Permafrost influences a number of processes which are relevant for local and global climate. For example, it is well known that permafrost plays an important role in global carbon and methane cycles. Less is known about the interaction between permafrost and ice sheets. In this study a permafrost module is included in the Earth system model CLIMBER-2, and the coupled Northern Hemisphere (NH) permafrost–ice-sheet evolution over the last glacial cycle is explored.
The model performs generally well at reproducing present-day permafrost extent and thickness. Modeled permafrost thickness is sensitive to the values of ground porosity, thermal conductivity and geothermal heat flux. Permafrost extent at the Last Glacial Maximum (LGM) agrees well with reconstructions and previous modeling estimates.
Present-day permafrost thickness is far from equilibrium over deep permafrost regions. Over central Siberia and the Arctic Archipelago permafrost is presently up to 200–500 m thicker than it would be at equilibrium. In these areas, present-day permafrost depth strongly depends on the past climate history and simulations indicate that deep permafrost has a memory of surface temperature variations going back to at least 800 ka.
Over the last glacial cycle permafrost has a relatively modest impact on simulated NH ice sheet volume except at LGM, when including permafrost increases ice volume by about 15 m sea level equivalent in our model. This is explained by a delayed melting of the ice base from below by the geothermal heat flux when the ice sheet sits on a porous sediment layer and permafrost has to be melted first. Permafrost affects ice sheet dynamics only when ice extends over areas covered by thick sediments, which is the case at LGM.
The existence and thickness of permafrost is a result of the history
of energy balance at the Earth's surface and the deep Earth heat
flow. Assuming that the geothermal heat flow did not notably
change over the Quaternary, the present permafrost state has been
shaped mainly by past surface ground temperature variations
Also, previous glaciation periods have played an important role in the evolution of permafrost. Thick ice sheets have a strong insulation effect on the ground below and effectively decouple the ground temperature from the air temperature over the ice. Below ice sheets permafrost can be melted from below by the geothermal heat flux. So, previously glaciated regions will show a lesser volume of frozen ground than unglaciated regions with similar climatic histories. In this regard it is important that Canada was heavily glaciated while most of Siberia had remained ice-free during the past glacial cycle. Thus, the present permafrost thickness in Siberia is much greater than in Canada, even though the climates are similar.
Not only is permafrost affected by ice sheets, but it can potentially also
affect ice sheet dynamics by influencing the basal conditions of the ice
sheets. Basal sliding requires the base of the ice sheet to be at pressure
melting point. This allows ice to melt at the base and to form a water layer
which facilitates sliding of the ice sheet by partly decoupling it from the
ground below
Several studies have investigated the subglacial conditions of the Laurentide
ice sheet (LIS) during the last glacial cycle.
The main limitation for long-term permafrost evolution evaluation is the lack
of coupled models including a permafrost component that are capable of
performing multimillennial transient simulations. All modeling studies on the
long-term evolution of permafrost have been performed by somehow prescribing
surface temperature changes as a boundary condition and ignoring the various
permafrost feedbacks on climate. Even this simplified offline modeling
approach is problematic because of the limited climate modeling available on
the glacial cycles timescale. As a workaround,
In this study a permafrost module is implemented into the coupled
climate–ice-sheet model CLIMBER-2. Ground surface temperature is modeled
explicitly. This updated version of CLIMBER-2 allows for the first time the
estimation of permafrost evolution during the last glacial cycle and beyond over
the whole Northern Hemisphere with a model forced only by atmospheric
Recently, a permafrost module has been included in CLIMBER-2
Given the very long characteristic timescales of deep permafrost evolution, the importance of model initialization is a relevant issue that has not received proper attention in the past. The dependence of present permafrost state on the initial conditions is also explored in this paper.
A newly developed permafrost module has been integrated into the CLIMBER-2
Earth system model of intermediate complexity
Up to now in CLIMBER-2 the geothermal heat flux was applied directly
at the base of the ice sheets
The 3-D temperature field in the ground is computed assuming that vertical
heat transfer occurs only through conduction and that horizontal heat fluxes
can be ignored. With these assumptions the vertical profile of temperature
(
Similarly to
We define a grid box to be permafrost if at least half of the water is
frozen, which formally translates into a condition on temperature:
The freezing/melting point temperature
As the ground is considered to be saturated, the following relations
apply:
Parameter description and values. Parameters where more than one value is listed are used in the sensitivity study. Bold values indicate the reference values.
Equation (
The lower boundary condition for the 1-D diffusion equation is given
by a constant in time but spatially varying geothermal heat flux
applied at 5
At the surface, over ice-free land, the computed MAGST is prescribed as
a boundary condition. The computation of the MAGST is based on the surface
energy and mass balance interface (SEMI) described in
Sediment thickness and mask from
The second term on the right represents heat diffusion toward the mean annual
ground temperature
Geothermal heat flux from
Longwave radiation is computed as in
If the ground surface is covered by water, e.g., by ocean or periglacial
lakes, the top ground temperature is set to 0
Comparison of present-day modeled mean annual ground
temperature (MAGT) with site level observations from
Different transient CLIMBER-2 simulations are used to estimate the permafrost
evolution over the last glacial cycle and beyond. Orbital variations
A set of experiments is performed to assess the sensitivity of modeled
permafrost extent and thickness to a number of poorly constrained parameters.
These parameters include surface porosity
Scatter of modeled and observed present-day mean annual
ground temperature (MAGT). Site level observations are from
Given the long timescales involved in permafrost evolution, the present-day
permafrost state has potentially a long memory of past climate variations. To
explore the convergence of the simulated present permafrost state and
permafrost evolution over the last glacial cycle, experiments are performed
starting at interglacials progressively further back in time (i.e., MIS 5
(Eemian), 126; MIS 7, 240; MIS 9, 330; MIS 11, 405 and MIS 19,
780
The modeled MAGST for present-day conditions is compared to site observations
in Fig.
