highest RMSE.
RegionRMSErNSBiasNo. of obs m w.e. yr-1 m w.e. yr-1Arctic Canada south0.960.610.110.1072Arctic Canada north1.060.19-0.440.521332Greenland1.090.660.140.1490Alaska1.360.650.380.06217South Asia east1.410.15-0.34-0.1981South Asia west1.530.620.38-0.09168Western Canada and the US1.730.690.41-0.40916Central Asia1.810.22-1.15-0.512519North Asia1.950.45-0.04-0.211335Central Europe2.030.26-0.650.309561Svalbard2.160.36-6.86-1.211647Caucasus and the Middle East2.230.30-0.890.33687Scandinavia2.400.530.200.6710 617New Zealand2.570.58-0.30-1.0945Low latitudes3.060.36-0.71-0.881016Southern Andes3.330.26-12.33-2.87118Global2.160.40-0.110.1930 421Model validation
The calibrated mass balance is validated against summer and winter
elevation-band specific mass balance for each region where data are available
(Fig. 4). For all regions, except Scandinavia in the summer, negative
Nash–Sutcliffe numbers are calculated for winter and summer
elevation-dependent mass balance (Table 4). The negative numbers arise
because the bias in the model is larger than the variance of the
observations. There are negative biases for nearly all regions, implying that
melting is overestimated in the summer and accumulation is underestimated in
the winter. This means that future projections of volume loss presented in
Sect. 4.2 might be overestimated.
Comparison between modelled and observed elevation-band specific
mass balance for winter (grey triangles) and summer (black dots). The
modelled mass balance is calculated using the tuned regional parameters from
the calibration procedure.
Winter (bold) and summer number of elevation-band mass
balance observations (No. of obs), root-mean-square error (RMSE), correlation
coefficient (r), Nash–Sutcliffe efficiency coefficient (NS), and mean bias
(Bias).
RegionNo. of obs RMSE m w.e. yr-1rNS Bias m w.e. yr-1Alaska1271271.822.430.380.76–7.54-2.88–0.29-2.09Western Canada and the US7677291.762.960.530.72–2.68-2.25–0.34-2.28Arctic Canada north49500.081.090.090.86–0.94-5.010.04-0.79Greenland28360.783.450.330.81–11.31-11.13–0.11-2.40Svalbard112211260.612.250.180.66–3.90-12.59–0.38-1.84Scandinavia534710 6791.521.690.610.78–0.780.32–0.68-0.77North Asia8548281.544.150.710.20–0.40-3.81–1.08-2.63Central Europe549648041.212.770.120.33–5.83-4.63–0.02-1.11Caucasus & the Middle East6026771.392.30–0.120.55–1.15-0.94–0.23-1.18Central Asia177817511.344.870.210.31–10.57-16.92–0.19-4.23Southern Andes34224.194.11–0.81-0.08–36.73-55.59–3.81-2.36New Zealand45453.376.170.420.32–10.63-17.82–0.01-5.87Global16 24920 8741.382.160.490.78–1.160.11–0.37-0.92
The reason for the negative bias is because the model underestimates the
precipitation and therefore the accumulation part of the mass balance is
underestimated. This is because our approach to correcting the coarse-scale
gridded precipitation for orographic effects is simple. We use a single
precipitation gradient for each RGI6 region and do not apply a bias
correction. A bias correction is often recommended because precipitation is
underestimated in coarse-resolution datasets. Gauging observations are sparse
in high-mountain regions and snowfall observations can be susceptible to
undercatch by 20 %–50 % (Rasmussen et al., 2012). Our precipitation
rates are generally too low because we do not bias-correct the precipitation.
Other studies use a bias correction that varies regionally (Radić and
Hock, 2011; Radić et al., 2014; Bliss et al., 2014). In those studies,
the precipitation at the top of the glacier was estimated using a bias
correction factor kp. The decrease in precipitation from the top
of the glacier to the snout was calculated using a precipitation gradient. To
account for the fact that the mass balance of maritime and continental
glaciers responds differently to precipitation changes, kp was
related to a continentality index. Our motivation for using a single
precipitation gradient for each RGI6 region and no bias correction was to
test the simplest approach first; however the resulting biases suggest that
this approach could be improved.
The impact of underestimating the precipitation is that we simulate negative
mass balance in winter at some observational sites (Figs. 5a and 4). To
demonstrate this, we compare the mass balance components for two glaciers:
the Leviy Aktru in the Russian Altai Mountains, which has negative mass
balance in the winter, and Kozelsky glacier in northeastern Russia, which has
no negative mass balance in the winter (See Fig. S9). Both glaciers are in
the north Asia RGI6 region, so they have the same tuned parameters for mass
balance. The simulated winter accumulation rates are much lower at Leviy
Aktru glacier than Kozelsky glacier, leading to negative mass balance at the
lowest three model levels below 2750 m.
