Introduction
Permafrost shapes approximately a quarter of the landmass of the Northern
Hemisphere and is thus one of the largest elements of
the terrestrial cryosphere. Permafrost occurs mainly in arctic regions which
will be strongly impacted by global warming. The recent and
predicted future warming of the global climate may lead to widespread thawing
which can trigger climatic feedbacks from local to global scale and severely
impact ecosystems, infrastructure and communities in the Arctic. Thawing
organic-rich permafrost is projected to spark substantial emissions of the
greenhouse gases CO2, CH4 and N2O
which may be relevant for future climate projections and
hereof derived mitigation strategies e.g.,. These processes are poorly represented in
the general circulation models (GCMs) used for the
Intergovernmental Panel on Climate Change report , but considerable
efforts are dedicated to better capturing the effects of permafrost thaw in future global assessments. Due to the large
thermal inertia of the frozen ground and associated long time periods
required for thawing, future projections critically depend on the knowledge
of current thermal ground conditions. However, the more than 15 years
old, but still widely used global permafrost map from the International
Permafrost Association features a very coarse scale
and lacks quantitative information on permafrost state variables, in
particular of ground temperatures. In order to improve such shortcomings,
derived a global high-resolution data set of permafrost probabilities based
on downscaled air temperatures from reanalysis data.
Permafrost is a thermally defined subsurface phenomenon. While satellite sensors
can map surface indicators of permafrost presence, such as landforms or vegetation
types, remote sensing technologies can not directly measure its physical state
variables, in particular ground temperature . Therefore,
monitoring and mapping of the ground thermal state is restricted to either direct point
observations or coarse-scale modeling using atmospheric circulation models.
However, there exist a variety of satellite data sets which can be employed
in numerical permafrost models to compute the thermal state of the ground, in
particular land surface temperature (LST) and snow water equivalent (SWE). In
a first proof-of-concept study, demonstrated the
potential of such concepts by forcing a transient ground thermal model at a spatial scale of 1 km by
time series of MODIS LST and downscaled GlobSnow SWE . While the agreement with measured in situ
data of ground temperatures and thaw depth is striking, the study also
highlights the considerable sensitivity of physically based approaches to
model parameters, which are generally not known for very large spatial
domains, e.g., an entire continent. On the other hand, field studies suggest
a considerable variability of ground temperatures at spatial scales much
smaller than 1 km e.g.,, which questions the
validity of a single model scenario per grid cell. Multi-scenario runs with
e.g., different snow depths and ground thermal properties (similar to tiling
approaches employed in GCMs) would be an elegant way to represent the
small-scale variability in a statistical way, but this implies a significant
increase in the computational demands if all combinations of model parameters
should be explored. In such a context, simple schemes with few parameters, such
as the modified Kudryavtsev or the the TTOP (temperature at the top of permafrost) approach
can offer advantages over more sophisticated models.
They have been developed to a state of operational maturity and are employed for
large-scale mapping of permafrost properties with a wide variety of input data
sets e.g.,.
In this study, we employ a simple semi-empirical equilibrium model
CryoGrid 1, based on the TTOP approach, with a small number of model
parameters in a statistical framework which is computationally efficient
enough to be applied for large spatial domains. We demonstrate high-resolution
statistical mapping of ground temperatures based on a combination of remotely
sensed land surface temperatures and reanalysis data. The model results are
benchmarked against measurements of ground temperatures in boreholes from the
“Thermal State of Permafrost” (TSP) data base
. The results suggest that
mapping of ground temperatures at continental scales is feasible, a variable
highly demanded by the scientific community, as well as policymakers and
industries in affected countries.
Modeling tools and satellite data sets
Study region and in situ data
The study focuses on the permafrost areas bordering the North Atlantic Ocean
which comprise a large gradient of ground temperatures, from permafrost-free
areas in Scandinavia to some of the coldest permafrost on Earth in northern Greenland and Ellesmere Island, Canada. In detail, the region ranges from the
Ural Mountains, Novaja Zemlja and Franz Josef Land in the east over
Scandinavia, Svalbard, Iceland and Greenland to the eastern parts of the
Canadian Archipelago. The area contains a wide range of permafrost
environments, from high-relief mountain ranges to wetlands and subarctic
mires underlain by permafrost, which makes it a well-suited test region for
a modeling scheme. In situ monitoring programs of ground temperatures in
boreholes have created a excellent record to which the model results
can be compared. In total, we employ 143 borehole temperatures in North America,
the Nordic region and western Russia (see Fig. ) from the “Thermal
State of Permafrost (TSP) Snapshot Borehole Inventory” .
In addition, regional-scale modeling studies have compiled maps of ground
temperatures and permafrost distribution at spatial scales of 1 km
e.g.,. The study is based on data sets from the 10-year
period 2003 to 2012, in which most of the validation data sets have been
compiled.
MODIS LST
The “Moderate Resolution Imaging Spectroradiometer” (MODIS) operationally
delivers remotely sensed land surface temperatures on global scale at
a spatial resolution of 1 km. The MODIS sensor is carried on board of
two satellites of NASA's “Earth Observing System”, Terra (launched in 2000)
and Aqua (launched in 2002). As such, a time series of more than 10 years is
available for the combined Terra/Aqua data set. For this study, we make use
of the level 3 products MOD11A1 (Terra) and MYD11A1 (Aqua) in the version 5.
They contain a day and a night value for LST each, so that four values per
day are available, thus in principle capturing the diurnal temperature cycle.
