Journal of Advances in Modeling Earth Systems
Supporting Information for
Comparison of effects of cold-region soil/snow processes and the uncertainties from model
forcing data on permafrost physical characteristics
Rahul Barman1 and Atul K. Jain1
1Department
of Atmospheric Sciences, University of Illinois, Urbana, IL 61801, USA
Contents of this file
Text S1
Figures S1 to S4
Tables S1 to S2
Text S1.
Equations of key processes relevant to permafrost calculations
1–2. Deep soil column, and multilayer snow physics
The representation of deep soil thermal dynamics is implemented throughout the
model as applicable. Originally, the total soil in the model was limited to 3.5 m (divided into 10
soil layers), with “zero” bottom boundary conditions for energy and water exchange
implemented at the bottom of the lowest layer. Subsequently, the thermally active soil column
was increased to ~50 m, using a total of 15 soil layers. The first 10 columns, which are
hydraulically active, are common between both energy and hydrology components. By
incorporating a deep soil column, the zero bottom boundary condition for the thermal
exchange was shifted to the bottom of the 15th soil layer.
Below the hydrologically active zone, soil properties are treated as that of bedrock.
Volumetric water content at saturation ( Q sat , bedrock ): 0.0
Thermal conductivity of dry soil ( l dry, bedrock ): 3.0 W/m/K
Thermal conductivity of soil solids ( l s, bedrock ): 3.0 W/m/K
1
Heat capacity of soil solids ( Cs, bedrock ): 2×106 J/m3/K
Soil matric potential ( Y sat , bedrock ): -1.5×10-5 mm
Clapp and Hornberger exponent ( bbedrock ): 0.0
Saturated hydraulic conductivity ( ksat , bedrock ): 0.0 mm/s
The multi-layer representation of snow contains up to 5 (dynamic) snow layers, and
includes representation of processes such as snow accumulation, melt, compaction, water
transfer across layers, sublimation, etc. A summary of these processes, as included in the model
is available in Baman et al., 2014b.
3. Soil organic carbon (SOC) driven impacts on soil thermal/hydrological properties
Physical properties of soil are assumed to be that of a weighted combination of mineral
soil and pure organic soil [Lawrence and Slater, 2008], in the functional form:
Ai = fsc, i Asc, i + (1- fsc, i )Amin, i
where Ai is the overall soil property in soil layer i, Asc, i the corresponding organic soil property,
and Amin, i the mineral soil property. The only exception to this general representation is the
saturated hydraulic conductivity, which is additionally determined using percolation theory
(described below). f sc, i is the weighing parameter, and is the density fraction of SOC in the
respective soil layer.
f sc, i =
r sc, i
r sc, max
Here, r sc, i is the SOC density for soil layer i, and r sc, max = 130 kgC/m3 is the maximum
assumed SOC density (equivalent to a standard bulk density of peat, from [Farouki, 1981].
Specific soil hydrological and thermal properties that are modified based on SOC are as follows:
(a) Volumetric water content at saturation (porosity): Q sat , i
Qsat, i = fsc, iQ sat, soc + (1- fsc, i )Q sat, min, i
where Q sat , soc is the porosity of organic material, assumed to be equal to 0.9 and is
typical of values in literature ~ 0.8—0.95 [Hinzman et al., 1991; Letts et al., 2000].
Q sat , min, i is the porosity of mineral soil.
Qsat, min, i = 0.489 - 0.00126(sand%vol )i
(b) Thermal conductivity of dry soil: l dry, i
ldry, i = f sc, i ldry, soc + (1- f sc, i )ldry, min, i
where l dry, soc is the dry thermal conductivity of organic soil, and it set to 0.05W/m/K (based on
typical values from ([Farouki, 1981]). l dry, min, i is the dry thermal conductivity of mineral soil:
0.135 r d, i + 64.7
2700 - 0.947 r d, i
where rd, i = 2700(1- Q sat , min, i ) is the bulk density of mineral soil.
