equations and pfts for soil thermal properties in lsms ......= 733 j kg-1 k-1 (ii) two lsms use the...
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Equations and PFTs for soil thermal properties in LSMs: Implications for the energy balance
TITL
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Anne Verhoef, Jirka Simunek, Lutz Weihermuller, Michael Herbst, Kris Van Looy, Carsten Montzka, Harry Vereecken, plus LSM collaborators
ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
LSM collaborators CABLE: Mark Decker Catchment: Randy Koster, Gabriรซlle De Lannoy (& Joe Santanello) CLM: David Lawrence JSBACH: Stefan Hagemann, inputs from Christian Beer and Philip de Vrese JULES: Anne Verhoef (inputs from Imtiaz Dharssi, Toby Marthews, Pier Luigi Vidale, Heather Ashton & John Edwards MPI-HM: Tobias Stacke NOAH-(MP): Yihua Wu and Michel Ek OLAM: Robert Walko ORCHIDEE: Agnรจs Ducharne and Fuxing Wang SSiB: Yongkang Xue, Qian Li SURFEX-ISBA: Aaron Boone and Sebastien Garrigues
OV
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OVERVIEW โข Joint ISMC and GEWEX
communities: Initiatives to improve soil and subsurface processes in current climate and hydrological models
โข Evaluation of pedotransfer functions and related functional descriptions for calculation of hydraulic and thermal soil properties in global climate models.
land surface model
ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
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๐ = ๐น๐๐๐ ๐๐ก + 1 โ ๐น๐ ๐๐๐๐ฆ
THERMAL CONDUCTIVITY, ๐
โข Soil thermal conductivity depends on
dry, ๐๐๐๐ฆ, and saturated conductivity,
๐๐ ๐๐ก, in combination with a soil moisture dependent weighting function, ๐น๐
โข Equations are required to estimate ๐๐๐๐ฆ, ๐๐ ๐๐ก and ๐น๐
โข These parameters, and their intrinsic
parameters all require โthermalโ PFTs
๐ = ๐0 + ๐1๐น๐ + ๐2 ๐น๐2
ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
Most LSM models use:
One uses:
Weighting function
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ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
WEIGHTING FUNCTION, ๐น๐ โข The weighting function,๐น๐, is
often the Kersten number, ๐พ๐, which is dependent on the relative saturation, ๐๐
โข Constant ๐พ varies between models
โข ๐๐ depends on moisture content, ๐, and saturated moisture content, ๐๐ ๐๐ก, and residual SMC, ๐๐ (for VG).
๐๐ =๐
๐๐ ๐๐ก ๐๐ =
๐ โ ๐๐๐๐ ๐๐ก โ ๐๐
Clapp & Hornberger/Brooks & Corey Van Genuchten, VG
๐พ๐ = ๐พ log ๐๐ + 1
Most LSMs: ๐น๐ = Kersten number, ๐พ๐
where ๐พ is generally one, but for some models is set to 0.7 for coarse soils.
Others use ๐พ = 0.7 for 0.05 < ๐๐ โค 0.1.
๐น๐ = ๐๐ for 2 others
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DRY THERMAL CONDUCTIVITY, ๐๐๐๐ฆ
โข generally dependent on (some of)
the soil texture fractions (sand, silt, clay), either explicitly or implicitly (via soil class look-up tables, LUTs).
โข Porosity, ๐๐ ๐๐ก , is an important parameter, and depends on hydraulic PFTs (in blue) Or Lu et al., 2007
Most LSMs use Johansen (1975), as also used by Peters-Lidard et al. (1998)
๐๐๐๐ฆ,๐๐๐ =0.135๐๐๐๐ + 64.7
๐๐๐๐ โ 0.947๐๐,๐๐๐๐
๐๐๐๐ฆ,๐๐๐ = โ0.56๐๐ ๐๐ก + 0.51
๐๐๐๐ฆ,๐๐๐ = ๐๐๐๐๐๐ ๐๐ก๐๐๐๐๐ ๐๐๐ ๐
One uses (Cox et al., 1999)
๐๐ = ๐ถ๐
๐๐ 1โ๐๐ ๐๐ก
Cj is a constant (1.16 for clay, 1.57 for silt and sand), and fj is the fraction of j = clay, silt, or sand ๐๐๐๐ฆ,๐๐๐ = 0.19
Alternatively
ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
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ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
SATURATED THERMAL CONDUCTIVITY, ๐๐ ๐๐ก โข The saturated thermal conductivity
generally depends on the thermal conductivities of the solid soil material, ๐๐ ๐๐๐ , liquid soil water, ๐๐๐๐, and ice, ๐๐๐๐, sometimes on
๐๐๐๐.
