Introduction
Permafrost is an important element of the terrestrial
cryosphere, which is likely to undergo major transformations in a warming
climate in the 21st century. At present, near-surface permafrost covers about
a quarter of the land area of the Northern Hemisphere, but future projections
with Earth system models (ESMs) suggest a reduction between 30 and 70 %
until 2100, depending on the applied anthropogenic emission scenario
e.g.,. Observations of the ground thermal
state are evidence that the ground is already warming in many permafrost
areas and near-surface permafrost is in the
process of disappearing from peripheral areas e.g.,.
In situ monitoring efforts are coordinated worldwide within the Global
Terrestrial Network for Permafrost GTN-P, www.gtnp.org;
, which is comprised of two components: (1) the
Circumpolar Active Layer Monitoring (CALM) with measurements of active layer
thickness at about 250 sites and (2) the thermal state of permafrost (TSP)
in which ground temperatures are measured in over 1000 boreholes with depths
ranging from a few to more than 100 m.
While GTN-P can deliver high-quality direct observations of permafrost state
variables, TSP and CALM sites represent point measurements on spatial scales
of 100 m and less. Transferring this knowledge to larger regions is
hampered by the considerable spatial variability of the ground thermal regime
(which limits the representativeness of a measurement) and the strong
concentration of TSP and CALM sites in a few regions, while vast permafrost
areas are not at all covered .
A possibility to infer ground temperatures on large spatial scales is the use
of grid-based models that use meteorological data as forcing. Spatially
distributed permafrost modeling was, for example, demonstrated by
and , forced by
interpolations of meteorological measurements, or by
and by downscaled
atmospheric model data. Remote-sensing data sets have been extensively used
to indirectly infer the ground thermal state through surface observations,
e.g., occurrence and evolution of thermokarst features
e.g.,, vegetation types characteristic for
permafrost or change detection of spectral indices
. As permafrost is a subsurface temperature
phenomenon, it is not possible to observe it directly from satellite-borne
sensors. However, remotely sensed data sets can be used as input for the
above-mentioned permafrost models .
demonstrated and evaluated a transient ground
temperature modeling scheme forced by remote-sensing data for a point in the
Lena River delta (LRD). In this work, we update and extend this earlier approach to
facilitate spatially distributed mapping of the ground thermal regime based
on satellite-derived data sets on surface temperature and snow cover. The
model results are compared to in situ observations of ground temperatures and
thaw depths, thus facilitating a coarse assessment of the performance of the
scheme regarding important permafrost variables.
The Lena River delta with the three stratigraphic classes
distinguished in the ground thermal modeling (Sect. ) and
sites with in situ observations (Sect. ) employed for model
validation. AN: Arga Island, north; AC: Arga Island, center; Dz: Dzhipperies
Island; Ku: Kurungnakh Island; OC: Olenyokskaya Channel, center; OM:
Olenyokskaya Channel, mouth; Sam: Samoylov Island; Sar: Sardakh Island; Tu:
Turakh Island.
Study area
The Lena River delta
The Lena River delta (LRD) is located in NE Siberia at the coast of the
Laptev Sea. It constitutes one of the largest river deltas in the Arctic,
covering an area of around 32 000 km2 between 72 and
74∘ N. The LRD is dominated by continuous permafrost in a
continental climate, with extremely cold winter and relatively warm summer
temperatures . Mean annual ground temperatures are
the on order of -10 ∘C, and the frozen ground is estimated to
extend to about 400–600 m below the surface
.
With elevations between 0 and 60 m a.s.l., the LRD can essentially
be regarded as “flat”, so medium- and low-resolution data sets
(1 km or coarser) can be employed without the need for topographic
corrections. However, the surface and ground properties feature a strong
heterogeneity at spatial scales of 1 m to 1 km with, for example,
a large number of small water bodies, that is not reflected in medium- and low-resolution data
sets. Despite such small-scale variability, the LRD can be classified in
three main geomorphological units (Fig. ), which have
distinctly different characteristics regarding their surface and subsurface
properties, such as ground ice contents, thermokarst features and vegetation
cover .
The first river terrace covers large parts of the eastern and
central delta. It is the youngest and most active part of the delta, shaped
by river erosion and sedimentation during the Holocene. Polygonal tundra with
mosses, sedges, grass and occasional dwarf shrubs dominates the surface
. The subsurface material consists
of silty sands and organic matter in alluvial peat layers with thicknesses up
to 5–6 m . Ice wedges of more than 9 m
depth have been described on the first terrace
. The ice contents in the
uppermost few meters reach 60–80 % in volume, while the mineral and
organic contents reach 20–40 and 5–10 %, respectively
. A considerable fraction
of the first terrace is composed of the modern floodplain of the Lena River
which is periodically inundated. These floodplain areas feature a different
ground stratigraphy, with sandy, generally well-drained soils with low
organic contents.
The second river terrace, located in the northwestern part of the
LRD, was created by fluvial deposits between 30 and 15 ka BP when
the sea level was lower than today. These sandy sediments generally feature
low ice and organic contents . Arga Island is
the biggest island of this terrace, and the geomorphologic unit is often
called Arga complex.
The third river terrace is composed of late Pleistocene sediments
which have not been eroded by the Lena River during the Holocene. It is
distributed in isolated islands in the southern margins of the LRD
. The third
terrace is part of the Yedoma region, which contains substantial quantities of
ground ice and organic carbon down to several tens of meters below the
surface . The Yedoma was accumulated during the
extremely cold climate of the last glacial period between 43 and
14 ka and contains ice wedges of more than 25 m depth
.
The vegetation consists of thick 0.1–0.2 m hummocky grass, sedge and moss
cover, and the upper horizon of the soil has a thick organic layer. Holocene
permafrost degradation resulted in the current complex thermokarst landscape
characterized by thermokarst lakes and drained basins
.