Cloudy regions are automatically detected and removed by the MODIS cloud mask
. In practice, frequent cloudiness leads to a drastic reduction of the data
density with prolonged periods without measurements. To cover the study
region, in total 16 MODISL LST tiles with an area of
1200km×1200 km each were employed (h15v01, h15v02,
h15v03, h16v00, h16v01, h16v02, h17v00, h17v01, h17v02, h18v00, h18v01,
h18v02, h18v03, h19v01, h19v01, h19v02, h20v02). For each of the tiles, a 10-year period from 2003 to 2012 was evaluated, so that more than 116 000
individual files were processed.
While the target accuracy of individual LST measurements is 1 K
, several studies from arctic region suggest
a significantly reduced accuracy both for individual measurements and hereof
derived long-term LST averages . This is in particular attributed to
prolonged cloudy periods with systematically different average surface temperatures
that are not captured by the satellite measurements. Furthermore, detection of clouds
is imperfect in particular during polar night conditions , so
that cloud top temperatures are contained in the MODIS LST time series. Validation
studies have shown that these effects can lead to a systematic cold-bias of
up to 3 K in seasonal averages .
It is therefore questionable if MODSIS LST
alone can be used to model ground temperatures. To overcome this problem, we
synthesize a composite of MODIS LST and ERA-interim reanalysis data as input
for the ground thermal model CryoGrid 1 (see Sect. ).
As exemplified by for the MODIS LST tile h18v00, the
land mask employed in the MODIS LST production algorithm is shifted by about
5 km for the tiles north of 80∘ N, so that land surface
temperatures are produced for sea areas, while they are missing for some land
areas. In the study region, this mainly affects the northern parts of Svalbard,
Greenland and Ellesmere Island.
Downscaled near-surface air temperatures from ERA-interim reanalysis
Reanalysis products provide global data sets of meteorological variables based
on atmospheric models in which a range of observations, such as meteorological surface observations, remotely
sensed sea surface temperatures, or vertical temperature and humidity
profiles from radio soundings, are assimilated. In this study, we make use of
air temperatures of the ERA-interim reanalysis , which is available from 1979 until now at a spatial resolution of
0.75∘×0.75∘. ERA-interim is the state-of-the-art
reanalysis product from the European Centre for Medium-Range Weather Forecast (ECMWF),
and it has been successfully employed in previous permafrost modeling studies
. While the atmospheric model can provide a gap-free
time series with four values per day (at 00:00, 06:00,
12:00, and 18:00 UTC), the coarse spatial resolution requires
a down-scaling scheme to correct for the difference between the true altitude
of a point and the coarse-scale ERA orography, which in the study region can
be as much as 1500 m in mountainous terrain. To obtain a downscaled
air temperature for a point in space and time,
propose a four-dimensional interpolation between different reanalysis grid
cells, pressure levels and time steps. Since only long-term freezing and
thawing degree days are required as input for CryoGrid 1
(Sect. ), a simplified version of this scheme similar
to is employed:
An average atmospheric lapse rate is derived for each day of year (DOY) and
MODIS grid cell, based on ERA-interim surface fields and the
700 mbar pressure level, which corresponds to an altitude of
approximately 3000 m, slightly higher than the highest
non-glacierized areas within the study region. For each DOY, all available
ERA-interim data from 2003 to 2012 are employed.
The downscaled air temperature is computed from the lapse rate and the
difference between the ERA orography (interpolated to the center position of
a MODIS grid cell) and the “true” altitude.
The “true” altitude of the 1 km MODIS LST grid cell is derived by
interpolation of the Global Multi-resolution Terrain Elevation Data 2010
(GMTED2010) at 30 arcsec resolution to the
center position of each MODIS 1 km grid cell. This data set is
specifically compiled for continental-scale applications and includes the
best available global elevation data. This procedure ensures that the spatial
and seasonal variability of the lapse rate is accounted for so that
e.g., inversions of the air temperature during winter in continental regions
can be reproduced.
Data fusion of MODIS LST and ERA-interim
Due to frequent cloudiness, the MODIS LST time series contains a large number
of gaps and only clear-sky LST averages can be derived from remote sensing
products alone. To eliminate or at least moderate the effect of clouds, the
MODIS LST time series is merged with the gap-free time series of downscaled
air temperatures from the ERA reanalysis (see Sect. ). For this
purpose, the acquisition time of each MODIS day and night LST measurement
(which varies by several hours from day to day) is converted to UTC, and the
ERA value closest in time to each LST measurement subsequently removed. From
the resulting time series, daily averages are computed from which freezing
and thawing degrees are derived. Depending on the cloudiness, the fraction of
MODIS LST measurements in the composite MODIS/ERA data set is variable
(Fig. ). In areas with frequent cloudiness, such as Iceland,
less than a quarter of the data points are derived from MODIS LST, while the fraction of
MODIS LST is more than 50 % in other areas.
Fraction of MODIS LST measurements in the combined MODIS/ERA surface
temperature product. Borehole sites from used for
validation of the modeled ground temperatures, note that a dot can represent
several boreholes. Further boreholes outside the displayed regions are
employed.
ERA snowfall
The average yearly snowfall from 2003 to 2012 was determined for each grid
cell by interpolation of the snowfall surface field coarse-scale ERA-interim
reanalysis data. These snowfall data are employed to determine the range of
the winter nf factors for the statistical modeling (in
conjunction with a remotely sensed land cover data, see below). While there are
well documented biases in the precipitation fields of the reanalysis e.g.,, it
captures large-scale precipitation patterns, such as the high snowfall in
the south Norwegian mountains close to the Atlantic Ocean. On the other hand, it cannot account for
small-scale variations of winter precipitation. However, since only the range
of possible nf factors is assigned in a statistical modeling
framework with many different model realizations (Sect. ),
utilizing large-scale precipitation patterns may indeed be adequate.
