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Possible Position of Table 2 .
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Model
configuration
The JMC and WH models were
configured using the approach of Elshamy et al . (2020), where
MESH was applied to three permafrost sites along the Mackenzie River
valley. Three families of model parameters were identified: soil column
configuration, soil texture, and surface canopy. Firstly, for soil
layering we employed the scheme of Elshamy et al. (2020) for both
sites. This extends to 51.24 m depth and has a fine discretization (9
layers) for the upper 2 meters of the soil, in line with the observed
ALT for both sites (Table 3 ). No-heat flux was used as the
lower boundary condition of the soil column. The effects of the lower
boundary condition were assumed negligible because of its limited impact
on the simulated soil temperatures for centennial timescale simulation,
as several studies reported (Nicolsky et al. , 2007; Lawrenceet al. , 2008; Hermoso de Mendoza et al. , 2020). Regarding
SDEP (depth to the bedrock), we used the gridded bedrock depth dataset
by Keshav et al. (2019b) to identify the mean value of SDEP for
the two sites: 7.00 m and 10.77 m for JMC and WH, respectively. SDEP is
an important parameter that plays a pivotal role in the simulation of
permafrost as it alters the thermal regime’s properties (conduction and
storage) and the system’s water storage/drainage (see (Elshamy et
al. , 2020) for further discussion).
Possible Position of Table 3 .
The
second set of parameters are soil texture parameters, which are used in
CLASS to parameterize the thermal and hydraulic properties; thus, they
strongly influence water and heat storage and movement/conduction.
Organic soils are characterized by large heat and moisture capacities
that regulate the effects of atmosphere on permafrost around the year
(Dobinski, 2011). Therefore, we focused on their representation in our
model setups. However, the available soil texture data are insufficient
to configure a deep model profile. Soil maps such as Cartographic
1:1000,000 Soil Landscapes of Canada (SLC) v2.2 (Centre for Land and
Biological Resources Research, 1996) and its gridded product (Keshavet al., 2019a) only offer data on the spatial characteristics of
soil, with no mention of variation with depth. The Global Soil Dataset
for Earth system models (GSDE: Wei et al. , 2014) provides gridded
texture information for 8 layers but only to a depth of 2.3m. Even
though the available borehole logs around (and at) the two sites provide
valuable geotechnical data, they lack necessary information on the
organic matter content and its thermal and hydraulic properties (the
logs provide a qualitative description of the soil components following
the USDA classification).
Therefore, the most feasible
approach was to test different configurations of the soil organic
matter, which can be parametrized either as Fully Organic Soil (FOS) or
as Mineral Soil with Organic content (MSO). CLASS uses organic matter
content within the mineral soil to update only the thermal properties
(heat capacity and thermal conductivity), similar to CLM 4.5 (Olesonet al. , 2013). We configured the soil column of JMC using the FOS
configuration for the upper 1.46 m (20 cm fibric + 40 cm hemic + 86 cm
sapric), and the rest of the soil column as silt loam with high organic
content (50% organic content) – full details are given in Elshamyet al. (2020). For the WH site, we configured the upper 0.81 m
using the MSO approach (silt loam with 50 - 60% organic content), and
the rest of the column as mineral (3.50m sand/silt fine-grained, the
rest as silty clay). The MSO configuration was selected for WH site
based on the outcomes of benchmarking simulations that yielded better
results (i.e. ALT and temperature envelopes) compared to the FOS
approach.
The last group of model parameters are those used to parametrize surface
canopy conditions. We used the CLASS manual (Verseghy, 2012) to identify
the associated parameter values for the two sites, given that JMC is
dominated by boreal forest, while evergreen shrubs cover the WH
site. Each setup is configured
with a single GRU using the single MESH column.
Experimental
design
The
setups for the two permafrost sites were designed to explore the
influence of the uncertain initial model states on the spin-up length
(i.e. length required for appropriate model warm-up) and its
extended effect on permafrost during a subsequent simulation period. We
utilized a single-year spin-up strategy for a maximum of 2000 annual
cycles, which is compatible with the available literature on LSM
permafrost modelling (Dankers et al. , 2011; Burke et al. ,
2013; Elshamy et al. , 2020). As discussed above, the single-year
approach is the simplest and most commonly employed method for
initializing LSMs (e.g. Rodell et al. , 2005; Nishimuraet al. , 2009; Burke et al. , 2013). However, the resulting
state-variables may suffer from an accumulated bias depending on the
spin-up year’s climate (Rodell et al. , 2005). Likewise, the other
available spin-up techniques (e.g. using a (detrended) sequence
of years and long transient simulation) do not resolve this issue (seeSection 1 ).