The three river terraces occur in clusters of at least a few square
kilometers (Fig. ) so they can be resolved by grid-based
mapping at 1 km scale. A model study by suggests
that the subsurface stratigraphies of the three river terraces lead to a
distinctly different ground thermal regime and susceptibility to future
surface warming. Spatially distributed permafrost modeling hence must account
for these geomorphological units and their characteristics of subsurface heat
transfer.
Field sites and in situ observations
The Samoylov permafrost observatory
Samoylov Island is an about 4 km2 large island
(72∘22′ N, 126∘28′ E) located at the southern
apex of the LRD, close to where the Olenyokskaya Channel flows out of the
main stem of the Lena River (Fig. ). It is situated on the
first river terrace and dominated by wet polygonal tundra and thermokarst
lakes and ponds of various sizes . A Russian–German
research station has been operating on Samoylov Island for more two decades
and facilitated scientific studies on energy and carbon cycling
e.g.,,
validation of satellite data sets and ESM
development e.g.
Permafrost temperatures have been increasing, and ice-wedge degradation is
occurring “subtly” on sub-decadal timescales, but with long-term
consequences for the hydrologic drainage . A detailed
overview on the climate, permafrost, vegetation and soil characteristics on
Samoylov Island is provided by . On Samoylov Island,
a long time series of meteorological and environmental variables is available
and forms an excellent basis for validation of
satellite data sets and ground thermal modeling . In the following, we briefly
describe the in situ data sets employed in this study
(Sects. and ):
Surface temperature: on Samoylov Island, surface (skin) temperature
has been measured continuously since 2002 by a downward-facing long-wave
radiation sensor (CG1, Kipp & Zonen, the Netherlands). The outgoing long-wave
radiation is converted to surface temperature using the Stefan–Boltzmann law
seefor details.
Snow depth and properties: on the point scale, snow depth
measurements have been conducted with an ultrasonic ranging sensor (SR50,
Campbell Scientific, USA; located close to the long-wave radiation sensor)
since summer 2003, but a few winter seasons are not covered due to sensor
failure. In addition, a spatially distributed survey of snow depths and
densities (216 points in polygonal tundra) was conducted in early spring 2008
(25 April to 2 May) before the onset of snowmelt .
The onset and termination of the snow cover were manually determined from
pictures taken by an automated camera system, with dates from 1998 to 2011
provided in .
Ground temperature: in this study, we make use of measurements of
active layer temperatures in a low-center polygon established in 2002 and
ground temperatures in a 26 m deep borehole since 2006
. The measurement site of the active layer
temperatures can be considered representative for the polygonal tundra of the
first river terrace . The deep borehole is located
near the southern bank of the island close to the research station in an area
with ground properties that differ from the “typical” stratigraphy of the
first terrace: the area around the borehole features sandier soils with low
organic contents that are generally well drained due to the proximity to the
river bank. In the course of an upgrade of the research station, new
buildings and structures were erected in the direct vicinity of the borehole
in summer 2012 (see Supplement), leading to much higher snow accumulation
around the borehole in the following winters (compared to the surrounding
terrain on Samoylov Island). Therefore, only borehole data until summer 2012
are used for comparison to model results.
Thaw depth: oriented at the measurement protocol for CALM sites
, thaw depths have been manually mapped on a grid
with 150 points in polygonal tundra on Samoylov Island since 2002. According
to the land cover classification in , the grid
points are located both on dry polygon rims and wet polygon centers. In most
years, several surveys are available covering the entire period from the
onset of thaw until maximum thaw depths are reached.
In situ observations in the LRD
Outside of Samoylov Island, only sparse observations on the ground thermal
regime are available. In 2009 and 2010, ground temperature measurements at
several meter depth were established in four boreholes distributed across
the LRD (Fig. ), all of which are located in rather
homogeneous surroundings (see Supplement for images):
Olenyokskaya Channel, mouth: located on the third terrace at the W edge
close to the Laptev Sea (72∘49′20.1′′ N,
123∘30′45.0′′ E).
Olenyokskaya Channel, center: located on the first terrace in the SW part
of the LRD (72∘33′56.9′′ N, 125∘03′52.3′′ E).
Kurungnakh Island: located on the third terrace in an alas
depression on Kurungnakh Island about 10 km SW of Samoylov Island
(72∘19′12.5′′ N, 126∘11′35.7′′ E). The installation
of the borehole destroyed the surface vegetation and thereby triggered
melting of excess ground ice and the formation of a thermokarst pond around
the borehole within 1 year (see Supplement). The ground temperature record
must therefore be considered disturbed and most likely features a warm bias
compared to the surrounding undisturbed terrain. We therefore only employ the
first 3 months of data following the drilling of the borehole.
Sardakh Island: located in the SE part of the LRD near the main channel
of the Lena River (72∘19′12.6′′ N,
127∘14′29.4′′ E). Sardakh is generally classified as part of the
third terrace due to similar surface cover and height above river level, but
the ground is actually comprised of Neogene sandstone with a cover of Yedoma
deposits . At the borehole site, melting of excess
ground ice has occurred since the installation of the borehole like in the
case of Kurungnakh, which has led to subsidence of the surface and the
formation of a pond around the borehole. This was observed for the first time
in summer 2012 (see Supplement), and we therefore exclude the later parts of
the borehole record from the comparison to model results.
For the second terrace, there are no measurements of ground temperatures
available.
Systematic measurements of thaw depths according to the CALM protocol have
not been conducted outside Samoylov Island. However, there exist observations
of thaw depths for single points in time and space for all three river
terraces, facilitating validation of regional differences in thaw depths:
First terrace: in addition to the comprehensive record on Samoylov Island,
a single measurement near the borehole site “Olenyokskaya Channel, center”
is available from the year 2010.