MODIS land cover
The land cover has strong implications for the small-scale distribution of
the snow cover: in areas with low vegetation or bare ground, redistribution
of snow due to wind drift can lead to a strong spatial variability of snow
depths and ground temperatures e.g.,. In contrast,
a more uniform snow depth is expected in forested areas. To represent such
effects in the modeling (Sect. ), the MODIS land cover product
MCD12Q1 for the year 2006 at a spatial resolution of 500 m is
employed. Due to the poor performance of the land cover classification in some
parts of the study region (see Sect. ), the 500 m
grid cells are aggregated to the 1000 m MODIS LST grid and the land
cover classes merged to two units: high vegetation/forest (“International
Geosphere–Biosphere Programme” (IGBP) classes 1 to 9, 11) and bare
ground/low vegetation (IGBP classes 10, 15, 16). The classes 12 to 14
(cropland/urban) occur only sparsely in permafrost areas and are treated like
the high vegetation class.
Statistical modeling with CryoGrid 1
CryoGrid 1 is an equilibrium model for ground temperatures
based on the TTOP approach
e.g.,. It computes mean annual ground
temperature (MAGT) based on thawing and freezing degree days
(TDDs and FDDs) of surface
temperatures, according to
MAGT=1τnfFDDs+rkntTDDsfornfFDDs+rkntTDDs≤01τ1rknfFDDs+ntTDDsfornfFDDs+rkntTDDs>0,
where τ is the period for which TDD and FDD are
evaluated, while rk, nf and
nt are semi-empirical parameters which aim to capture a variety of key
processes in a single variable. The winter nf factor relates
the freezing degree days at the surface (here derived from MODIS/ERA) to the
freezing degree days at the ground surface as
FDDgs=nfFDDs.
It thus captures the insulating effect of the snow cover which is a result of
snow depth, the thermal properties of the snow cover, and the ground thermal
regime itself. For bare surfaces, this variable is unity, while
nf factors as low as 0.2–0.3 are reported from in situ
measurements e.g., for high snow cover in
Scandinavia. The summer nt factor is defined in a similar way as
TDDgs=ntTDDs.
If air temperatures are employed as surface forcing
TDDs, variable nt factors are considered to
account for differences in air and ground surface temperatures
e.g.,. In this study, we assume remotely sensed
LST in conjunction with ERA-interim to be a satisfactory representation of
ground surface temperature and set nt to unity. In case of a
dense canopy, where MODIS LST may rather represent top-of-canopy instead of
surface temperatures,
a different nt may be required, but such conditions rarely occur in permafrost
areas in the study region. The active layer
damping factor rk gives rise to the thermal offset between
average ground surface and ground temperatures .
It is related to the average thermal conductivities in the active layer in
fully thawed and frozen states (kt, kf) as
rk=kt/kf, so that it is
closely related to the water/ice content of the soil. The thermal
conductivities of water and ice
(kw= 0.45 Wm-1K-1,
ki≈ 2.2 Wm-1K-1) confine the range
of physically possible values of rk between one for dry soil or
rock and approximately 0.2 for pure water.
Intervals of input parameters assumed in the
TTOP modeling. SFERA: average yearly snowfall from
ERA-interim reanalysis in m of water equivalent.
class
nf,min
nf,max
nt
rk, min
rk, max
bare ground/low vegetation
0.725–0.625×SFERA
1
1
0.8
1
high vegetation/forest
0.625–0.625×SFERA
0.925–0.625×SFERA
1
0.7
0.9
The statistical modeling is based on the assumption that
FDDs and TDDs can be exactly
determined from the MODIS/ERA-composite, while the two remaining variables in
Eq. (), nf and rk are unknown and only
confined by physically plausible limits (note that nt= 1 is
assumed). For each of the land cover units “high vegetation/forest” and
“bare ground/low vegetation” (Sect. ), upper and lower
bounds for nf and rk are defined
(Table ), oriented at physical constraints and published
values from previous studies. However, the upper and lower bounds of
nf and rk are also tuning parameters which can be
adjusted to achieve the best possible match between model and observations
(Sect. ) for each land cover unit. We emphasize that remotely
sensed data sets on precipitation or snow depth from which the
nf factors could be estimated are
not available at 1 km scale and the interval of possible values for
nf was chosen according to large-scale ERA-interim snowfall
data (Sect. ). For the “bare ground/low vegetation” class,
the upper bound for nf is set to 1, since
bare-blown spots without insulating snow cover can occur. The lower bound
decreases with increasing snow
fall, i.e. for areas with high snow fall, the spread of possible snow depths
and thus nf-values is larger than for areas with low snowfall. For the
mountain areas in Norway, assumed a minimum nf
of 0.3, while the minimum lower bound of nf is around 0.1 for Norway in
this study. However, employed grid-cell averages
of snow depths to calculate nf, while in this study the lower bound of
nf aims to represent the areas with maximum snow depths within each grid
cell (e.g., snow drifts). The parameterization of nf vs. snow depth applied
by to represent such small-scale variability of snow
depths yields nf values between 0.1 and 0.2 for snow depths of several
meters, which regularly occur in the Norwegian mountain areas, in agreement
with the choice in this study. For the “high vegetation/forest” class,
both upper and lower bound for the winter nf-factor decrease linearly with
snow fall, while the difference between minimum and maximum nf is held
constant. The rk values are chosen close to 1 for both classes, which
implies that large changes in the thermal conductivities do not occur. Areas
with potentially large thermal offsets (i.e. low rk values), such as wetlands
or extensive block field areas , are clearly not
represented by this choice. However, with the currently available land cover
products, it is not possible to reliably detect such areas (see Sect. ),
so that they cannot be accounted for by the employed scheme. Furthermore, variations of altitude and exposition within
grid cells are an additional source of spatial variability of ground temperatures which is not
accounted for in the presented model scheme. In mountain areas with strong topographic variations, the spatial variability of
ground temperatures within a grid cell is most likely underestimated.