Simulated and observed elevation-dependent winter mass balance when
grid boxes with a glacier area of less than 100, 300, and 500 km2 are
excluded. The colour identifies the RGI6 regions shown in Fig. 2. The RMSE,
correlation coefficient, and number of glaciers are listed.
Simulated and observed elevation-dependent summer mass balance when
grid boxes with a glacier area of less than 100, 300, and 500 km2 are
excluded. The colour identifies the RGI6 regions shown in Fig. 2. The RMSE,
correlation coefficient, and number of glaciers are listed.
The simplistic treatment of the precipitation lapse rate also leads to
instances in which the model simulates positive mass balance in the summer at
some locations (Figs. 6a and 4). We show the summer mass balance components
for the same two glaciers in Fig. S10. Positive mass balance is simulated at
Kozelsky glacier because accumulation exceeds the melting. This suggests
that the precipitation gradient (19 % per 100 m for north Asia) is overly
steep in the summer at this location.
Another reason we underestimate the accumulation is due to the partitioning
of rain and snow based on an air temperature threshold of 0 ∘C. The
0 ∘C threshold is likely too low, resulting in an underestimate of
snowfall. When precipitation falls as rain or snow it adds liquid water or
ice to the snowpack. The specific heat capacity of the snowpack is a function
of the liquid water (Wk) and ice content (Ik) in each layer (k)
Ck=IkCice+WkCwater,
where Cice=2100 JK-1 kg-1 and Cwater=4100 JK-1 kg-1. The liquid water content is limited by the
available pore space in the snowpack; therefore changes in the snowfall (ice
content) control the overall heat capacity. The underestimate in the ice
content reduces the heat capacity, which causes more melting than observed.
Other modelling studies have used higher air temperature thresholds:
1.5 ∘C (Huss and Hock, 2015; Giesen and Oerlemans, 2012),
2 ∘C (Hirabayashi et al., 2010), and 3 ∘C (Marzeion et al.,
2012). An improved approach would use the wet-bulb temperature to partition
rain and snow, which would include the effects of humidity on temperature.
Alternatively, a spatially varying threshold based on precipitation
observations could be used. Jennings et al. (2018) showed, by analysing
precipitation observations, that the temperature threshold varies spatially
and is generally higher for continental climates than maritime climates.
Winter mass balance is simulated better than summer mass balance, which is
seen by the lower root-mean-square errors for winter in Table 4. Furthermore,
the biases are larger in the summer than in the winter (Table 4). It is
likely that the simple albedo scheme, which relates albedo to the density of
the snowpack surface, performs better in the winter when snow is accumulating
than in summer when there is melting. Figures 5b–d and 6b–d show the
winter and summer mass balances for all observation sites when area
thresholds of 100, 300, and 500 km2 are applied to the validation. There
is an improvement in the simulated summer mass balance when the glaciated
area increases. This is seen by the improved correlation in Fig. 6d in which
the validation is repeated but only grid boxes with a glaciated area greater
than 500 km2 are considered. This indicates the model is better at
simulating summer melting over regions with a large ice extent than over
regions with a small glaciated area.
List of high-end climate change CMIP5 models that are downscaled
using HadGEM3-A. The years when the CMIP5 models pass +1.5,
+2, and +4∘C global average warming relative to the
pre-industrial period are shown.
Glacier volume projections are made for all regions, excluding Antarctica,
for a range of high-end climate change scenarios. This is defined as climate
change that exceeds 2 and 4 ∘C global average warming, relative to
the pre-industrial period (Gohar et al., 2017). Six models fitting this
criterion were selected from the Coupled Model Intercomparison Project Phase
5 (CMIP5). A new set of high-resolution projections were generated using the
HadGEM3-A Global Atmosphere (GA) 6.0 model (Walters et al., 2017). The sea
surface temperature and sea ice concentration boundary conditions for
HadGEM3-A are supplied by the CMIP5 models. All models use the RCP8.5
“business as usual” scenario and cover a wide range of climate
sensitivities, with some models reaching 2 ∘C global average warming
relative to the pre-industrial period, quickly (IPSL-CM5A-LR) or slowly
(GFDL-ESM2M) (Table 5). The models also cover a range of extreme wet or dry
climate conditions. This is important to consider for glaciers in the central
and eastern Himalayas, which accumulate mass during the summer months due to
monsoon precipitation (Ageta and Higuchi, 1984) and because future monsoon
precipitation is highly uncertain in the CMIP5 models (Chen and Zhou, 2015).