One uses
Most LSMs use (from Johansen, 1975?):
Or
๐๐ ๐๐ก = ๐๐ ๐๐๐1โ๐๐ ๐๐ก๐๐๐๐
๐๐ ๐๐กโ๐๐ข๐๐๐๐๐๐ ๐๐ก๐ข
๐๐ ๐๐ก =
1.58 ๐๐๐๐ฆ < 0.25
1.58 + 12.4 ๐๐๐๐ฆ โ 0.25 0.25 < ๐๐๐๐ฆ < 0.3
2.2 ๐๐๐๐ฆ > 0.3
๐๐ ๐๐ก = ๐๐๐๐ฆ ๐๐๐๐๐๐ ๐๐ก๐ข
๐๐๐๐
๐๐ ๐๐ก๐
๐๐๐๐๐๐ ๐๐ก
Soil solid conductivity (see next slide)
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SOIL SOLID THERMAL CONDUCTIVITY, ๐๐ ๐๐๐ โข The saturated thermal conductivity
generally depends on the thermal conductivities of the solid soil material, ๐๐ ๐๐๐ , liquid soil water, ๐๐๐๐, and ice, ๐๐๐๐, sometimes of
๐๐๐๐.
Some use:
In a number of LSMs, ๐๐ ๐๐๐ is assumed to be dependent only on the thermal conductivity of the mineral soil solids as given by (Johansen, 1975):
๐๐ ๐๐๐ = ๐๐๐ข๐๐๐ข๐๐
1โ๐๐๐ข
๐๐ ๐๐๐ =๐๐๐ข๐๐ ๐๐๐ + ๐๐๐๐๐ฆ๐๐๐๐๐ฆ
๐๐ ๐๐๐ +๐๐๐๐๐ฆ
๐๐๐ข the thermal conductivity of quartz, having a value of 8.8 or 7 W m-1 K-1
๐๐ is the thermal conductivity of other minerals, generally set to 2 or 3 W m-1 K-1
๐๐๐ข = 0.038 + 0.0095๐๐๐ด
๐๐ ๐๐๐ = 7.0 ๐๐ ๐๐๐ = 3.44
ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
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SOIL HEAT CAPACITY, ๐ถโ โข Theory (e.g. Van Wijk & de Vries, 1963) states soil heat capacity depends on
the specific heat capacities (ci) of the solid soil material, liquid soil, water, ice, and air, their densities (๐๐ ) and volume fractions (๐๐ ).
โข Alternatively we can use the volumetric heat capacity
โข Some models use a constant ๐ถโ(= 2.19ร106; independent of soil type), i.e. its values remain unchanged despite changes in ๐, whereas others uses values ranging between 1.93 ร106 for sand to 2.48ร106, for clay.
๐ถโ = ๐๐๐๐๐๐๐๐๐๐๐๐ + ๐๐๐๐๐๐๐๐๐๐๐๐ + ๐๐๐๐๐๐๐๐๐๐๐๐ + ๐๐๐๐๐๐๐๐๐๐๐๐ + ๐๐๐๐๐๐๐๐๐๐๐๐
๐๐๐๐ = 1 โ ๐๐ ๐๐ก ๐๐๐๐ = ๐ ๐๐๐๐ + ๐๐๐๐ + ๐๐๐๐ + ๐๐๐๐ + ๐๐๐๐ = 1.0
๐ถโ = ๐๐๐๐๐ถ๐๐๐ + ๐๐๐๐๐ถ๐๐๐ + ๐๐๐๐๐ถ๐๐๐ + ๐๐๐๐๐ถ๐๐๐ + ๐๐๐๐๐ถ๐๐๐
ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
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CALCULATION OF MINERAL HEAT CAPACITY, ๐๐๐๐ OR ๐ถ๐๐๐ โข The main PTF for heat capacity relates to the way ๐๐๐๐ or ๐ถ๐๐๐ is calculated.