Second terrace: in summer 2005, thaw depths were recorded at several sites
on Turakh Island (72∘56′24.4′′ N, 123∘47′54.9′′ E)
in the southwestern LRD near exposures at the shoreline and at a drill core
site . Another manual
thaw depth measurement was performed in the northern part of Arga Island
(73∘29′39.2′′ N, 124∘22′33.1′′ E) in 2010. These
observations are the only available ground truth information for the second
terrace in the model period 2000–2014. Two additional observations are
available from summer 1998 from the central part of Arga Island
(73∘20′18.5′′ N, 124∘12′30.5′′ E) near Lake Nikolay
and on Dzhipperies Island
(72∘51′14′′ N, 125∘50′22′′ E) near Lake
Yugus-Jie-Kuyele
. While these cannot be compared to model output in
a strict sense, they confirm the general order of magnitude of thaw depths on
the second terrace.
Third terrace: thaw depth measurements are available from two distinct
areas. At the W edge of the LRD, the thaw depth was recorded near the
borehole site “Olenyokskaya Channel, mouth” in summer 2010. At three dates
in July and August 2013, thaw depths were recorded at nine locations in the S
part of Kurungnakh Island, near the so-called “Lucky Lake”
(72∘17′41.0′′ N 126∘9′34.0′′ E). The nine locations
are contained within six 1 km model grid cells.
Methods
In this study, we update and extend the satellite data-based transient
modeling of the ground thermal regime as outlined in
to an area of approximately 16 000 km2 within
the LRD. The general idea is to employ time series of remotely sensed surface
temperatures and snow depths to force a transient ground thermal model.
The CryoGrid 2 ground thermal model
CryoGrid 2 is a transient 1-D ground thermal model based on Fourier's law of
heat conduction . The model does not account
for changing subsurface water contents due to infiltration and
evapotranspiration, but instead assigns fixed values for the porosity and
saturation of each grid cell. Freezing/thawing of soil water/ice is accounted
for by a temperature-dependent apparent heat capacity
e.g., which is determined by the soil freezing
characteristic according to the formulation by . The
apparent heat capacity and thermal conductivity of each layer are computed
according to the volumetric fractions of water/ice (determined by the
temperature), air and sediment matrix material composed of a mineral and an
organic component. A more detailed description of the model physics and the
numerical solvers is provided in .
CryoGrid 2 is capable of representing the annual buildup and disappearance
of the snow cover by adding or subtracting grid cells according to a time series
of snow water equivalent (SWE; which must be provided as part of the forcing
data), but it only allows for constant thermal properties of the snow grid cells
(both throughout the snow pack and over time). For this study, we assign a
functional dependency between snow thermal conductivity ksnow and
density ρsnow according to :
ksnow=kiceρsnowρwater1.88,
with kice and ρwater denoting the thermal
conductivity of ice and the density of water, respectively. This
parameterization performed well over a wide range of snow densities and types
in a dedicated validation study . Furthermore, the
snow density is employed to compute the volumetric heat capacity of the snow
and to convert snow water equivalent to snow depth. As a result, the thermal
properties of the snow pack are described by only a single parameter, the
snow density ρsnow, for which an extensive set of in situ
observations is available from Samoylov Island .
Subsurface properties and additional model parameters
At 1 km resolution, it is not possible to resolve small-scale differences of
surface and subsurface properties. Therefore, we only distinguish the three
river terraces as the main geomorphological units within the LRD for which we
define “typical” subsurface stratigraphies based on available field
observations (Sect. ). The stratigraphies are provided in
Table , while the boundaries of the terraces
(Fig. ) are based on
gridded to 1 km. For all terraces, a saturated bottom layer with
mineral content of 70 vol % is assumed, corresponding to densified
fluvial deposits underlying the modern delta
.
Subsurface stratigraphies for the three LRD terraces with volumetric
fractions of the soil constituents and sediment type assigned to each
layer.
Depth (m)
Water/ice
Mineral
Organic
Air
Type
First terrace
0–0.15
0.6
0.1
0.15
0.15
sand
0.15–9
0.65
0.3
0.05
0.0
silt
>9
0.3
0.7
0.0
0.0
sand
Second terrace
0-10
0.4
0.6
0.0
0.0
sand
>10
0.3
0.7
0.0
0.0
sand
Third terrace – Yedoma
0–0.15
0.3
0.1
0.1
0.5
sand
0.15–20
0.7
0.25
0.05
0.0
sand
>20
0.3
0.7
0.0
0.0
sand
For the first terrace, a 0.15 m thick upper layer with high porosity and
organic content is assigned, which is not entirely saturated with water or
ice . Below, the ground is
assumed to be saturated, but the porosity remains high, corresponding to the
ice-rich sediments. Based on field observations on Samoylov Island
, fine-grained silty
sediments dominate the matrix material, with organic contents of
approximately 5 vol %. The depth of this layer is set to 9 m, based on
observations for the depth of ice wedges in the first terrace
. Note that these ground properties are also
assigned to the active floodplain areas within the first terrace
(Sect. ), which cannot be meaningfully delineated at 1 km
scale. In such floodplain areas, the model results must therefore be
considered with care. Furthermore, the polygonal tundra landscape features a
strong variability in surface soil moisture and vegetation and sediment
conditions over distances of a few meters , which
cannot be captured by the single stratigraphy employed for the modeling.
The sandy sediments of the second terrace largely lack an organic upper
horizon ,
so a uniform upper layer with typical porosity of sand is prescribed
(Table ).
The third terrace is dominated by a relatively dry organic top layer with
high porosity , followed by
a thick layer with very high ice contents (and organic contents of
5 vol %), corresponding to the late Pleistocene Yedoma deposits
. While the mineral fraction
of this layer in reality is composed of fine-grained silty sediments, we
assign “sand” as sediment type (Table ) to account
for the freezing characteristic of the extremely ice-rich ground which can be
expected to resemble that of free water/ice rather than that of saturated
silt.