l dry, min, i =
(c) Thermal conductivity of soil solids: l s, i
2
ls, i = fsc, i ls, soc + (1- fsc, i )ls, min, i
where l s, soc is the thermal conductivity of organic soil solid, and it set to 0.25W/m/K [Farouki,
1981]. l s, min, i is the dry thermal conductivity of mineral soil:
8.80(sand%vol )i + 2.92(clay%vol )i
(sand%vol )i + (clay%vol )i
(d) Heat capacity of soil solids: C s, i
Cs, i = fsc, iCs, soc + (1- fsc, i )Cs, min, i
where C s, soc is the heat capacity of organic soil solids, equal to 2.5×106 J/m3/K [Farouki, 1981].
Cs, min, i ( J/m3/K) is the heat capacity of mineral soil solids:
l s, min, i =
2.128(sand%vol )i + 2.385(clay%vol )i 6
10
(sand%vol )i + (clay%vol )i
(e) Saturation soil matric potential: Y sat , i
Y sat, i = fsc, i Y sat, soc + (1- fsc, i )Y sat, min, i
where Y sat , soc is the saturation soil matric potential of organic soil, equal to -10.3 mm [Letts et
al., 2000]. Y sat , min, i ( mm) is the saturation soil matric potential of mineral soil:
l s, min, i =
Y sat , min, i = 10.0 ´101.88-0.0131(sand%vol )i
(f) Clapp and Hornberger exponent: bi
bi = fsc, ibsoc + (1- fsc, i )bmin, i
where bsoc is the Clapp and Hornberger exponent of organic soil, equal to 2.7 [Letts et al., 2000].
bmin, i (-) is the Clapp and Hornberger exponent of mineral soil:
bmin, i = 2.91+ 0.159(clay%vol )i
(g) Saturated hydraulic conductivity: k sat , i
k sat , i is determined based on results from percolation theory [Berkowitz and Balberg,
1992; Stauffer and Aharony, 1994], based on “percolating” and “non-percolating” fractions of
organic soil.
ksat , i = ( f sc, i ´ f perc, i )ksat , soc + funcon, i ksat , uncon, i , for
where ksat , soc is the saturated hydraulic conductivity of organic soil, equal to 0.1 mm/s.
Percolating fraction ( f perc, i ) is zero unless greater than a certain threshold called the
percolation threshold: . fthreshold = 0.5
f perc, i = (1- fthreshold )-0.139 ( fsc, i - fthreshold )0.139 fsc, i when fsc, i > fthreshold
f perc, i = 0 when f sc, i < fthreshold
The unconnected fraction is equal to fraction of mineral soil plus fraction of "nonpercolating" organic soil.
funcon, i = (1- f sc, i ) + (1- f perc, i ) f sc, i
The unconnected hydraulic conductivity ( ksat , uncon, i ) is a series addition of mineral and
organic soil conductivities.
3
ksat , uncon, i
æ 1- f sc, i f sc, i - f perc, i ö
= funcon, i ç
+
k sat , soc ÷ø
è k sat , min, i
-1
where ksat , min, i is the saturated hydraulic conductivity of mineral soil, a function of soil texture.
ksat , min, i = 0.0070556 ´10 -0.884+0.0153(sand%vol )i
4. Snow compaction
For tundra and prairie snow, the model implements compaction of snow driven by
winds. The parameterization is based on [Schaefer et al., 2009] and dependent on the global
snow classification system [Sturm et al., 1995]. This is parameterized by increasing the density
of new fallen snow with wind speed, and air temperature.
rnew = rmin + DrT + DrW
where
r new is the density of new fallen snow, r min is the minimum possible new snow density
(50 kg/m3), DrT is a temperature correction factor, and DrW is a wind correction factor. Preexisting in the model, all snow classes include DrT which is dependent on air temperature ( Tair
, oC) [Judson and Doesken, 2000].
DrT = 0, for Tair < -15
DrT = 1.7(Tair +15)1.5 , for Tair ³ -15
DrW is dependent on wind speed (u, m/s), and parameterized based on results from
wind tunnel tests [Sato et al., 2008].