For each grid cell, CryoGrid 1 is run for 30 values of nf and
rk (in equally spaced intervals from the lower to the upper
limit), yielding a total 900 different values for the mean annual ground
temperature (MAGT). The statistics of these values is a representation
of both the small-scale (i.e. <1km) variability of model
parameters and the model uncertainty due to the generally unknown “true”
parameter distribution of a grid cell. As final result, we calculate the
average of all 900 realizations of MAGT, as well as the standard
deviation, and the maximum and minimum MAGT.
Results
Comparison to in situ data
We compare the mean of all model realizations to in situ measurements of
ground temperatures from the “IPA-IPY Thermal State of Permafrost (TSP)
Snapshot Borehole Inventory” documented in more detail
for North America , Russia ,
and the Nordic areas . While this data basis
provides only a single value for ground temperatures measured at different
depths and different points in time, it is the most extensive compilation of
permafrost temperatures available for model validation (see
Sect. ). For comparison, we generally select the grid
cell closest to the borehole location. For boreholes located close to
a larger water body, a nearby grid cell located at least 1 km from
the shore is employed to avoid contamination of the MODIS LST record with
surface temperatures from the water body. For the boreholes north of
80∘ N (five boreholes near Alert, Ellesmere Island, Canada), no
MODIS LST measurements are available due to the erroneous land mask
(Sect. ). We therefore use the closest grid cell featuring
MODIS LST measurements east of Alert which is located on land. The results of
the comparison are displayed in Fig. , with 12
boreholes located in North America (Canadian Archipelago), 69 in the Nordic area
(Scandinavia, Greenland, Svalbard, Iceland) and 62 in Russia. For each
borehole, the error bars represent one SD of the results of all model
realizations for a grid cell which depends on the ranges of nf
and rk. For the large majority of the boreholes, the agreement
between measured and modeled ground temperatures is better than
2 ∘C, with 67 (47 %) contained within one, 108
(75 %) within two and 128 (90 %) within three SDs of all
model realizations from the mean (see Supplement).
Measured vs. modeled ground temperatures for 143 borehole sites
. The error bars represent one SD of all model
realizations, the dashed lines are the ±2 ∘C intervals
around the 1:1 line (in solid).
Histogram of the difference between modeled and measured ground
temperatures for 143 borehole sites .
A histogram of deviations between measured and the mean modeled ground
temperatures is displayed in Fig. . It roughly follows
a Gaussian distribution with width of 1.2 ∘C. For 60 %
of the boreholes, the mean of all model realizations is within
1 ∘C of the measurement, while the agreement is better than
2 ∘C for 93 % and better than 2.5 ∘C for
97.5 % of the boreholes. From the comparison with in situ
measurements, we conclude that the accuracy of the modeled ground
temperatures is on the order of 2 to 2.5 ∘C for the study
region. There is no significant regional bias for Russia and for the Nordic
areas, while there is a slight cold-bias for the available boreholes in North
America. However, the latter cannot be fully secured due to the comparatively
weak data basis of only 12 boreholes, all of which are assigned large model
standard deviations of 1.9 to 2.7 ∘C (see Supplement) which
indicate a potentially large spatial variability of ground temperatures.
While the borehole data of the TSP network are well suited to validate the
large-scale performance of the modeling, only very few quantitative studies
on the spatial variability of ground temperatures within areas of a model
grid cell exist to which the ensemble of all model realizations could be
compared. Recently, presented a 1-year data set of
ground surface temperature measurements based on 40 to 100 temperature
sensors distributed in three areas of approximately 0.5 km2, located
in Svalbard and southern Norway. Since the thermal offset between average ground
surface and ground temperatures is considered small for the sites, we compare
the measured distribution of average ground surface temperatures (AGST) to
the ensemble of modeled ground temperatures. For Finse
(60∘34′ N, 7∘32′ E),
30 % of the temperature sensors displayed AGSTs below
0 ∘C, compared to 51 % of the model realization for the
MODIS grid cell comprising the study site (for ground temperatures). The
measured range of AGST was -2 to +2.5 ∘C, while minimum and
maximum modeled ground temperatures were -2.2 and +2.1 ∘C.