There are a number of options used in the LSMs: โข (i) Employ the same value for all soil types โข (ii) Use different values (tabulated) for each soil class, โข (iii) Use different values per soil class, calculated as a function of texture:
(i) One uses ๐ถ๐๐๐= 1.942ร106 (Johansen, 1975), as one of its options. Others use ๐ถ๐๐๐= 2.0ร106; ๐๐๐๐ = 850 J kg-1 K-1, or ๐๐๐๐ = 733 J kg-1 K-1
(ii) Two LSMs use the same values for ๐ถ๐๐๐ = ๐๐๐๐๐๐๐๐ for 11 USDA soil type as given in Pielke (2002) based on McCumber (1980), see also McCumber and Pielke (1981)
(iii) A range of PTFs can be found, e.g. :
๐ถ๐๐๐ = ๐๐๐๐๐ฆ๐ถ๐๐๐๐ฆ + ๐๐ ๐๐๐๐ถ๐ ๐๐๐ + ๐๐ ๐๐๐ก๐ถ๐ ๐๐๐ก
๐ถ๐๐๐ = (๐๐ ๐๐๐๐ถ๐ ๐๐๐ + ๐๐๐๐๐ฆ๐ถ๐๐๐๐ฆ ) ( ๐๐ ๐๐๐ + ๐๐๐๐๐ฆ
ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
RES
ULT
S: T
HER
MA
L C
ON
DU
CTI
VIT
Y
RESULTS, thermal conductivity
โข Per soil type: large difference in ๐ between models
โข Considerably different functional shapes between models
0
0.5
1
1.5
2
2.5
3
3.5
0 0.2 0.4 0.6 0.8 1Th
eram
l co
nd
uct
ivit
y [
W m
^-1
K^
-1]
Relative saturation [-]
Jules1
Jules2
OLAM_BC
OLAM_VG
ISBA
CLM
JSBACH
CABLE
ORCHI DEE
NOAH
SSiB
Tessel
0
0.5
1
1.5
2
2.5
3
3.5
0 0.2 0.4 0.6 0.8 1
Th
eram
l co
nd
uct
ivit
y [
W m
^-1
K^
-1]
Relative saturation [-]
Jules1
Jules2
OLAM_BC
OLAM_VG
ISBA
CLM
JSBACH
CABLE
ORCHI DEE
NOAH
SSiB
Tessel
Loam
Clay
0
0.5
1
1.5
2
2.5
3
3.5
0 0.2 0.4 0.6 0.8 1
Th
eram
l co
nd
uct
ivit
y [
W m
^-1
K^
-1]
Relative saturation [-]
Jules1
Jules2
OLAM_BC
OLAM_VG
ISBA
CLM
JSBACH
CABLE
ORCHI DEE
NOAH
SSiB
Tessel
Sand
ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
RES
ULT
S: H
EAT
CA
PAC
ITY
RESULTS, HEAT CAPACITY
โข Per soil type: considerable difference in Ch between models
โข In some cases, different slopes between models
0
500000
1000000
1500000
2000000
2500000
3000000
3500000
0 0.2 0.4 0.6 0.8 1
Hea
t C
ap
aci
ty [
J m
-^3 K
^-1
]
Relative saturation [-]
Jules1
Jules2
OLAM_BC
OLAM_VG
ISBA
CLM
JSBACH
CABLE
ORCHI DEE
NOAH
SSiB
CABLE_SLI
Tessel
Sand
0
500000
1000000
1500000
2000000
2500000
3000000
3500000
0 0.2 0.4 0.6 0.8 1
Hea
t C
ap
aci
ty [
J m
-^3 K
^-1
]
Relative saturation [-]
Jules1
Jules2
OLAM_BC
OLAM_VG
ISBA
CLM
JSBACH
CABLE
ORCHI DEE
NOAH
SSiB
CABLE_SLI
Tessel
Loam
0
500000
1000000
1500000
2000000
2500000
3000000
3500000
0 0.2 0.4 0.6 0.8 1
Hea
t C
ap
aci
ty [
J m
-^3 K
^-1
]
Relative saturation [-]
Jules1
Jules2
OLAM_BC
OLAM_VG
ISBA
CLM
JSBACH
CABLE
ORCHI DEE
NOAH
SSiB
CABLE_SLI
Tessel
Clay
ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
CO
MPA
RIS
ON
USI
NG
HYD
RU
S M
OD
EL
MODEL RUNS, USING MODEL-SPECIFIC THERMAL (& hydraulic) properties
โข Runs with Hydrus 1-D for 14 years (2001-2014) of half-hourly data from Avignon, model outputs are hourly
โข 2 LSMs are compared in the next slides
โข Bare soil, soil profile of 50 cm, no vapour flow, free drainage
โข Sand, Loam, clay
โข LSM thermal equations have been implemented into Hydrus-1D
โข Effects on energy- and water balance have been investigated
โข Effect on soil (surface) temperature and soil moisture content
ISMC conference/workshop on the future of PedoTransfer
Functions, New Orleans 10 December 2017
CO
MPA
RIS
ON
USI
NG
HYD
RU
S M
OD
EL
Net radiation, Sand