DrW = 0, for u < 2
- r min ù
ér
DrW = (u - 2) ê topref
ú , for u ³ 2
3
ë
û
where rtopref is the maximum observed density of the wind slab layer for the tundra and prairie
classes (Table S1). Based on observational limits, r new is restricted to be within maximum
observed wind slab densities (dependent on snow class).
rnew = MINIMUM ( rnew , rtopref )
5. Depth hoar formation
The effects of depth hoar development are approximated by superimposing a two-layer
vertical density stratification profile over the snow layers (up to five). Two parameters define
the two-layer density stratification: (a) the bottom layer fraction ( fbot ), and (b) the difference in
density between two layers (Δρ). fbot varies with snow depth (D)
fbot =
f
1+ e
bot max
Dslope ( Dhalf -D)
where fbot max is the maximum observed value of fbot (Table S1). Dslope and Dhalf are the fbot
4
slope and half point.
Dhalf =
Dmax + Dmin
2
Dslope =
10
Dmax - Dmin
where Dmin is the minimum snow depth where a bottom layer forms and Dmax is the snow
depth where fbot reaches a maximum value (Table S1).
Δρ depends on both D and ρbulk.
Dr = abs( rtopref - r botref )
fbot
fbot max
e
-
( rbulk - rbulkobs )2
2
s bulkobs
where rtopref and rbotref are reference densities for the top and bottom layers of the two layer
vertical density profile (Table S1). rbulkobs and s bulkobs are the mean and standard deviation of
observed bulk density corresponding to maximum horizontal stratification in the snowpack
(assumed to occur in late winter) (Table S1).
Next, the snow thermal conductivities are modified, based on the depth hoar fraction in
snow (= fbot , calculated previously) in the tundra and taiga snow classes. The total depth of
depth hoar ( Ddh ) is: Ddh = fbot D . From this, the depth hoar in each snow layer ( Ddh, j ) is
calculated, where j is a snow layer. Subsequently, the effective thermal conductivity of a snow
layer (j), including depth hoar effects ( l eff , j ) is calculated as:
l eff , j =
l j l dh
l dh + (l j - l dh )(
Ddh, j
)
dz j
where, l j is thermal conductivity of a snow layer before depth hoar adjustment, l dh is thermal
conductivity of a pure depth hoar layer characteristic of snow class, and dz j is the depth of the
snow layer. For this calculation, a thermal conductivity of 0.18 W/m/K for tundra depth hoar and
0.072 W/m/K for taiga depth hoar are assumed based on field observations [Sturm and Benson,
1997].
6. Latent heat from phase change
Upon update, the snow/soil temperatures are evaluated to determine if phase change
will take place as:
5
(a) Ti
n+1
> T f and Wice, i > 0 in snow/soil layer i (melting in soil and snow layers)
(b)
Ti n+1 < T f and Wliq, i > 0 in snow layer i (freezing in snow layers)
(c)
Ti n+1 < T f and Wliq, i > Wliq, i, max in soil layer i (freezing in soil layers)
where Ti n+1 is the soil layer temperature after solution of the tridiagonal equation set, T f is the
freezing temperature of water (273.15 K), Wice, i and Wliq, i are the mass of ice and liquid water
(kg/m2) in each snow/soil layer, respectively, and Wliq, i, max is the maximum supercooled water
in soil layer i [Koren et al., 1999; Niu and Yang, 2007].
7. Super-cooled water
Maximum supercooled water ( Wliq, i, max , kg/m2) in soil layer i is represented as:
-1/Bi
é 10 3 L f (T f - Ti ) ù
Wliq, max, i = Dziq sat, i ê
ú , when Ti < T f
ë gTiy sat, i
û
where Ti is soil temperature, T f is the freezing temperature (273.15 K), L f is the latent heat of
fusion (3.37 × 105 J/kg), g is acceleration due to gravity (9.8 m/s2), y sat, i and Bi are the soil
saturated matric potential (mm) and Clap and Hornberger exponent [Clapp and Hornberger,
1978], respectively. Note that, original formulations of y sat, i and Bi were dependent on soil
minerals only; in the current version of the model, these parameters are also additionally
dependent on soil organic fraction (formulations from [Lawrence and Slater, 2008]).