For the Juvvasshøe site (61∘41′ N,
8∘23′ E), 76 % of the measured AGSTs were
below 0 ∘C, compared to 77 % of the model
realizations. The modeled temperature range (-3.8 to 1.2 ∘C)
was slightly larger than the measured range of AGST (-2 to
+1.5 ∘C). For Ny-Ålesund
(78∘55′ N, 11∘50′ E), the
modeled temperatures are slightly cold-biased, with measured borehole
temperatures of -2.3 ∘C compared to a mean
of all model realizations of -3.8 ∘C. Nevertheless, the
modeled temperature range of 4.9 ∘C between minimum and maximum
corresponds well to the range of measured AGST (-4.5 to
+0.5 ∘C). Finally, the spatial variability of ground
temperatures has been modeled for the high-Arctic Zackenberg site in NE
Greenland, taking into account the spatial variability of the snow cover,
ground surface and ground properties . For
the period 2002–2012, modeled annual average ground temperatures at
1 m depth range from -9.0 to -3.5 ∘C, while the
model realizations of CryoGrid 1 yield a temperature range from -11.0 to
-2.9 ∘C. While not a validation in a strict sense, the
satisfactory to good agreement for these few examples suggests that the
ensemble of all model realizations can represent the small-scale spatial
variability of ground temperatures, at least for the land cover class “bare
ground/low vegetation”. Similar field data sets or modeling studies do not
exist for the “high vegetation/forest” class, so that is not possible to
benchmark the modeled temperature range at this point.
Modeled ground temperatures in the North Atlantic permafrost region
The model approach facilitates large-scale mapping of the ground thermal
regime on a continental scale. As shown in the previous section, the
comparison to in situ measurements suggests that the mean of all model
realizations reproduces the ground thermal regime within an accuracy of 2 to
2.5 ∘C. Figure displays the resulting ground
temperature map for the permafrost regions bordering the North Atlantic Ocean.
The modeled ground temperatures span a wide range, from
-15 ∘C in northern Greenland and Ellesmere Island to more than
+5 ∘C in southern Scandinavia. Ground temperatures below
0 ∘C are modeled in the Canadian Archipelago, Greenland,
Iceland, Svalbard, the Scandinavian Mountains and the coastal regions of the
Pechora Sea east of the Kanin Peninsula. In the high elevations of the Ural
Mountains, subzero temperatures occur as far south as 60∘N.
In the lowlands east of the Ural Mountains, negative modeled ground temperatures
reach significantly farther south compared to the west side. In northern Scandinavia
and Russia, large areas with modeled ground temperatures just above
0 ∘C exist, for which it is not possible to establish
permafrost presence or absence considering the accuracy of 2 to
2.5 ∘C accuracy limit (see Sect. ). The
modeled permafrost distribution in the North Atlantic region is in good
qualitative agreement with the “classic” permafrost map of the IPA based on
field evidence , including prominent features like the
asymmetry of the permafrost extent east and west of the Urals.
Average MAGT of all model realizations for the North Atlantic
study region. 1: Ellesmere Island; 2: Pechora Sea; 3: Kanin Peninsula; 4:
Ural Mountains; 5: Kola Peninsula. Glacierized areas from Natural Earth
(www.naturalearthdata.com).
Standard deviation of MAGT of all model realizations for
the North Atlantic study region. 1: Ellesmere Island; 2: Pechora Sea; 3: Kanin
Peninsula; 4: Ural Mountains; 5: Kola Peninsula. Glacierized areas from
Natural Earth (www.naturalearthdata.com).
The standard deviation of all model realizations is displayed in
Fig. . The highest values of around 3 ∘C
are reached in the northern and eastern Greenland, as well as on Baffin Island, areas with a
large number of freezing degree days that are classified as “bare ground/low
vegetation” and hence are assigned a wide range of nf values.
The large spread therefore stems from the strong variability of winter ground
surface temperatures reflected in the term nf FDD in
Eq. (). Permafrost areas further south, e.g., in Scandinavia,
feature lower numbers of FDD and hence a smaller standard deviation,
generally between 1 and 2 ∘C. Areas classified as “high vegetation/forest”
have standard deviations of 1 ∘C or less, mainly due to the smaller range
of winter nf factors, which reflect the more homogeneous snow cover in such areas.
Average MAGT of all model realizations for Greenland and
Iceland. 1: Scoresby Sound; 2: Tasilaq region; 3: Disko Bay; 4: Nuuk region;
5: Sprengisandur; 6: Tröllaskagi Peninsula. Glacierized areas from
Natural Earth (www.naturalearthdata.com).
At 1 km spatial resolution, it is meaningful to “zoom” into
subregions for a detailed assessment of the ground thermal regime.
Figure displays a ground temperature map for Greenland
and Iceland, with a significantly finer resolution compared to the
25 km scale assessment of . In the
ice-free parts of northern Greenland, modeled ground temperatures range from -10
and -15 ∘C, while they gradually increase southwards in the
ice-free regions of northeastern Greenland to around -3 ∘C in the
Scoresby Sound region. Further south, only few ice-free land areas exist on
the east coast, but subzero ground temperatures are modeled in the Tasilaq
region at 65.5∘ N. On the west coast, the permafrost extends from
the outer coast line to the ice sheet in the extensive ice-free land regions
south of Disko Bay, with modeled ground temperatures warmer than
-5 ∘C. Starting just north of Nuuk, the coastal areas become
permafrost-free, but subzero ground temperatures are still modeled at higher
elevations in southern Greenland.
In Iceland, subzero ground temperatures are restricted to the interior,
ranging from the central Sprengisandur between Hofsjökull and
Vatnajökull north of the mountain ranges of the Tröllaskagi
Peninsula, where active rock glaciers suggest a periglacial environment
. The modeled permafrost extent is in good
agreement with previous regional estimates based on mean annual air
temperatures .
Average MAGT of all model realizations for Scandinavia.
1: Hardangervidda; 2: Finnmarksvidda; 3: Kola Peninsula. Glacierized areas
from Natural Earth (www.naturalearthdata.com).