The HadGEM3-A data are bias-corrected using a trend-preserving statistical
bias method that was developed for the first Inter-Sectoral Impact Model
Intercomparison Project (ISIMIP) (Hempel et al., 2013). This technique uses
WATCH forcing data (Weedon et al., 2011) to correct offsets in air pressure,
temperature, longwave and shortwave downward surface radiation, rainfall,
snowfall, and wind speed but not specific humidity. The method adjusts the
monthly mean and daily variability in the GCM variables but still preserves
the long-term climate signal. The HadGEM3-A was bilinearly interpolated from
its native resolution of N216 (∼60 km), onto a 0.5∘ grid, to
match the resolution of the WATCH forcing data, which were used for the bias
correction. The daily bias-corrected surface fields from the HadGEM3-A are
used to run JULES offline to calculate future glacier volume changes. The
bias correction was only applied to data up until the year 2097, which means
the glacier projections terminate at this year. A flow chart of the
experimental setup is shown in Fig. 7. The HadGEM3-A climate data were
generated and bias-corrected for the High-End cLimate Impact and eXtremes
(HELIX) project.
Flow chart showing the experimental setup to calculate future
glacier volume. * The bias correction method is described by Hempel et
al. (2013).
Percentage ice volume loss, relative to the initial volume (ΔV), and ice loss in millimetres of sea level equivalent (SLE) for the end of the
century (2097). Percentage volume losses are shown for low, medium, and high
elevation ranges as well as for all elevations. The data show the
multi-model mean ± 1 standard deviation. The conversion of volume to SLE
assumes an ocean area of 3.618×108 km2. The initial area and
volume from the Randolph Glacier Inventory version 6 are listed in columns 1
and 2.
Glaciated areas are divided into 18 regions defined by the RGI6 with no
projections made for Antarctic glaciers because the bias correction technique
removes the HadGEM3-A data from this region. JULES is run for this century
(2011 to 2097) using the best regional parameter sets for mass balance found
by the calibration procedure (Table 2). No observations were available to
determine the best parameters for Iceland and the Russian Arctic; therefore
global mean parameter values are used for these regions. End of the century
volume changes (in percent) are found by comparing the volume at the end of the
run (2097) to the initial volume calculated from the RGI6. Regional volume
changes expressed in percent for low (0–2000 m), medium (2250–4000 m),
high (4250–9000 m), and all elevation ranges (0–9000 m) are listed in
Table 6. The total volume loss over all elevation ranges is also listed in
millimetres
of sea level equivalent in Table 6 and plotted in Fig. 10. Maps of the
percentage volume change at the end of the century, relative to the initial
volume, are contained in the Supplement in Figs. S1–S7.
Regional glacier volume projections using the HadGEM3-A ensemble of
high-end climate change scenarios.
A substantial reduction in glacier volume is projected for all regions
(Fig. 8). Global glacier volume is projected to decrease by 64±5 % by
end of the century, for which the value corresponds to the multi-model mean ±
1 standard deviation. The regions which lose more than 75 % of their
volume by the end of the century are Alaska (-89±2 %), western
Canada and the US (-100±0 %), Iceland (-98±3 %), Scandinavia
(-98±3 %), the Russian Arctic (-79±10 %), central Europe (-99±0 %), Caucasus (-100±0 %), central Asia (-80±7 %), South
Asia west (-98±1 %), South Asia east (-95±2 %), low latitudes
(100±0 %), southern Andes (-98±1 %), and New Zealand (-88±5 %). The HadGEM3-A forcing data show these regions experience a strong
warming. In most regions this is combined with a reduction in snowfall
relative to the present day, which drives the mass loss (Fig. 9). Regions
most resilient to volume losses are Greenland (-31±5 %) and Arctic
Canada north (-47±3 %). In the case of Arctic Canada north, snowfall
increases relative to the present day, which helps glaciers to retain their
mass. There is a rapid loss of low-latitude glaciers, which has also been
found by other global glacier models (Marzeion et al., 2012; Huss and Hock,
2015). Our model overestimates the melting of these glaciers for the
calibration period (Fig. 3), so this result should be treated with a degree
of caution. Some of the high-latitude regions, particularly Alaska, western
Canada and the US, Svalbard, and north Asia, experience very large volume
increases at their upper elevation ranges. This would be reduced if the model
included glacier dynamics, because ice would be transported from higher
elevations to lower elevations. The ensemble mean global sea level equivalent
contribution is 215.2±21.3 mm. The largest contributors to sea level
rise are Alaska (44.6±1.1 mm), Arctic Canada north and south (34.9±3.0 mm), the Russian Arctic (33.3±4.8 mm), Greenland (20.1±4.4), high-mountain Asia (combined central Asia and South Asia east and west),
(18.0±0.8 mm), southern Andes (14.4±0.1 mm), and Svalbard (17.0±4.6 mm). These are the regions which have been observed by the Gravity
Recovery and Climate Experiment (GRACE) satellite to have lost the most mass
in the recent years (Gardner et al., 2013).
Regional temperature and snowfall changes relative to the present day
(2011–2015) from the HadGEM3-A ensemble over glaciated grid points. The
ensemble mean is shown in the solid line and the range of model projections
are shown in the shaded regions.