The thermal conductivity of the mineral fraction of the sediment matrix
required for the calculation of the soil thermal conductivity
is set to 3.0 Wm-1K-1, as in
previous modeling studies on Samoylov Island
. The
sensitivity study by showed that the snow thermal
properties are the most important model parameter controlling the simulated
ground thermal regime. Therefore, the snow density (which controls snow
depth, heat capacity and thermal conductivity, Sect. ) is a
crucial parameter for which spatially or temporally distributed data sets
covering the entire LRD are not available. However, an extensive set of
measurements from polygonal tundra on Samoylov Island suggests snow densities
of 225±25 kgm-3 Fig. 6b,
for polygon centers with well-developed snow cover,
so it is possible to
explicitly account for the uncertainty of this important parameter by
conducting model runs for a range of snow densities. For comparison to
in situ data (Sects. , ),
we present model runs with confining values of 200 and 250 kgm-3
(thus providing a range of ground temperatures), while the spatially
distributed model runs (Sect. ) are conducted with
an average snow density of 225 kgm-3. Note that the confining
values represent 1 standard deviation and that higher and lower snow
densities occur regularly .
Model forcing data
CryoGrid 2 requires time series of surface (i.e., skin) temperatures and snow
water equivalent as forcing data sets.
Surface temperature: as temperature forcing at the upper model
boundary, a product synthesized from clear-sky land surface temperatures
(LST) from the Moderate Resolution Imaging Spectroradiometer (MODIS) and 2 m
air temperatures from the ERA-Interim reanalysis was
applied. For this purpose, the daily MODIS level 3 LST products MOD11A1 and
MYD11A1 in the version 005 were employed, which
deliver four LST values per day (Terra and Aqua satellites, day- and
nighttime LST each). The merging procedure is similar to that described in
, in which spatially distributed data sets of
freezing and thawing degree days were generated. In essence, gaps in the
MODIS LST record due to cloud cover are filled by the reanalysis data, which
creates a data record with homogeneous data density and has the potential to
moderate the cold bias of temporal averages of surface temperatures computed
from clear-sky MODIS LST .
During cloudy skies, differences between air and surface temperatures are
strongly reduced compared to clear-sky conditions
e.g.,, so air temperatures can be regarded as
an adequate proxy when MODIS LST is not available due to cloud cover. Note
that this gap-filling procedure assumes that air temperatures from the
ERA-Interim reanalysis are not strongly biased. For melting snow, surface
temperatures are confined to the melting point of ice, while air temperatures
can be positive. Positive values of the surface temperature forcing are
therefore set to 0 ∘C if a snow cover is present (see below). For
this study, we create a time series of weekly averages of surface
temperatures to force the CryoGrid 2 model. The reanalysis data, which are
available at 0.75∘ resolution, are interpolated to the center point
of each MODIS LST pixel (in the sinusoidal projection native to MOD11A1 and
MYD11A1 data). The satellites carrying the MODIS instrument were launched in
2000 (Terra) and 2002 (Aqua), respectively, while ERA-Interim reanalysis is
available since 1979. The synthesized time series used for model forcing
therefore extends from 15 May 2000 to 31 October 2014 and thus covers the
period for which remotely sensed LST data from at least one satellite are
available. For the first 2 years, the data density of MODIS LST measurements
in the composite product is lower than after summer 2002, when LST
measurements from Aqua become available. Spatially, the fraction of the
successful MODIS LST retrievals is relatively constant throughout the LRD,
varying between 50 and 55 %. In summer and fall, retrieval fractions are
generally lower (40–50 %) than winter and spring (55–70 %),
indicating more frequent cloudy conditions in summer and fall.
Snow depth: similar to the procedure outlined in
, a weekly snow water equivalent product was
synthesized from GlobSnow SWE (25 km
resolution) and the MODIS level 3 Snow Cover (SC) products MOD10A1 and
MYD10A1 (; 0.5 km resolution), which for
clear-sky conditions deliver two values of binary flags (1: snow; 0: no snow)
per day (one for Terra and Aqua each). The latter products were averaged over
the 1 km sinusoidal grid of the MODIS LST data and the two satellites,
yielding a number between 0 and 1 for each day with available data,
corresponding to the fraction of successful retrievals at the 0.5 km pixel
level flagged as “snow”. We then applied a “maximum change” detection
algorithm to the data set to determine the most likely dates for the start
and the end of the snow cover in each 1 km pixel. For this purpose, we
compute the fractions of 1 km values with values of 0 and 1, respectively,
both within a window of 4 weeks before and after each date. The snow start
date is determined as the date for which the sum of fractions of 0 before and
fractions of 1 after is largest. This sum can be up to 2 when there are
100 % retrievals flagged as snow-free before and 100 % retrievals
flagged as snow covered before the date. For the snow end date, the opposite
criterion is applied, i.e., the sum of the fractions of 1 before and
fractions of 0 after features a maximum. Note that the large window is
required as prolonged cloudy periods often occur in the study area, for which
no measurements are available. The MODIS SC products cover the same periods
as the MODIS LST data (see above).
GlobSnow SWE (Daily L3A SWE, level 2.0;
) data
are derived from passive microwave remote sensors, which are not affected by
clouds, so a gap-free daily time series is in principle available for the
entire model period from 2000 to 2014. The GlobSnow processing algorithm is
based on a data assimilation procedure, which also takes in situ measurements
at World Meteorological Organization stations into account
. For the LRD, the closest station is located at
Tiksi, about 50 km to the E, while the closest stations to the W are
several hundred kilometers away. The station measurements are interpolated in
space to obtain an SWE background field which is then weighted against SWE
information derived from the passive microwave sensor by means of forward
modeling of snowpack microwave emission using the HUT model
. In the data assimilation procedure, a spatially
constant snow density of 240 kgm-3 is assumed, which is in the
range of the in situ measurements on Samoylov Island
(Sect. ).
The SWE values in the LRD (see Sect. ) are typically below
the critical threshold of about 150 mm above which SWE can no longer
be reliably derived from passive microwave retrievals
. On the other hand, SWE retrieval is hampered
for shallow snow cover and for wet melting snow, so the start and the
end of the snow season is not well covered by GlobSnow. Furthermore, water
bodies constitute a major error source e.g.,
and generally lead to underestimation of SWE, in particular when the ice
cover is thin . Due to admixing of microwave
radiation emitted from the ocean, the number of SWE retrievals is very small
or even zero in the coastal areas of the LRD, so almost half of the area
of the LRD could not be included in the modeling. The boundary of the final
model domain was finally chosen so that all validation sites
(Fig. ) are located within. In a few cases (in particular the
sites AN, Tu and OM, Fig. ), the available SWE data had to be
extrapolated by about one grid cell, or 25 km, which seems adequate
considering the smoothness of the remote-sensing-derived SWE field in the
LRD.