Fraction of model realizations with
MAGT<0 ∘C inferred from the statistical modeling.
Permafrost zonation corresponding
to continuous (>90 % of all realizations
MAGT<0 ∘C), discontinuous (50–90 %) and
sporadic (10–50 %) permafrost. 1: Finnmarksvidda; 2: Kola
Peninsula; 3: Kanin Peninsula; 4: mouth of the Pechora River; 5: Ural Mountains.
Glacierized areas from Natural Earth (www.naturalearthdata.com).
On Svalbard, modeled ground temperatures in the ice-free areas range from
-2 to -3 ∘C at the west coast to -5 to -6 ∘C
in the ice-free parts of Nordaustlandet. In Scandinavia, the southernmost
areas with subzero modeled ground temperatures are located at high elevations
in the south Norwegian mountains. Within the accuracy, the modeled ground
temperatures agree well with the spatially distributed modeling of
, showing rather warm permafrost with ground
temperatures generally warmer than -3 ∘C. In general, more
areas are mapped with subzero temperatures compared to the previous study
(especially in the Hardangervidda area), but the differences in the absolute
modeled temperatures are mostly less than 1.5 ∘C (see also
Sect. ), and patchy permafrost is known to exist in
these regions . In northern Scandinavia, permafrost is
modeled in higher elevations of the Swedish and Norwegian mountains. In the
latter, the pattern is again in agreement with the regional assessments of
and who employed
CryoGrid 1 with gridded air temperature and snow depth products.
In the rolling plains of the Finnmarksvidda, the model shows temperatures
just above 0 ∘C, while sporadic permafrost is found in
high-lying fell areas and palsa mires . In this
area, the model approach clearly fails to reproduce the permafrost patterns.
Most likely, a main reason is the employed MODIS land cover product, in which
almost the entire area is uniformly classified as “open shrubland” (and
thus as “high vegetation/forest” in our approach), although it is
characterized by a complex pattern of fell areas, tree-less mires and areas
covered by mountain birch forest. If the model is applied to the area with
the parameter set for the “bare ground/low vegetation class”
(Table ), subzero ground temperatures are modeled for
a large part of the area. Therefore, the model approach would indeed yield
a pattern of permafrost and permafrost-free areas if a land cover product
capable of distinguishing mountain birch forest from bare fell and tundra
areas is employed. The same issue applies to modeled ground temperatures on
the Kola Peninsula in Russia, where ground temperatures around
0 ∘C are modeled for the northern and eastern parts.
Permafrost probability maps from statistical modeling
With an estimated accuracy of 2 to 2.5 ∘C, it is impossible to
delineate exact boundaries for the permafrost extent of the study region
based on the mean of all model realizations. Around the thaw threshold, the
statistical model approach features model realizations below and above
0 ∘C, depending on the input parameters nf and
rk. However, permafrost and permafrost-free areas coexist in this
transition zone also in nature. This long-known fact
e.g., gave rise to the classification
system “continuous” (>90 % of an area underlain by permafrost),
“discontinuous” (50–90 %), and sporadic (<50 %)
permafrost, as defined by the IPA long before the advent of sophisticated
modeling techniques .
In contrast to model approaches with only a single model realization for each
grid cell, the ensemble of realizations of CryoGrid 1 facilitates deriving
a similar permafrost zonation from the modeling. Figure
displays the fraction of model realizations with subzero ground temperatures
in the same classes as the IPA permafrost map for Scandinavia and western Russia.
The potential permafrost extent is larger than in Figs.
and , with the most significant differences in lowland
areas in Scandinavia and Russia. The interior of northern Scandinavia (for which the
mean of all model realizations is above 0 ∘C,
Sect. ) is classified as sporadic permafrost in this
approach, which is in good agreement with observed field evidence for this
area. In Russia, sporadic to discontinuous permafrost is modeled from the
Kola and Kanin peninsulas to the mouth of the Pechora River, east of which
the permafrost is classified as continuous. Also in this probability map, the
individual permafrost zones extend significantly further south on the east
side of the Ural Mountains than on the west side.
This asymmetric permafrost distribution around the Ural Mountains is
a prominent feature in the IPA permafrost map , which
the presented satellite-based modeling approach is capable of reproducing. In
contrast, the global map of , which also delivers
comparable probabilities of permafrost occurrence, shows a more or less
symmetric permafrost extent around the Urals. Further pronounced differences
occur on the eastern tip of the Kola Peninsula where the map by
shows no permafrost, other than the IPA
permafrost map and the satellite-based modeling approach. Compared to the IPA
map, the transition zone from permafrost-free areas to the continuous
permafrost zone in NW Russia is broader in the satellite-based map, which is
an indication that some model scenarios (i.e. combinations of model
parameters) do not occur in nature. A similar broadening of the transition
zones is visible in the probability map of .
Discussion
Uncertainties and prospects for improvements
The equilibrium model
The TTOP-approach is one of the older modeling
schemes conceived to obtain ground temperatures and thus permafrost
occurrence from near-surface meteorological variables
e.g.,. It delivers a “mean
annual ground temperature” at the depth corresponding to the top of the
permanently frozen ground under the strong assumption that the ground thermal
regime is in thermal equilibrium with the applied surface forcing data
(Appendix ). Since this assumption is violated to a certain
degree for real-world conditions, a comparison to in situ measurements, as
conducted in Sect. , is not a straight-forward task. For a
typical geothermal gradient of 0.025 ∘C m-1, measured
MAGTs would be less than 1 ∘C warmer than modeled MAGTs for
borehole depths of up to 40 m. On the other hand, ground temperatures
have been warming by a similar magnitude even at depths of 10 to 20 m
in the model period , so that recorded
borehole temperatures
may represent colder climate conditions compared to the model period. With the
equilibrium approach, it is thus principally impossible to exactly reproduce
ground temperatures that can be measured in the field. However, we note that the
combined uncertainty due to measurement depth and transient effects is not
necessarily systematic, and presumably well below the estimated accuracy of the
modeling scheme of 2 K for most boreholes.