To investigate which parts of the energy balance are driving the future melt
rates, we show the energy balance components averaged over all regions and
all elevation levels in Fig. 11. Future melting is caused by a positive net
radiation of approximately 30 W m-2 that is sustained throughout the
century. This is comprised of 18 W m-2 net shortwave radiation, 3 W m-2
net longwave radiation, 5 W m-2 latent heat flux, and 4 W m-2 sensible
heat flux. The largest component of the radiation for melting comes from the
net shortwave radiation. The upward shortwave radiation comprises direct
and diffuse components in the VIS and NIR wavelengths. The
VIS albedo decreases because melting causes the ice surface to darken. In
contrast, the NIR albedo increases because the ice is heating up,
emitting radiation in the infrared part of the spectrum.
(a) Regional percentage volume losses at the end of the
century (2097), relative to the initial volume and (b) volume losses
expressed in sea level equivalent contributions. The large red dots represent
the multi-model mean and the small black dots are the individual HadGEM3-A
model runs.
Ensemble mean energy balance components averaged over all glaciated
regions and all elevation bands when the model is forced with HadGEM3-A
data.
The downward and upward longwave radiation are increasing in the future; however,
the net longwave radiation contribution to the melting is small. The downward
longwave radiation increases because of the T4 relationship with air
temperature, whereas the upward longwave radiation increases because the
glacier surface is warming. The latent heat flux from refreezing of meltwater and the sensible heat from surface warming are also small components
of the net radiation balance.
Mass balance components
In this section we examine how the surface mass balance components vary with
height and how this will change in the future. Figure 12 shows the
accumulation, refreezing, and melting contributions to mass balance averaged
over low, medium, and high elevation ranges for the period 1980–2000.
Sublimation is excluded because its contribution to mass balance is
relatively small. As expected, there is more melting in the lower elevation
ranges and more accumulation at the higher elevation ranges. The refreezing
component, which includes refreezing of meltwater and elevated adjusted
rainfall, shows no clear variation with height. This is because the
refreezing component can both increase and decrease with height. Refreezing
can increase towards lever elevations because there is more rain and melted
water. It can also decrease if the snowpack is depleted or if there is not
enough pore space to hold water because previous refreezing episodes have
converted the firn into solid ice. The largest accumulation rates occur in
Alaska (5.3 m w.e. yr-1) and western Canada and the US
(7.3 m w.e. yr-1) between 4250 and 9000 m and the largest melt rates are
found in the Caucasus and Middle East (-7.4 m w.e. yr-1) and the low
latitudes (-7.6 m w.e. yr-1).
Modelled annual surface mass balance components: accumulation,
refreezing, and melting for the period 1980–2000 for RGI6 regions. To make
the figure easier to read, melting is given as a positive sign and sublimation
is excluded because its contribution is very small. Mass balance components
are averaged over low (0–2000 m), medium (2250–4000 m), and high
(4250–9000 m) elevation ranges.
Global mass balance components for three elevation ranges. The
historical period is calculated using the WFDEI data and the future period is
the multi-model means of all GCMs. The bars show the averages over the time
periods for accumulation, refreezing, melt, and mass balance rates.
Figure 13 shows how the global annual mass balance
components vary with time for low, medium, and high elevation ranges.
There is a reduction in accumulation and refreezing at all elevation ranges
towards the end of the century. Melt rates decrease at medium and high
elevation ranges because glacier mass is lost at these altitudes; therefore
less ice is available to melt (see Fig. S8 for the future cumulated mass
balances as a function of height). Melt rates are constant at the low
elevation ranges because there remain substantial quantities of ice
available to melt at the end of the century in Greenland, Arctic Canada north
and south, Svalbard, and the Russian Arctic. At high elevations mass balance is
reduced from -2.2 m w.e. yr-1 (-177 Gt yr-1) during the
historical period (1980–2000) to -0.35 m w.e. yr-1
(-28 Gt yr-1) by the end of the century (2080–2097). Similarly, for
the medium elevation ranges mass balance decreases from
-0.56 m w.e. yr-1 (-26 Gt yr-1) to
-0.24 m w.e. yr-1 (-11 Gt yr-1).
Parametric uncertainty analysis
The standard deviation in the volume losses presented above are relatively
small. This is because only a single GCM was used to downscale the CMIP5
data (HadGEM3-A). The uncertainty in the ensemble mean reflects the impact
of the different sea surface temperature and sea ice concentration boundary
conditions, provided by the CMIP5 models, on the HadGEM3-A climate. Other
sources of uncertainty in the projections can arise from the calibration
procedure, observational error, initial glacier volume and area, and
structural uncertainty in the model physics. It is beyond the scope of this
paper to investigate all the possible sources of uncertainty on the glacier
volume losses. Instead we discuss the impact of parametric uncertainty in
the calibration procedure in the following section.