As a first step, the daily SWE data were interpolated from the Northern
Hemispherical Equal-Area Scalable Earth Grid (EASE-Grid) projection (25 km resolution) to the 1 km sinusoidal grid of the
MODIS LST data. We subsequently assign linearly increasing SWE from the date
identified as the most likely snow start date (using the MODIS SC product,
see above) and the next available GlobSnow SWE measurement. The same
procedure is applied for the snow end date. Note that this procedure can
result in a step-like increase or decrease of the snow depth, if a valid
GlobSnow SWE value is available for the identified start and end date. As a
final step, the daily time series is averaged to the same weekly periods as
the employed surface temperature forcing (see above), and SWE is converted to
snow depth with the applied snow density (Sect. ). The use of
medium-resolution MODIS SC facilitates correcting the coarse-scale GlobSnow
SWE product regarding the start and the end of snow cover period, both of
which can crucially influence the modeled ground thermal regime.
Nevertheless, passive microwave-derived SWE is associated with considerable
uncertainty in the LRD. We therefore compare the model snow forcing to
in situ measurements from Samoylov Island (Sect. ) and
to independent spatial SWE data sets (Sect. ,
Supplement).
Model setup
For each 1 km grid cell, the ground thermal regime was simulated for a
specific ground stratigraphy and forcing time series of surface temperatures
and snow depths. In the vertical direction, the ground between the surface
and 100 m depth is discretized in 163 layers, which increase in size from
0.02 m near the surface (until 1.5 m depth so that the active layer is
modeled at maximum resolution) to 10 m near the bottom, similar to
the setup in . Within the snow cover, the
minimum layer size of 0.02 m is prescribed. At the lower boundary, a
constant geothermal heat flux of 50 mWm-2 is assumed, as
estimated from a 600 m deep borehole 140 km east of Samoylov Island
.
To estimate a realistic initial temperature profile, a model spin-up is
performed to achieve steady-state conditions for the forcing of the first 5 model years, using the multistep
procedure outlined in detail in
. In a first step, the model is run to
estimate the average temperature at the ground surface (i.e., below the snow
cover in winter), for which the steady-state temperature profile in the
ground is assigned to all grid cells (considering the geothermal heat flux at
the bottom and the thermal conductivity of all grid cells). In a second step,
CryoGrid 2 is run twice for the first 5 model years, so that the annual
temperature cycle to the depth of zero annual amplitude is reproduced. The
simulations for the entire time series can thus be initialized by a
temperature profile that is both adequate for the upper and the lower parts
of the model domain. We emphasize that the initialization procedure limits
the CryoGrid 2 results to the uppermost few meters of the soil domain since
deeper temperatures are still influenced by the surface forcing prior to the
model period, for which satellite measurements and thus model forcing data
are not available.
(a) Daily average surface temperatures measured on Samoylov
Island vs. surface
temperatures synthesized from MODIS LST and ERA-Interim reanalysis.
(b) Difference between satellite-derived LST and in situ
measurements for monthly averages of periods when in situ measurements are
available (see a). See text.
Discussion and outlook
Model forcing
Surface temperature
Validation studies have revealed a significant cold bias of long-term
averages derived from MODIS LST in Arctic regions
, which is attributed to the
overrepresentation of clear-sky situations and deficiencies in the cloud
detection during polar night conditions . The same
bias is found for Samoylov Island (Fig. ), for which
averages directly computed from MODIS LST measurements are cold-biased by
about 1–2 ∘C for most of the year. In this study, we therefore
employ a gap-filling procedure with ERA-Interim near-surface air
temperatures. During cloudy periods, reanalysis-derived air temperatures may
indeed facilitate an adequate representation of surface temperatures, as the
near-surface temperature gradient is smaller compared to clear-sky conditions
e.g.,.
As demonstrated by for
the N Atlantic region, the composite product features a considerably reduced
bias and is significantly better suited as input for permafrost modeling than
the original MODIS LST record. However, a small, but consistent, cold bias of
about 0.8 ∘C remains. This could be explained by the fact that the
gap-filling procedure only applies to gaps due to clouds that are
successfully detected but does not remove strongly cold-biased LST
measurements of cloud top temperatures
that regularly occur when the
MODIS cloud detection fails. Here, further improvements seem feasible,
e.g., through simple plausibility criteria when comparing the remotely sensed
LST against meteorological variables of the ERA-Interim reanalysis data set. However,
such methods are most likely sensitive towards a range of factors, such as
land cover and exposition (which strongly influence the true surface
temperature), so they should be carefully developed and validated for a
range of sites. Based on in situ measurements, suggest
that snow-covered ground dew point temperatures are a better
approximation for surface temperatures compared to air temperatures at
standard height. However, observations on Samoylov Island display only a
small offset between snow surface and air temperatures, with the difference
increasing from near zero in early winter to about 1 ∘C in late
winter Table 3, . The reason for this is most
likely that the ground heat flux is a strong heat source especially in early
winter , which warms the surface and thus prevents
formation of a strong near-surface inversion. Therefore, we consider air
temperatures an adequate proxy for snow surface temperatures in the LRD, but
dew point temperatures should clearly be considered for gap filling in the
snow-covered season in future studies. We conclude that surface temperatures
synthesized from MODIS LST and near-surface air temperatures from the
ERA-Interim reanalysis are an adequate choice for the purpose of ground
thermal modeling in the LRD, at least in homogeneous terrain, although it may
introduce a slight cold bias in modeled ground temperatures.
Snow
As demonstrated by , snow depth and snow thermal
properties are crucial factors for correctly modeling ground temperatures in
the LRD. In this light, the coarsely resolved estimates of GlobSnow SWE must
be considered the key source of uncertainty for the thermal modeling.