Land surface temperature
In this study, land surface temperatures are derived from satellite
measurements during clear-sky conditions, while air temperatures from
reanalysis products are employed for cloud-covered periods when satellite
measurements are unavailable. This approach combines the strengths of both
products – the capacity of satellite sensors to provide actual measurements of
the footprint area at a high spatial resolution, and the dense, gap-free time
series of the reanalysis
product. On the other hand, it strongly reduce the uncertainty associated
with both input data sets when used separately: even when downscaled with
altitude, reanalysis products only provide a large-scale temperature field
which does not account for the heterogeneity of the surface temperature
caused by spatially variable surface conditions. Employing only MODIS LST and
thus clear-sky LST to calculate long-term averages can result in a serious
bias since cloudy periods with a significantly different surface temperature
regime are not contained e.g. However, these validation studies also concluded that
a significant number of highly erroneous measurements due to undetected
clouds is contained in the MODIS LST time series. These measurements are not
removed in the synthesized MODIS/ERA time series, which could in principle
introduce a bias in the freezing and thawing degree days. Since including ERA
reanalysis data strongly increases the total number of values in the time
series, these biased values will attain a smaller weight in the
FDDs and TDDs calculation compared
to employing MODIS LST only, so that their influence is moderated.
Nevertheless, it should be investigated if highly erroneous MODIS LST can be
detected by a consistency check with downscaled ERA air temperatures, e.g., by
setting a threshold value for the difference between the two temperatures.
In this study, the ERA-interim reanalysis is employed to complement
satellite-based LST measurements. Since a large number of operational
meteorological observations are assimilated in the reanalysis
, independent validation data sets are rare especially in
Arctic regions. Over the central Arctic ocean during summer,
found near-surface temperatures to be
warm-biased by up to 2 ∘C, but the performance improved at
higher altitudes. For Ireland, the performance for near-surface temperatures
was excellent with a root mean square error of generally less than
0.5 ∘C, but a slight warm bias during the winter months
. While these examples give a hint on the
expected accuracy, the performance should be investigated further, especially
in regions with pronounced topography. The coarse-scale temperature field of
the ERA-interim reanalysis is downscaled using high-resolution topography
and a seasonal lapse-rate calculated from the surface and the
700 mbar levels. The similar downscaling scheme presented by
, which is based on a 4-D interpolation between
all available pressure levels and time steps, did not provide satisfactory
results for grid cells with elevations below the ERA orography. This case is
common e.g., at the coasts of Svalbard and Greenland, where the elevation
difference can be more than 1000 m. In these cases, the interpolation
relies on the “near-surface lapse rate”, i.e. the modeled temperature
difference between the surface and the first pressure level, which is
subsequently extrapolated to altitudes far below the surface level. In
particular if an ERA grid cell is snow-covered, this near-surface lapse-rate
can feature strong temperature inversions, so that extrapolation to lower
altitudes leads to a strong cold-bias of the downscaled temperature. To
moderate the effect of near-surface stratifications, we employ an “average
lapse rate” for the entire ERA air column between the surface and the
700 mbar pressure level located at approximately the elevation of the
highest non-glacierized areas in the study region. We emphasize that the
procedure cannot account for many regional and local climate and weather
conditions, such as temperature inversions in valley systems. Downscaling of
reanalysis data using e.g., the Weather Research and Forecasting (WRF) Model,
though computationally expensive, may be a way to overcome such difficulties
.
Land cover
For each 1 km grid cell, the range of possible values for
nf and rk is assigned based on the MODIS land cover
product and large-scale snowfall data sets. Hereby, the main goal is to
distinguish areas with bare ground or low vegetation, where strong
redistribution of snow due to wind drift can occur, from areas with trees and
high vegetation where the snow cover is more uniform. At least in some areas,
the performance of the MODIS land cover product in distinguishing between the
two classes seems to be poor: in the rolling plains of Finnmarksvidda,
northern Norway, mountain birch forest alternates with bare fell areas, while the
entire area is classified as “open shrubland” in the MODIS land cover and
thus as “high vegetation/forest” in the modeling. In the studied region,
this problem is restricted to northern Scandinavia and Russia, where permafrost
occurs close to and within forested areas. In regions with more extensive
forest cover in permafrost areas, this issue should be investigated in more
detail. The new global land cover classification delivered by the “Climate
Change Initiative” of the “European Space Agency” ESA CCI,
may constitute an improved product for permafrost
modeling, but its performance in distinguishing areas with low trees and
shrubs from bare tundra should be investigated in more detail. However, with
this product, it may be feasible to distinguish additional classes which
differ in their parameter ranges employed in the modeling
(Table ), at least in regional applications. Ideally,
a pan-arctic land cover classification should be compiled which is
specifically tailored for permafrost applications. Such a product should not
only deliver information on the vegetation and surface state, but also on
subsurface properties, which could e.g., be employed to better estimate the
rk factors in the presented model scheme.