In the calibration procedure the mass balance was tuned to obtain an optimal
set of parameters for each RGI6 region; however, there may be other plausible
parameter sets that perform equally well (i.e. for which the RMSE between the
observations and the model is small). The principle of “equifinality”, in
which the end state can be reached by many potential means, is important to
explore because some parameters may compensate for each other. For example,
the same mass balance could be reached by increasing the wind scale factor,
which enhances melting, or decreasing the precipitation gradient, which would
reduce accumulation. To identify the experiments that perform equally well,
we identify where there is a step change in the gradient of the RMSE for each
RGI6 region. A similar approach was used by Stone et al. (2010) to explore
the uncertainty in the thickness, volume, and areal extent of the present-day
Greenland ice sheet from an ensemble of Latin hypercube experiments. The step
change in the RMSE is identified using the change-point detection algorithm
called findchangepts (Rebecca et al., 2012; Lavielle, 2005) from the MATLAB
signal processing toolbox. The algorithm is run to find where the mean of the
top 10 experiments (excluding the optimal experiment) changes the most
significantly. For each RGI6 region the step changes in the RMSE are shown in
Fig. 14.
Calibration experiments ranked according the root-mean-square error
between simulated and observed mass balance profiles for RGI6 regions. There
are 198 experiments but only the top 30 have been plotted to make the figure
easier to read. The red dots indicate experiments that perform equally well.
JULES is rerun for each of the downscaled CMIP5 experiments and for each
parameter set that is defined as performing equally well (see Table S1 in the
Supplement for a list of the parameter sets that perform equally well). The
volume losses expressed in millimetres of sea level equivalent are shown in Fig. 15.
The effects of the parametric uncertainty on the volume losses vary
regionally, with the largest impact found for central Europe and Greenland.
Regional volume losses including parametric uncertainty in the calibration are
summarised in Table 7. Including calibration uncertainty in this way gives an
upper bound of 247.3 mm of sea level equivalent volume loss by the end of the
century.
Regional volume losses expressed in sea level equivalent including
parametric uncertainty in mass balance parameters. The solid lines show the
volume loss for each downscaled CMIP5 GCM using the optimum parameter sets.
The dashed lines are for runs which use other equally “good” parameter sets
based on the RMSE.
Regional ensemble mean, minimum, and maximum volume losses for 2097 in
sea level equivalent (mm) when the present-day mass balance is calibrated
in different ways. Columns 1–3: mass balance is calibrated by minimising the
RMSE. Columns 4–6: mass balance is calibrated using an ensemble of equally
plausible RMSE values. Columns 7–9: mass balance is calibrated by minimising
the RMSE, minimising the bias, and maximising the correlation coefficient.
Optimum parameter Equally plausible RMSE Extra performance metrics SLEmeanSLEminSLEmaxSLEmeanSLEminSLEmaxSLEmeanSLEminSLEmaxAlaska44.642.545.843.840.545.843.638.246.3Western Canada & the US2.82.82.82.82.82.82.82.82.8Arctic Canada north35.831.839.132.824.339.137.222.361.8Arctic Canada south18.114.820.817.913.721.120.314.824.1Greenland20.112.925.720.46.730.223.514.031.8Iceland9.38.79.59.38.79.59.48.59.5Svalbard17.010.020.718.410.023.619.710.025.8Scandinavia0.60.60.60.60.60.60.60.60.6Russian Arctic33.325.739.233.325.739.236.625.142.8North Asia0.30.30.30.30.20.40.30.30.4Central Europe0.30.30.30.30.10.30.30.20.3Caucasus & the Middle East0.20.20.20.20.20.20.20.20.2Central Asia8.06.78.88.05.99.38.15.99.5South Asia west8.18.08.27.86.78.27.97.18.2South Asia east1.91.92.01.81.52.01.81.62.0Low latitudes0.20.20.20.20.20.20.20.20.2Southern Andes14.414.214.514.414.214.614.414.214.6New Zealand0.10.10.20.10.10.20.10.10.2Global215.2181.5238.9212.6162.2247.3227.1166.1281.1Global SLEmax–SLEmin57.385.1115.0
Another way to explore the uncertainty in the volume projections caused by the
calibration procedure is to use different performance metrics to identify the
best parameter sets. In addition to using RMSE, we calculate the best parameter
sets by (1) minimising the absolute value of the bias and (2) maximising the
correlation coefficient. The best regional parameter sets are different
depending on the choice of performance metric used (see Tables S2 and S3 in
the Supplement). For 12 regions, minimising the bias results in higher
precipitation lapse rates than when RMSE values are used to select
parameters. This suggests the bias in many regions is caused by
underestimating the precipitation lapse rates. As discussed above, this could
be due to the fact the grid box mean WFDEI precipitation was not bias-corrected. Glacier volume projections are generated by repeating the
simulations using these two additional performance metrics to identify the best
parameter sets. The uncertainty in the global volume loss when the extra
performance metrics are used is approximately double the uncertainty arising
from the different climate forcings (Fig. 16, Table 7). When extra
performance metrics are used, the upper bound volume loss increases to
281.1 mm of sea level equivalent by the end of the century.