The performance of GlobSnow SWE has been evaluated on continental scales
by comparison to systematic in situ data sets
. For Eurasia, surveys
spanning the entire snow season were compared from
1979 to 2000. For shallow snow (approximately SWE < 60 mm), GlobSnow
SWE tends to overestimate observed values slightly, but the relationship
between measurements and GlobSnow retrievals is on average linear. When SWE
exceeds approximately 100 mm, the GlobSnow algorithm tends to underestimate
measured SWE, and for values larger than 150 mm the signal from
passive microwave retrievals saturates and SWE can no longer reliably be
detected . For the LRD, both in situ measurements
and GlobSnow values indicate that SWE is generally below this critical
threshold, so saturation effects most likely do not play a role for the
uncertainty. The Eurasia data set is strongly biased towards sites in steppe
environments and the boreal forest zone where SWE retrieval is
affected by the canopy, e.g.,, while northern tundra
areas with characteristics similar to the LRD are strongly undersampled. A
more representative data set is available from an extensive transect across
northern Canada , for which comparison of
GlobSnow SWE retrievals yielded an RMSE of 47 mm and an average bias
of -36 mm. The average SWE of 120 mm
was significantly larger than in the LRD,
so it is not meaningful to transfer the absolute uncertainties. When using
relative uncertainties, on the other hand, we arrive at a similar RMSE as for
the comparison of the time series on Samoylov Island (0.06 m, see
Sect. ): for N Canada, a relative RMSE of around
40 % was found, which corresponds to an absolute RMSE of 0.065 m
in snow depth, when scaled to the average of around 0.16 m on
Samoylov Island (Fig. f). Although the character of the
two data sets differs (spatial transect vs. multi-year point measurement),
the good agreement is an indication that the GlobSnow performance in the LRD
could be similar to N Canada. We emphasize that the RMSE corresponds to
undirected fluctuations around the average value, which has much less
influence on the modeled average ground thermal regime (Figs. ,
) than a systematic bias.
Water bodies strongly affect microwave emission of the ground, which is
known to lead to underestimation of SWE in passive microwave-based retrievals
. For the
above-mentioned N Canada data set, water bodies might explain the significant bias
of 36 mm , but the average values
(120 mm) are also sufficiently high that saturation effects
are likely to contribute to the bias. In the
LRD, water bodies are abundant features (Fig. ), so
GlobSnow retrievals are likely to be affected. Using a Landsat
and MODIS (MODIS water mask) based land cover
classifications, we estimate the water fraction in the employed 25 km grid
cells in the Lena River delta to be between 12 and 30 %, with a single
grid cell in the E part reaching 37 % (of which more than half is
estimated to be river arms, see below). Almost three quarters of the grid
cells feature water fractions of less than 20 %. However, relatively
shallow thermokarst lakes dominate in the LRD, which at least partly freeze to
the bottom in winter ,
so microwave emission becomes similar to land areas, although in particular
the wavelength dependency of the effect may be complex
. Furthermore, the winter discharge of the Lena
River is very low compared to other northern rivers, as the catchment is
largely located in the continuous permafrost zone .
We estimate the winter discharge to be only about 10 % of summer averages
Fig. 2 in , and large river areas identified as
water in summer-derived satellite imagery must fall dry in winter, which
decreases the water fraction in the central and eastern part of the delta
(where the water fractions are highest) considerably. Furthermore,
shallow river arms and even coast-near areas of the Laptev Sea
also freeze to the bottom, so we expect the true
“open water” fraction relevant for microwave emission in winter to be
significantly lower than the open water fractions obtained from summer
imagery (see above) suggest. This is corroborated by the comparison to
in situ measurements for Samoylov Island (Fig. )
situated in a relatively water-body-rich area where we find a satisfactory
performance for GlobSnow. The largest impact on SWE retrievals is most likely
during lake freezing and snow cover buildup in fall, when GlobSnow SWE
retrievals must be considered highly uncertain. In the future, enhanced SWE
retrieval algorithms taking the effect of water bodies explicitly into account
e.g., may become available.
The spatial resolution of 25 km is insufficient to capture the
considerable spatial variability of snow depths in the LRD both on the
modeling scale of 1 km and the considerably smaller scales where the
snow distribution is strongly influenced by the microtopography
. Studies with equilibrium models have demonstrated
that the latter can to a certain degree be captured by statistical approaches
that employ an (estimated) distribution of snow depths to obtain
distributions of ground temperatures for each grid cell
. However,
with the transient modeling scheme employed in this study, new issues arise
that strongly complicate the application of a statistical representation of
snow cover. First, spatial differences in snow depth will inevitably lead to
a different timing of the snow melt which could influence in particular the
modeled active layer thickness. Such small-scale differences of the snow
start date cannot be captured by the 0.5 km scale MODIS SC product.
Secondly, it is not clear how the distribution of snow depths can be
translated to forcing time series of snow depths that are required for the
CryoGrid 2 modeling. In some areas, snow depths may be relatively constant
from year to year, while there may be strong interannual variations at other
sites. Such temporal evolution is not contained in the distribution of snow
depths, and computationally demanding deterministic snow redistribution
models e.g., may be required to overcome such
problems.
In the coastal regions of the LRD, GlobSnow SWE does not provide a sufficient
number of retrievals, so that the annual dynamics of the snow cover can be
captured. In general, these regions must be excluded from the model domain.
In this study, we chose to extrapolate the GlobSnow SWE retrievals to
adjacent regions, so that more validation sites could be covered. The same
issue applies to regions with pronounced topography, which precludes the use
of the modeling scheme for mountain permafrost area.
The snow density is a crucial parameter, as it controls both the snow
depth (since SWE is used as driving input data), the snow volumetric heat
capacity and the snow thermal conductivity. In this study, the snow density
was assumed to be constant in time and space, with the values determined by
in situ measurements similar
to. While this may be
adequate for the relatively small model domain of the LRD, spatially
distributed information on typical snow densities
e.g., would be required for application on larger
scales.