The long timescales involved in deep permafrost buildup and the dependence of
permafrost on surface temperature, and therefore also on ice sheet history,
represent a challenge for model initialization. The present-day modeled
permafrost used for model evaluation is the result of a transient
climate–ice-sheet–permafrost model simulation over the past
780 000
The ability of the model to correctly simulate the area covered by permafrost
rests mainly on a correct simulation of MAGST. A comparison of modeled
permafrost area with continuous permafrost extent estimates indicates that
permafrost extent is generally well captured by the model, particularly over
North America (Fig.
Comparison of modeled present-day permafrost thickness with
estimates from boreholes. Permafrost thickness data for Canada are
from
Biases in MAGST have a major impact on permafrost thickness. This is evident
in the overestimation of the permafrost thickness over parts of southern
Siberia, where modeled ground temperatures are too low
(Fig.
Scatter of modeled and observed permafrost thickness
estimated from boreholes. Permafrost thickness data for Canada
(blue) are from
It has to be pointed out that permafrost thickness observations shown
in Figs.
Simulated permafrost thickness depends on the choice of uncertain
parameter values. A sensitivity analysis is performed to quantify the
relative importance of the various parameters. Higher ground porosity
values (either higher
Heat conductivities of rock and sediments have a strong effect on modeled
permafrost depth. In general, an increased conductivity in the top part of
the ground layer favors the penetration of cold surface temperatures
downward, causing a cooling and therefore a deepening of the permafrost
layer. On the other hand, a higher conductivity of the bottom ground layer
increases the temperature gradient due to the geothermal heat flux and
consequently shallows the permafrost layer. These opposite effects are
evident in Fig.
Permafrost thickness is very sensitive to the applied geothermal heat flux.
In fact, using two different geothermal heat flux databases
Sensitivity of present-day permafrost thickness to surface
porosity
The width of the temperature range where freezing occurs in the ground,
As already shown in
Applying the geothermal heat flux at 5
Evolution of
The reason for the relatively small effect of permafrost on ice sheet
dynamics throughout most of the glacial cycle, except for LGM, can be found
in the sediment thickness distribution over the continents. Over most of
Canada and Scandinavia the sediment layer has been gradually thinned or
almost completely removed by ice sheet erosion over the Pleistocene glacial
cycles
LGM (25–20
Using the more recent global estimates of the geothermal heat flux
from
NH area of permafrost not covered by ice sheets and NH permafrost volume are
strongly affected by ice sheets. Both area and volume are much larger over
Eurasia than over North America (Fig.
Present-day modeled NH permafrost area is around 15 million square kilometers, which is very close to the mode of the
PMIP3 models
Evolution of permafrost area and permafrost volume over the
last glacial cycle. Eurasian
The area of permafrost not covered by ice sheets is relatively
independent of porosity and geothermal heat flux, while the permafrost
volume strongly depends on these parameters
(Fig.
Permafrost area and thickness at LGM, which is close to the time of maximum
areal extent of Eurasian permafrost, are shown in Fig.
Modeled permafrost thickness at LGM, corresponding to the time of maximum areal extent of permafrost over Eurasia. Grey dots show grid cells covered by ice sheets.
White areas below the ice sheets in Fig.
Figures
Evolution of ground surface temperature and ice thickness
Same as Fig.
Same as Fig.
Same as Fig.
In western Siberia permafrost is generally thinner, and permafrost thickness
is therefore more sensitive to surface temperature variations
(Fig.
At the same latitude over North America permafrost behaves radically
different (Fig.
A site further south (around 50
Present-day permafrost disequilibrium for the two model runs
with different geothermal heat fluxes:
The evolution of the 3-D ground temperature field introduces a very long
timescale into the climate–ice-sheet system. Presently, ground temperature
and therefore permafrost thickness are far from equilibrium over some regions
(Fig.
Starting from the temperature profile in equilibrium with present-day ground
surface temperature given by Eq. (
Permafrost volume evolution in simulations initialized with the same initial conditions but started at interglacial periods progressively further back in time. Top: Eurasia; bottom: North America.
The slow convergence of permafrost thickness in some regions
highlights the importance of proper initialization when considering
permafrost evolution. Starting from equilibrium conditions at LGM or
the Eemian as was done in previous studies
Present-day permafrost thickness differences between model runs started during different interglacial periods as indicated over each panel.
In this study a permafrost module has been included in the climate–ice-sheet
model CLIMBER-2. The model is shown to perform reasonably well at reproducing
present-day permafrost extent and thickness. Modeled permafrost thickness is
sensitive to the choice of some parameter values, in particular ground
porosity and thermal conductivity of sediments and rock. Using different
global data sets of geothermal heat flux also has a strong impact on
simulated permafrost thickness. A realistic spatial distribution of
geothermal heat flux and ground properties is therefore important for an
accurate site-level simulation of ground temperature profiles and permafrost,
as was already shown in
Permafrost extent at LGM agrees well with reconstructions and previous
modeling estimates showing a southward expansion of permafrost down to almost
50
Present-day permafrost thickness is found to be far from equilibrium over
deep permafrost regions of central Siberia and the Arctic Archipelago, where
permafrost is presently up to 200–500
Over the last glacial cycle permafrost has a relatively modest impact on
simulated NH ice sheet volume, except at LGM, when including permafrost
increases ice volume by about 15
The contribution from phase changes in Eq. (
The ground temperature profile at equilibrium can be derived by setting the
time derivative terms in Eq. (
M. Willeit acknowledges support by the German Science Foundation DFG grant GA 1202/2-1. Edited by: V. Rath