Multi-model mean (black line) and ensemble spread (shaded) global
volume loss in sea level equivalent. Panel (a) shows the volume loss when
optimum parameter sets are selected by minimising the RMSE and
(b) is volume loss when optimum parameter sets are selected using
additional performance metrics (minimising RMSE, minimising the bias, and
maximising the correlation coefficient).
Comparison with other studies
We compare our end-of-the-century volume changes (excluding parametric
uncertainty) to two other published studies which used the CMIP5 ensemble
under the RCP8.5 climate change scenario (Huss and Hock, 2015; Radić et
al., 2014). Other studies exist, but these include the volume losses from
Antarctic glaciers, which makes a direct comparison difficult (Marzeion et
al., 2012; Slangen et al., 2014; Giesen and Oerlemans, 2013; Hirabayashi et
al., 2013). Huss and Hock (2015) listed regional percentage volume change and
sea level equivalent values in their study while Radić et al. (2014)
listed sea level equivalent values only (see the comparison of Tables S4 and S5
in the Supplement).
Our end-of-the-century percentage volume losses compare reasonably well to
Huss and Hock (2015) for central Europe, Caucasus, South Asia east,
Scandinavia, the Russian Arctic, western Canada and the US, Arctic Canada north,
north Asia, central Asia, low latitudes, and New Zealand but are significantly
higher in the southern Andes, Alaska, Iceland, and Arctic Canada south. The
uncertainty in our percentage volume losses is smaller than that of Huss and
Hock (2015) because we only use a single GCM to downscale the CMIP5
experiments while Huss and Hock (2015) use 14 CMIP5 GCMs.
We estimate the end-of-century global sea level contribution, excluding
Antarctic glaciers, to be 215±20 mm, which is higher than 188 mm
(Radić et al., 2014) and 136±23 mm (Huss and Hock, 2015) caused
mainly by greater contributions from Alaska, southern Andes, and the Russian
Arctic. These three regions are discussed in turn.
For the southern Andes our estimates are approximately double (14.4 mm)
those
of the other studies (5.8 mm, Huss and Hock, 2015; 8.5 mm, Radić et
al., 2014). This region has the largest negative bias in the calibrated
present-day mass balance (-2.87 m w.e. yr-1; see Table 3). To explore
the effects of correcting the calibration bias on the ice volume projections,
we subtract the bias values listed in Table 3 from the future annual mass
balance rates. Each grid box is assumed to have the same regional mass balance
bias. The bias-corrected volume losses are listed in Table S5 in the
Supplement. For the southern Andes, the volume losses are much closer to the
other studies (7.6 mm) when the bias is corrected. The impact is less for
the other regions where the biases are smaller. For the Russian Arctic our
volume losses are higher than the other studies but that should be
interpreted with caution because there were no observations available in this
region to obtain a tuned parameter set (global mean parameters were used
instead). In Alaska the bias in annual mass balance is small
(0.06 m w.e. yr-1), so correcting the bias has little effect on the
volume loss projection for this region. Applying the bias correction
increases the global volume loss from 215±20 to 223±20 mm;
therefore the difference between our model and the other studies cannot be
explained by the bias in the calibration.
It is likely that our sea level equivalent contributions are higher than the other studies
because the climate forcing data are different. The HadGEM3-A model uses
boundary conditions from a subset of RCP8.5 CMIP5 models with the highest
warming levels. Furthermore, the HadGEM3-A data have a higher resolution
(approximately 60 km) than the CMIP5 data, which were used by the other two
studies. This means our model should, in theory, be more accurate at
reproducing regional patterns in precipitation and temperature over complex
terrain, which is important for calculating mass balance.
Discussion
The robustness of the glacier projections depends on how well the model can
reproduce present-day glacier mass balance. Our calibrated seasonal mass
balance contains a negative bias (accumulation is underestimated, and melting
is overestimated), which suggests the projections of volume loss might be
overestimated. One of the main shortcomings of the calibration and validation
of mass balance is that only a single type of observations is used. These data
were used because we wanted to ensure the model could reproduce variations in
accumulation and ablation with height when the elevated tiling scheme was
introduced. Point mass balance observations are affected by local factors
such as aspect, avalanching, and debris cover and there is a possibility that
these local factors affect parameter sets chosen for the entire RGI region. This
could be improved by using observations from satellite gravimetry and
altimetry, such as that described by Gardner et al. (2013), to obtain a
quantitative estimate of the model performance at the regional scales.