0 8 16 24
-100
01
00
20
03
00
40
0
Time (hours)
Net
rad
tion
(W
m-2
)
July
August
September
October
November
December
Tessel
OLAM_VG
Net radiation, Sand, multi-year diurnal monthly average
CO
MPA
RIS
ON
USI
NG
HYD
RU
S M
OD
EL
0 8 16 24
02
040
60
80
10
0
Time (hours)
La
ten
t h
ea
t flu
x (
W m
-2)
July
August
September
October
November
December
Tessel
OLAM_VG
Evaporation, Sand, multi-year diurnal monthly average
CO
MPA
RIS
ON
USI
NG
HYD
RU
S M
OD
EL
0 8 16 24
-50
05
01
00
15
02
00
25
030
0
Time (hours)
Se
nsib
le h
ea
t flu
x (
W m
-2)
July
August
September
October
November
December
Tessel
OLAM_VG
Sensible heat flux, sand, multi-year diurnal monthly average
CO
MPA
RIS
ON
USI
NG
HYD
RU
S M
OD
EL
0 8 16 24
-200
-10
00
10
020
0
Time (hours)
Su
rfa
ce S
oil
he
at flu
x (
W m
-2)
July
August
September
October
November
December
Tessel
OLAM_VG
Soil heat flux, sand, multi-year diurnal monthly average
CO
MPA
RIS
ON
USI
NG
HYD
RU
S M
OD
EL
0 8 16 24
-10
01
02
03
04
0
Time (hours)
Su
rfa
ce
Te
mp
era
ture
Second half of year
July
August
September
October
November
December
Tessel
OLAM_VG
Surface temperature, sand, multi-year diurnal monthly average
CO
MPA
RIS
ON
USI
NG
HYD
RU
S M
OD
EL
0 8 16 24
0.0
00
.05
0.1
00
.15
0.2
00
.25
0.3
0
Time (hours)
Su
rface
Mo
istu
re c
on
ten
t
July
August
September
October
November
December
Tessel
OLAM_VG
Surface SMC, sand, multi-year diurnal monthly average
CO
MPA
RIS
ON
USI
NG
HYD
RU
S M
OD
EL
0 8 16 24
-10
010
20
30
40
Time (hours)
Surf
ace T
em
pera
ture
Second half of year
July
August
September
October
November
December
ORCHIDEE
OLAM_VG
0 8 16 24
-10
010
20
30
40
Time (hours)
Second
nod
e T
em
pera
ture
Second half of yearJuly
August
September
October
November
December
ORCHIDEE
OLAM_VG
Below: exact same hydraulic functions, but two different thermal functions, (solid line LSM 1, dashed line LSM 2) Small effect on EB fluxes and Ts, but considerable effect on deeper soil temperatures Causes differences values, amplitudes and phase-shifts: implications for soil freezing and permafrost applications
CO
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CONCLUSIONS
โข Very different shapes for ๐(๐) curve, and considerable differences in ๐ถโ(๐), between LSM models
โข Some LSM models have errors in their basic equations; some model teams have now corrected these
โข PTFs for parameters in these thermal property functions vary considerably between models.
โข They include a hydraulic PFT for porosity
โข PFTs depend on soil texture and porosity/dry bulk density, as well as quartz content
CO
NC
LUSI
ON
S
CONCLUSIONS, CโED
โข The combined effect of the choice of thermal and hydraulic equations on the energy and water balance is large
โข When only the thermal properties differ, the main effect is on deeper soil temperatures
โข This has implications for modelling of permafrost regions or soil respiration, for example
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NEXT STEPS
โข Assess influence for vegetated surfaces (reduced)
โข Use measured thermal properties to test validity of models
โข Select preferred and/or adjust equations/PTFs
โข Make recommendations to LS and Hydrological modellers