Precipitation and snow depth
The presented ground temperature map is compiled without employing fine-scale
data sets on precipitation or snow depth. Instead, only plausible ranges of
values for nf are assigned, which account for both total winter
precipitation (i.e. spatially averaged snow depth) and wind redistribution of
snow. In a recent study for Svalbard and Norway,
demonstrated that annual average ground surface temperatures within areas of
approximately one modeling grid cell (1 km) vary by up to
5 ∘C in areas with pronounced wind drift, while a borehole can
only provide one point value sampled from the distribution of ground
temperatures. The modeling approach explicitly accounts for this spatial
variability by computing ground temperatures for a whole range of
nf value. We find that the agreement with borehole
temperatures, despite using large-scale data sets of winter precipitation, is
around ±2 ∘C and thus similar to natural spatial
variability of ground temperatures.
Deterministic vs. statistical modeling of ground temperatures
In the version employed for this study (Eq. ), the TTOP approach
accounts for the insulating effect of the snow cover, as well as the thermal
offset between mean annual ground surface and ground temperatures. The
complex physical processes which give rise to these effects, are lumped into
one variable each (nf and rk) which must be
adjusted to achieve adequate results. While both nf and
rk are in principle empirical constants, they are subject to
physical constraints which confines them to a certain range. Other than
deterministic modeling schemes which seek to employ a single set of model
parameters for each grid cell, we use the cumulative information content of
many realizations, i.e. combinations of different parameters selected from
the physically possible range (Sect. ). Due to its
simplicity and the small number of input parameters, the TTOP-approach is
computationally efficient enough to compute a large number of realizations.
The scheme can be expected to deliver adequate results if the uncertainty due
the simplified model (Appendix ) is smaller than the
uncertainty due to the unknown model parameters. We note that the model
approach can not separate the spatial variability of the input parameters
within a model grid cell from the uncertainty due to generally unknown values
of these parameters. Ideally, it delivers a range of possible MAGTs,
in which the true range of MAGTs as documented by measurements,
e.g., is contained. While the agreement between modeled and
measured ranges is excellent for the few in situ data sets on small-scale
spatial variability of ground temperatures (Sect. ), more
work and in particular improved validation data sets are needed for a robust
assessment of modeled and true ranges of MAGTs.
More sophisticated modeling schemes e.g., feature
significantly more model parameters which are required to achieve a realistic
description of physical processes. While these parameters can generally be
estimated to a certain level of confidence in regional-scale applications
e.g.,, their variation and spatial
distribution is hard to access on continental to global scale. It is
therefore questionable whether the performance of such computationally
expensive schemes is better than the simple CryoGrid 1 model. Furthermore,
the significant number of input parameters and the computational costs make
sensitivity studies with many realizations unpractical, at least for many
grid cells. In the CryoGrid 1 based scheme, however, a sensitivity is
performed for each grid cell so that confidence limits for the results can be
given. On the point scale, performed
a sensitivity analysis for a transient permafrost model. They found modeled
ground temperatures to vary by up to 4 ∘C if the input
parameters related to snow and soil properties were allowed to vary within
physically plausible limits. This suggests that on a continental scale the
performance of more sophisticated schemes could be on the order of the much
simpler TTOP approach.
Towards a global high-resolution ground temperature map
The “classic” permafrost map compiled by the IPA more than 15 years
ago is based on available field evidence for
permafrost occurrence and properties. Since then, new global data sets have
become available which so far have only rarely been used for permafrost
mapping on large spatial scales. An exception is the global approach by
who derived the probability of permafrost
occurrence at 1 km scale from downscaled air temperatures (obtained
from atmospheric model output) using empirical probability functions.
In this study, we have demonstrated the continental-scale application of
a statistical model approach with global satellite data sets and a reanalysis
product as input data. In addition to probabilities of permafrost occurrence
as in, the approach facilitates mapping of
ground temperatures and thus quantifying the thermal state of the permafrost.
The model was successfully applied to an area of more than
5 million km2 with strong spatial differences in ground
temperatures and a wide variety of permafrost landscapes which suggests that
the approach is scalable to include the entire contiguous permafrost extent
on the Northern Hemisphere, an area of approximately 23 million km2
. Hereby, it may become necessary to refine the
parameterizations for the ranges of nf and rk
(Table ), possibly by introducing functional dependences
on other environmental variables. A main uncertainty is the performance in
forested regions which could not be sufficiently investigated in the North
Atlantic study region. At least in the case of dense forests or strong off-nadir
angles, remotely sensed LST may represent top-of-canopy temperatures instead
of skin temperatures at the ground or snow surface, as required by
CryoGrid 1. Thus, it should be investigated whether this effect leads to
a reduced accuracy or even a systematic bias of modeled ground temperatures.
In addition to a global mapping, the presented method is also feasible for
regional-scale applications, especially if improved data sets on e.g., surface
cover, air temperature or snow depth are available. An example is the ground
temperature map of Norway compiled by through
application of CryoGrid 1 with gridded air temperature data sets, which could
be improved both by integrating remotely sensed LST and by accounting for the
subgrid variability of the snow cover in a statistical framework. However, we
emphasize the semi-empirical nature of the model approach so that it should
only be applied in areas with sufficient in situ data sets for validation.
Furthermore, in mountain areas with strong topographic variations,
satellite-based LST measurements at 1 km scale cannot sufficiently
capture variations of altitude and exposition, so that the modeling scheme at
best can be expected to deliver a first-order approximation of the permafrost
distribution.