One of the notable differences between our study and other global glacier
models is that our tuned precipitation lapse rates are very high, for
example, 24 % per 100 m for South Asia west and 19 % per 100 m for central
Asia. Other models have used lower precipitation lapse rates
(1–2.5 % per 100 m, Huss and Hock, 2015; 3 % per 100 m, Marzeion et al.,
2012), but they also bias-correct precipitation by multiplying by a scale
factor. This scaling factor can be considerably high. Giesen and
Oerlemans (2012) found that precipitation needed to be multiplied by a factor
of 2.5 to obtain good agreement with mass balance observations. Radić and
Hock (2011) derived, through calibration of present-day mass balance, a
precipitation scale factor of as high as 5.6 for Tuyuksu and Golubina
glaciers in the Tien Shan. Our lapse rates are high because we do not bias-correct the precipitation using a multiplication factor for the present day.
For the future GCM data the grid box mean precipitation was bias-corrected
using the ISIMIP technique. The negative bias that we obtain when validating
the present-day mass balance suggests that snowfall is underestimated in our
model. A future study using this model could test whether bias-correcting the
precipitation before applying the lapse rate correction improves the
simulated mass balance.
This is the first attempt to implement a glacier scheme into JULES and so the
model has many limitations. One of the key shortcomings is that glacier
dynamics is not included (glacier area does not vary). The transport of ice
from higher elevations to lower elevations is not included. This process
could be included in future work by adding a volume–area scaling scheme
(Bahr et al., 1997) or a thickness parameterisation based on glacier slope
(Marshall and Clarke, 2000). Volume–area scaling has been used
to model glacier dynamics in coarse-resolution (0.5∘) models in which
all glaciers in a grid box are represented by a single ice body (Kotlarski et
al., 2010; Hirabayashi et al., 2010). The current configuration of elevated
glaciated and unglaciated tiles in JULES makes it well suited to a
volume–area scaling model. This would be implemented by growing (shrinking)
the elevated glaciated tiles if mass balance is positive (negative) at each
elevation band. In the case in which the elevated ice tile grows the unglaciated
tile would shrink at that elevation band or vice versa.
The volume–area scaling law has been used successfully to model the dynamics
of individual glaciers (Radić et al., 2014; Giesen and Oerlemans, 2013;
Marzeion et al., 2012; Slangen et al., 2014) but has some limitations when
applied to coarse models in which glaciers are consolidated into a single
grid box. The volume–area scaling law relates volume to area using a constant
scaling exponent, which is typically derived from a small sample of glacier
observations (Bahr et al., 1997). One of the drawbacks is that the law is
non-linear, meaning the exponent derived from individual glaciers would
overestimate the volume of a large ice grid box such as in our model
(Hirabayashi et al., 2013). Furthermore, the exponent may not accurately
represent the volume–area relationship in other geographical regions. To
overcome these issues a spatially variable scaling exponent could be created
using the newly available 0.5∘ data on volume and area contained in
the RGI6.
Another limitation of the model, which may be problematic for same
applications, is that the grid box mean precipitation is not conserved when
precipitation is adjusted for elevation. This correction was necessary to
obtain enough accumulation in the mass balance at high elevations. One way to
conserve water mass would be to reduce the precipitation onto the
non-glaciated area of the grid cell. This would represent horizontal mass
movement within the grid box from windblown snow and avalanching.
A further limitation of the model is the simple treatment of katabatic winds,
which is modelled by scaling the synoptic wind speed. This could be improved
by parameterising katabatic winds based on the grid box slope and the
temperature difference between the glacier surface and the air temperature
using the Prandtl model (Oerlemans and Grisogono, 2002). Another drawback of
the model is the coarse resolution of the grid boxes, which makes it unfeasible
to include some process that affects local mass balance such as hillside
shading, avalanching, blowing snow, and calving. The model could, however, be
run on a finer resolution using higher-resolution climate forcing data.
While this modelling projects considerable reduction in glacier mass for all
mountain ranges by the end of this century, it is clear that many of the
world's mountain glaciers will evolve in ways that are currently difficult to
model. For instance, paraglacial processes during deglaciation lead to
enhanced rock falls and debris flows from deglaciating mountain slopes and
these deliver rock debris to glacier surfaces. This produces debris-covered
glaciers and these are common in many mountain regions, including in Alaska,
the arid Andes, central Asia, and in the Hindu Kush–Himalayas. Thick debris cover
(decimetres to metres) limits ice ablation (e.g. Lambrecht et al., 2011;
Pellicciotti et al., 2014; Lardeux et al., 2016; Rangecroft et al., 2016) and
reverses the mass balance gradient, with comparatively higher ablation rates
up-glacier than at the debris-covered terminus. This significantly influences
glacier dynamics (Benn et al., 2005), and with inefficient sediment
evacuation eventually leads to the transition from debris-covered glaciers to
rock glaciers (e.g. Monnier and Kinnard, 2017). In the context of continued
climate warming, the transition from ice glaciers to rock glaciers may
enhance the resilience of the mountain cryosphere (Bosson and Lambiel, 2016).