6
Figure S1. Map of snow class distribution, poleward of 45oN. The data is based on [Sturm et al.,
1995].
7
Figure S2. Spatial differences in mean annual values of meteorological fields between two
reanalyses datasets, the CRUNCEP and the NCEP/NCAR, poleward of 45oN. Here, Δ =
CRUNCEP - NCEP/NCAR. For illustration, the mean annual values were obtained using data
from the years 2000—2004. (a) ΔTavg: average temperature, (b) ΔPrecip: total precipitation, (c)
ΔSrad: incoming short-wave radiation, (d) ΔLWdown: incoming longwave radiation, (d) ΔQ:
specific humidity, and (f) ΔWind: wind speed.
8
Figure S3. Mean annual air temperatures in the two reanalysis datasets used in this study,
poleward of 45oN.
9
Figure S4. Map of mean annual wind speed (annually averaged data during 2000—2004) in
CRUNCEP, poleward of 45oN. Only wind speeds over the tundra, taiga, and prairie snow classes
(Fig. S1) are shown, which are impacted by wind compaction of snow; other areas are shown in
grey.
10
1
Class
2
3
4
5
fbotmax (-)
Dmin (m)
Dmax (m)
rtopref
rbotref
rbulkobs
s bulkobs
(kg/m3)
(kg/m3)
(kg/m3)
(kg/m3)
Reference
month
Tundra
0.3
0.0
0.1
350
100
261.11
68.21
April
Taiga
0.7
0.0
0.7
300
200
213.37
49.46
March
Maritime
0.8
0.2
0.8
200
300
286.50
80.98
February
Ephemeral
0.8
0.2
0.8
250
350
321.29
82.32
February
Prairie
0.8
0.2
0.8
350
250
272.42
61.06
February
Alpine
0.8
0.2
0.7
200
300
267.80
56.85
February
Table S1. Snow class dependent parameters for wind compaction of snow, and depth hoar formation. Values are taken from [Schaefer et al.,
2009].
11
6
7
Fluxes
Annual estimates
Observations
(Source)
LE (W/m)
22.98 (FLUXNET-MTE)
Model simulations
NEW
OLD
NEW-NO-DH
20.57
21.11
20.50
8
9
10
11
12
13
14
15
16
-
NEW-NO-DS
NEW-NO-SOC
NEW-NO-WIND
20.55
21.02
20.71
17.76
16.90
17.59
0.54
0.55
0.54
8.43
8.00
8.33
-
22.23 (MODIS)
H (W/m2)
22.72 (FLUXNET-MTE)
17.74
16.75
17.66
LE/(LE+H) (-)
0.50 (FLUXNET-MTE)
0.54
0.56
0.54
7.01 (GRDC)
8.45
8.01
8.49
Runoff (103 Km3)
-
-
Table S2. Comparison of biogeophysical fluxes in the vegetated NHL region (45—90oN), between observational estimates and selected model
simulations. Observational estimates of latent heat (LE), sensible heat (H) are available from FLUXNET-MTE [Jung et al., 2011]. Additionally, LE
is also available from MODIS [Mu et al., 2011; Mu et al., 2007; Zhao et al., 2006]. All but the runoff estimates from Global Runoff Data Centre
(GRDC) [Fekete and Vorosmarty, 2011; Fekete et al., 1999] were constructed using annually averaged output/data during 2000—2004.
Reanalyses driven energy fluxes from the current version of the model have documented negative biases with respect to the compared
observational sources; in the NHL region these occur due to negative biases in radiation (short- and long-wave components) and biases in other
meteorological fields from these reanalyses, with respect to site-level flux tower data [Barman et al., 2014a; b]. With respect to the respective
NHL aggregated fluxes in NEW, the divergences across the simulations are equal to ~3% for LE, 5.7% for H, and 5.7% for Runoff.
12
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