The end and start of the snow cover have been determined at a comparatively
high spatial resolution of 1 km using the MODIS SC product
(Fig. ), which corresponds to a downscaling
of the coarsely resolved GlobSnow SWE product for these important periods.
Furthermore, the performance of the GlobSnow SWE product is relatively poor
for very shallow snow depths and for wet (melting) snow
, which is to a certain extent moderated by
prescribing the snow start and end dates.
The CryoGrid 2 model
In this study, CryoGrid 2 is employed for a relatively short period of
approximately 15 years, so the model initialization deserves a critical
discussion . A model spin-up to periodic
steady-state conditions was performed for the first 5 years of forcing data,
i.e., from summer 2000 to summer 2005. Ground temperatures in deeper soil
layers are strongly influenced by the choice of the initial condition, and
the modeled temperatures should not be interpreted further. Therefore, we
restrict the comparison to in situ measurements to the uppermost 3 m
of soil and for the period following 2002 for active layer measurements
(Figs. , ) and after 2006 for
ground temperatures in 2–3 m depth (Figs. ,
). In both cases, the model results are sufficiently
independent of the initialization , which must
therefore be considered a minor source of uncertainty.
The applied ground stratigraphy has a significant direct influence on the
simulations results, both on ground temperatures and thaw depths
compare. For this study, three landscape units
with associated “typical” stratigraphies were defined, which facilitate
capturing the observed large-scale differences in particular for the thaw
depth (Sect. ). However, a significant small-scale
variability of ground properties is superimposed on these large-scale
differences, giving rise to a significant variability of thaw depths and
ground temperatures that are not captured at 1 km scale. An example is the
in situ record of thaw depth measurements at 150 points on Samoylov Island,
for which the model scheme can capture the interannual variations of the mean
very well (Fig. ). However, with an average standard
deviation of 0.06 m the measurements feature a considerable spread
that is most likely explained by small-scale
differences in ground properties, surface temperature and possibly snow
cover. Another example is the borehole site on Samoylov Island, for which the
“typical” ground stratigraphy for the first terrace is clearly not
applicable (Fig. ). In principle, such subgrid
effects could be captured by running the model scheme not only for a single
realization per grid cell, but for an ensemble of model realizations
reflecting the statistical distribution of ground stratigraphies and
properties within a grid cell. Such a scheme could also be extended to
account for a subgrid distribution of snow depths by assigning different snow
depths according to a defined distribution, e.g.,
to the ensemble members. In addition to a considerable increase in
computation time (e.g., a factor of 100 for 100 ensemble members), field data
sets with statistical information on ground stratigraphies are generally
lacking for the LRD. A simpler way could be aggregating high-resolution
land cover data sets e.g., to the 1 km grid, so
that fractional information on the land cover can be obtained. Assuming that
each land cover class can be assigned a typical subsurface stratigraphy, the
model scheme could be run for all land cover classes/stratigraphies present
within one 1 km grid cell.
The model physics of CryoGrid 2 does not account for a range of processes
that may influence the ground thermal regime in permafrost areas, such as
infiltration of water in the snow pack and soil
, or
thermokarst and ground subsidence due to excess ground ice melt. The latter
can strongly modify the ground thermal regime, as demonstrated by
, which makes a comparison of model results to in
situ measurements at thermokarst-affected sites (Kurungnakh, Sardakh,
Sect. ) challenging. Furthermore, small water
bodies and lakes can strongly modify the ground thermal regime both in the
underlying ground and in the surrounding land areas
, so the model results are
questionable in areas with a high fraction of open water areas
. While more sophisticated model schemes
can simulate the ground thermal regime
of such features, a spatially distributed application is challenging: in
general, higher-complexity models require additional input data and model
parameter sets e.g., precipitation for a water balance model,
, for which the spatial and temporal distributions are
poorly known. Furthermore, the model sensitivity may vary in space depending
on the interplay of different model parameters and input data
, which makes it harder to judge the
uncertainty of model results.
The modeled ground thermal regime
The validation results suggest a model accuracy of 1–2 ∘C for
multi-annual average ground temperatures
(Fig. ) and around 0.1–0.2 m for
annual maximum thaw depths (Table ). On the one hand, high
ground temperatures are modeled along the large river channels in the
southern part of the LRD. These areas also feature high average surface
temperatures (Fig. ) which could at least partly be
related to warm water advected by the Lena River. Surface temperatures
derived from remote sensors have a significant advantage over data sets
derived from atmospheric modeling, which in general cannot reproduce such
effects. On the other hand, the modeled ground temperatures are clearly
influenced by ground stratigraphy. As evident in Fig. , the
second terrace is systematically warmer than the adjacent first terrace,
which is not visible in the temperature forcing (Fig. ).
This finding is corroborated by the sensitivity analysis
(Table ) which showcases the importance of a sound
representation of ground thermal properties, in particular in and just below
the active layer, for correct modeling of ground temperatures. These
differences are at least partly related to stratigraphy-dependent thermal
offsets between average ground surface and ground temperatures caused by
seasonal changes of subsurface thermal conductivities due to freezing and
thawing .
Thaw depths are to an even larger extent determined by the ground
stratigraphy. On the third terrace, a comparatively dry organic-rich layer
with low thermal conductivity limits the heat flux so the underlying
ice-rich layers experience only a limited amount of thawing. As a
consequence, the thaw progression hardly extends below the uppermost layer,
yielding thaw depths of around 0.3 m and less. On the first terrace,
this effect is somewhat reduced (thinner and wetter organic top layer and
lower water ice contents below), while the second terrace lacks the organic
top layer and as a consequence experiences considerably deeper thawing than
the two other stratigraphic units. In addition, the summer surface forcing
strongly impacts thaw depths. Within the first terrace, the model results
yield a pronounced north–south gradient of thaw depths (Fig. )
which is related to the pattern of thawing degree days
(Fig. ).