As a single year of forcing is
cycled, a complete spin-up would theoretically be achieved if the model
states at year m are identical to year m +1. However,
achieving a highly precise state equilibrium is not always necessary or
feasible, especially for global-scale simulations due to the immense
computational cost (Rodell et al. , 2005). We focused on soil
temperature profiles and soil moisture (both frozen and liquid) profiles
for the stabilization analysis. Previous studies considered either soil
temperature (e.g. Burke et al. , 2013; Elshamy et
al. , 2020) or total (unpartitioned) soil moisture (e.g. Rodellet al. , 2005; de Goncalves et al. , 2006; Shrestha and
Houser, 2010). We considered a tolerance of 0.1°C for temperature states
(the same accuracy of permafrost thermal measurements) and 0.01
m3 m-3 for liquid and frozen water
states of each soil layer. The stabilization length (i.e. number
of spin-up cycles) was defined from when the differences in selected
states are less than the identified thresholds, and we used the last
timestep of each cycle in the stabilization analysis. There is no
consensus among LSMs communities on defining the convergence criteria
for adequate model initialization (Yang et al. , 1995). For
example, Burke et al. (2013) considered a successful
initialization of JULES had been achieved when the variation of soil
temperature during spin-up is less than 0.2°C. Employing high thresholds
could lead to biased state-variables, while lower thresholds are not
feasible for large-scale applications due to their extensive
computational cost.
To account for the impact of the initial year’s climate, we selected
five climatic conditions based on the total annual precipitation and
mean annual air temperature, as per the suggestion by Sapriza-Azuriet al. (2018). We used the WFDEI dataset to identify these,
namely wet year (high precipitation), dry year (low precipitation), cold
year (low temperature), warm year (high temperature), and an average
year (for both precipitation and temperature). Table 4summarizes the climate conditions for the two permafrost sites using a
hydrological year (i.e. Oct 1st to Sep
30th).
Similarly, to account for the
effects of initial soil moisture content, we considered 21 different
uniform cases covering the spectrum of soil water content (water and ice
content), as summarized in Fig. 4. These are non-equilibrium
states but address the subjectivity of initial soil water content
selection/configuration in previous studies. For instance, Rodellet al. (2005) and Shrestha and Houser (2010) defined initial soil
moisture as 70% and 10% of saturation for wet and dry conditions,
respectively, unlike Cosgrove et al. (2003) and de Goncalveset al. (2006) who quantified these conditions as 100% and 0%
saturation, respectively. The two relevant permafrost studies by
Sapriza-Azuri et al. (2018) and Elshamy et al. (2020),
which utilized the same model as here (MESH/CLASS), did not address this
issue. For the dry experiment, with zero saturation for liquid water
content, CLASS constrains the residual water content at a value of 4%
for mineral soil (MSO configurations). For the FOS configurations, the
residual liquid content (or retention capacity) is a function of the
organic soil sub-type and varies between 4% and 22%, as mentioned inSection 2.1 .
All models were set with the same
initial condition for soil temperature, defined as 0°C along the whole
profile, except for the bottom temperature, which was extrapolated from
the available temperature records following Elshamy et al.(2020), specified as 0.8°C and 0.5°C for the JMC and WH sites,
respectively. We assumed uniform initial profiles for soil temperature
and moisture contents due to the simplicity of this approach, and to
avoid subjectivity in defining a non-uniform profile, especially for
temperature. However, the model is shown to rapidly adjust to
self-consistent states. Therefore, each site has a total of 105 1-D
scenarios {5 climate conditions x 21 soil moisture conditions},
covering distinctive climate and soil moisture conditions. Subsequently,
we ran all scenarios for a simulation period of 1979-2016 to assess the
impact of uncertainty in initial conditions on various aspects (seeFig. 1 and Table 1 ) of permafrost dynamics. The
analysis incorporated quantitative assessment of simulated permafrost in
terms of root mean square error (RMSE) for the temperature profiles and
ALT error (Bias) over the same period, whenever there were observations.
Possible Position of Table 4.