As a result, better assessment of the response of the mountain cryosphere to
climate warming will depend on a clearer understanding of glacier–rock
glacier relationships.
There are three key strengths to the JULES glacier model. Firstly, we include
variations in orography within a climate grid box, which is important to
calculate elevation-dependent glacier mass balance. Kotlarski et al. (2010)
developed a glacier scheme for the REMO regional climate model by lumping
glaciers into 0–5∘ grid boxes in an approach similar to ours, but they
did not have a representation of subgrid orography. Instead glacier grid boxes
received double the grid box mean snowfall, glacier ice had a fixed albedo, and
a constant lapse rate was applied to adjust temperatures. They concluded that
to reproduce mass balance trends over the Alps, the scheme needed to include
subgrid variability in atmospheric parameters within a grid box.
Secondly, the model uses a full energy balance scheme to calculate glacier
melting. This is a more physically based approach than the widely used
temperature index models, which relate melting to temperature using a degree
day factor (DDF). The DDF lumps all the energy balance components into a
single number, meaning that the effects of changing wind speed, cloudiness, and
radiation on melt rates cannot be considered. Changes in solar radiation can
be an important driver of melting. Huss et al. (2009) studied long-term mass
balance trends for a site in the Alps and showed that melting was stronger
during the 1940s than in recent years despite more warming. This was because
summer solar radiation was higher during the 1940s. Moreover, temperature
index models have been found to be less accurate with increasing temporal
resolution (for example on daily time steps) (Hock, 2005). In this paper, we
present a brief analysis of the future global energy balance fluxes, but how
the fluxes vary for individual regions and elevation levels could be
investigated further. Finally, the glacier scheme is coupled to a land
surface model, which presents opportunities for further studies. For
instance, the model could be used to investigate the impact of climate change
on river discharge in glaciated catchments in Asia, South America, or the
Arctic.
Conclusions
The first aim of this study was to add a glacier component to JULES to
develop a fully integrated model to simulate the interactions among
glacier mass balance, river runoff, water abstraction by irrigation, and crop
production. To do this we added two new surface types to JULES: elevated
glaciated and unglaciated tiles. This allows us to calculate
elevation-dependent mass balance, which can be used to study the response of
glaciers to climate change. Glacier volume was modelled by growing or
shrinking the snowpack, using the elevation-dependent mass balance, but
glacier dynamics was not included. Present-day mass balance was calibrated
by tuning albedo, wind speed, temperature, and precipitation lapse rates to
obtain a set of regionally tuned parameters which are then used to model
future mass balance. Winter and summer mass balances are reproduced
reasonably well for regions where the glaciated area is large; however, the
model performs poorly for small glaciers, particularly in the summer. The
fully integrated model is potentially a useful tool for studying the impacts of climate change on water resources in glaciated catchments.
The second aim of this study was to make glacier volume projections for the
future under a range of high-end climate change scenarios. The ensemble mean
volume loss ± 1 standard deviation is -64±5 % for all glaciers
excluding those on the periphery of the Antarctic ice sheet. The small
uncertainties in the multi-model mean are caused by the sensitivity of
HadGEM3-A to the boundary conditions supplied by the CMIP5 models. Our end-of-the-century global volume loss is 215±20 mm, which is higher than
values reported by other studies. This is because we used a subset of CMIP5
models with the highest warming levels to drive the model and glacier
dynamics not included, which results in more mass loss than other studies
that include dynamics. Including parametric uncertainty in the calibration
procedure results in an upper bound global volume loss of 281.1 mm of sea level
equivalent by the end of the century. The projected ice losses will have an
impact on sea level rise and on water availability in glacier-fed river
systems.
The glacier scheme is included in JULES v4.7. The source code can be
downloaded by accessing the Met Office Science Repository Service (MOSRS)
(requires registration): https://code.metoffice.gov.uk/ (last access: 23 June 2017).
The code used for
this study is in https://code.metoffice.gov.uk/svn/jules/main/branches/dev/sarahshannon/vn4.7_va_scaling (last access: 23 June 2017).
The supplement related to this article is available online at: https://doi.org/10.5194/tc-13-325-2019-supplement.
SS wrote the paper and all the co-authors gave input for the writing. SS, RS, and AW contributed to the JULES source code.
MH created the 0.5∘ glacier area and thickness data from the RGI6 dataset. JC generated the high-resolution HadGEM3-A data and AK preformed the bias correction.
The authors declare that they have no conflict of
interest.
Acknowledgements
This research was funded by the European Union Seventh Framework Programme
FP7/2007-2013 under grant agreement no. 603864. We would like to
thank the Natural Environment Research Council (NERC) for the use of the
Joint Analysis System Meeting Infrastructure Needs (JASMIN) supercomputer
cluster. We wish to thank Ben Marzeion and the anonymous referee for their useful comments, which helped to improve the paper.Edited by: Christian
Beer
Reviewed by: Ben Marzeion and one anonymous referee
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