Towards remote detection of ground temperature and thaw depth in permafrost
areas
The presented model approach can compute ground temperatures and thaw depths
for an area of more than 10 000 km2, largely based on remotely
sensed data sets. Other than in satellite-based approaches with much simpler
steady-state models , the time
evolution of the ground thermal regime is explicitly accounted for in the
transient approach using CryoGrid 2. Our results suggest that the annual
temperature amplitude to about 2–3 m depth is generally captured, while a
longer time series is needed to evaluate and secure multi-annual trends, in
particular since the first part of the model period is affected by the
initialization. However, with the ever extending record of high-quality
satellite data, remote detection of trends in permafrost temperatures may
become feasible in the coming years.
With sufficient computational resources provided, the presented scheme could
in principle be extended to the entire Northern Hemisphere, for which
GlobSnow retrievals are available. However, at present such application is
limited by a number of shortcomings and complications: first, the model scale
of 1 km2 may be sufficient to represent the ground thermal regime in
lowland tundra landscapes like the LRD but is significantly too coarse for
heterogeneous terrain, e.g., in mountain areas .
Since the grid cell size is determined by the spatial resolution of the
remotely sensed land surface temperatures, it could only be improved with the
deployment of higher-resolution remote sensors for surface temperature (which
must also feature a high temporal resolution). The snow density is a crucial
parameter in the model scheme which has been determined from in situ
measurements in this study. For application on larger domains, spatial
differences in snow density must be considered, which might be obtained, for
example, from simple empirical relationships with climate variables
. Furthermore, remotely sensed data sets of snow
water equivalent are lacking in many regions, in particular in coastal and
mountain areas (compare Fig. ), and the spatial resolution
of 25 km is hardly sufficient to capture the spatial distribution of
snow in the terrain in complex landscapes. Furthermore, operational SWE
retrievals are associated with considerable uncertainty in lake-rich tundra
areas . In many permafrost areas, this can be
expected to result in a strongly reduced accuracy, so significantly simpler
schemes might provide similar results. Another
crucial issue is the lack of a standardized pan-arctic product on subsurface
properties, which combines spatially resolved classes with information on
subsurface stratigraphies and thermal properties. There exists a variety of
such products on the regional and local scales, but they strongly differ in
their quality and classes which are derived for different purposes. A
pan-arctic homogenization effort similar to what has been accomplished for
permafrost carbon stocks is therefore needed in
order to obtain meaningful results with a transient ground thermal model,
such as CryoGrid 2.
Despite such challenges, transient ground temperature modeling forced by
remote-sensing data offers great prospects for permafrost monitoring in
remote areas that are not covered by in situ measurements. The good
performance regarding thaw depths and the timing of the seasonal thaw
progression (Fig. ) suggests that the results may even help
in estimating the release of greenhouse gases as a consequence of active layer
deepening in a warming climate .
Conclusions
We present a modeling approach to estimate the evolution of the
ground thermal regime in permafrost areas at 1 km spatial and weekly
temporal resolution, based on a combination of satellite data and reanalysis
products. The scheme is applied to an area of 16 000 km2 in the Lena
River delta in northeastern Siberia where measurements of ground temperatures
and thaw depths are available to evaluate the performance. The approach is
based on the 1-D ground thermal model CryoGrid 2, which calculates the time
evolution of the subsurface temperature field based on forcing data sets of
surface temperature and snow depth for each grid. As forcing data, we
synthesize weekly average surface temperatures from MODIS Land Surface
Temperature products and near-surface air temperatures from the ERA-Interim
reanalysis. For snow depth, low-resolution remotely sensed GlobSnow Snow
Water Equivalent data are combined with higher-resolution satellite
observations of snow extent facilitating an adequate representation of the
snow start and end dates in the model. For the subsurface domain, a
classification based on geomorphological mapping has been compiled, which can
resolve the large-scale differences in, for example, ground ice and soil-water
contents. The model was subsequently run for a period of 14 years
(2000–2014) and the results compared to observations of the ground
temperatures and thaw depths at nine sites.
The forcing data sets in general agree well with multi-year in situ
observations. Monthly average surface temperatures are reproduced within
1 ∘C or less, while the snow start and end dates in most years agree
within 1 week. In a few years, larger deviations of up to 3 weeks
occur.
The comparison of model results to in situ measurements suggests that
the approach can reproduce the annual temperature amplitude. Multi-annual
averages of ground temperatures at 2–3 m depth are reproduced with an
accuracy of 1–2 ∘C, while comparison of monthly averages yielded an
overall RMSE of 1.1 ∘C and a cold bias of 0.9 ∘C for the
model results. However, due to the small number of validation sites, this
accuracy assessment must be considered preliminary.
Modeled thaw depths in general agree with in situ observations within
0.1–0.2 m. At one site, comparison with a multi-annual time series
of thaw depth measurements suggests that the model scheme is capable of
reproducing interannual differences in thaw depths with an accuracy of
approximately 0.05 m.
A sensitivity analysis showcases the influence of the subsurface
stratigraphy on both ground temperatures and thaw depths, with temperature
differences up to 2 ∘C and thaw depth differences of a factor of
3 between classes for the same forcing data.
The highest average ground temperatures are modeled for grid cells close
to the main river channels and areas featuring sandy sediments with low
organic contents in the northwestern part of the Lena River delta. The lowest
modeled ground temperatures occur in the eastern part of the delta towards
the coastline and in areas with ice-rich Yedoma sediments.
The lowest thaw depths are modeled for Yedoma in the southern parts of
the delta as well as in areas with both low snow depths and cold summer
surface temperatures in the northeastern part. The deepest thaw depths are
found in areas where the stratigraphy assigns mineral ground with low ice and
organic contents.
The results of this study encourage further development of satellite-based
modeling of the ground thermal regime in permafrost areas on continental
scales. The largest obstacles are the lack of a standardized classification
product on subsurface stratigraphies and thermal properties as well as
shortcomings and limitations of the currently available remote products on
snow depth and snow water equivalent (see Sect. ). If
such limitations can be overcome, remote-sensing-based methods could
complement and support ground-based monitoring of the ground thermal regime.