Equations and PFTs for soil thermal properties in LSMs ......= 733 J kg-1 K-1 (ii) Two LSMs use the same values for 𝐶 =𝜌 𝑐 for 11 USDA soil type as given in Pielke (2002)

Equations and PFTs for soil thermal properties in LSMs: Implications for the energy balance

TITL

E SL

IDE

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, Gabriëlle 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: Agnès Ducharne and Fuxing Wang SSiB: Yongkang Xue, Qian Li SURFEX-ISBA: Aaron Boone and Sebastien Garrigues

OV

ERV

IEW

OVERVIEW • Joint ISMC and GEWEX

communities: Initiatives to improve soil and subsurface processes in current climate and hydrological models

• Evaluation of pedotransfer functions and related functional descriptions for calculation of hydraulic and thermal soil properties in global climate models.

land surface model



THER

MA

L P

RO

PER

TIES

TH

EOR

Y

𝜆 = 𝐹𝜃𝜆𝑠𝑎𝑡 + 1 − 𝐹𝜃 𝜆𝑑𝑟𝑦

THERMAL CONDUCTIVITY, 𝜆

• Soil thermal conductivity depends on

dry, 𝜆𝑑𝑟𝑦, and saturated conductivity,

𝜆𝑠𝑎𝑡, in combination with a soil moisture dependent weighting function, 𝐹𝜃

• Equations are required to estimate 𝜆𝑑𝑟𝑦, 𝜆𝑠𝑎𝑡 and 𝐹𝜃

• These parameters, and their intrinsic

parameters all require ‘thermal’ PFTs

𝜆 = 𝜆0 + 𝜆1𝐹𝜃 + 𝜆2 𝐹𝜃2



Most LSM models use:

One uses:

Weighting function

THER

MA

L P

RO

PER

TIES

TH

EOR

Y



WEIGHTING FUNCTION, 𝐹𝜃 • The weighting function,𝐹𝜃, is

often the Kersten number, 𝐾𝑒, which is dependent on the relative saturation, 𝑆𝑒

• Constant 𝛾 varies between models

• 𝑆𝑒 depends on moisture content, 𝜃, and saturated moisture content, 𝜃𝑠𝑎𝑡, and residual SMC, 𝜃𝑟 (for VG).

𝑆𝑒 =𝜃

𝜃𝑠𝑎𝑡 𝑆𝑒 =

𝜃 − 𝜃𝑟𝜃𝑠𝑎𝑡 − 𝜃𝑟

Clapp & Hornberger/Brooks & Corey Van Genuchten, VG

𝐾𝑒 = 𝛾 log 𝑆𝑒 + 1

Most LSMs: 𝐹𝜃 = Kersten number, 𝐾𝑒

where 𝛾 is generally one, but for some models is set to 0.7 for coarse soils.

Others use 𝛾 = 0.7 for 0.05 < 𝑆𝑒 ≤ 0.1.

𝐹𝜃 = 𝑆𝑒 for 2 others

THER

MA

L P

RO

PER

TIES

TH

EOR

Y

DRY THERMAL CONDUCTIVITY, 𝜆𝑑𝑟𝑦

• generally dependent on (some of)

the soil texture fractions (sand, silt, clay), either explicitly or implicitly (via soil class look-up tables, LUTs).

• Porosity, 𝜃𝑠𝑎𝑡 , 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)

𝜆𝑑𝑟𝑦,𝑚𝑖𝑛 =0.135𝜌𝑚𝑖𝑛 + 64.7

𝜌𝑚𝑖𝑛 − 0.947𝜌𝑏,𝑚𝑖𝑛𝑑

𝜆𝑑𝑟𝑦,𝑚𝑖𝑛 = −0.56𝜃𝑠𝑎𝑡 + 0.51

𝜆𝑑𝑟𝑦,𝑚𝑖𝑛 = 𝜆𝑎𝑖𝑟𝜃𝑠𝑎𝑡𝑋𝑐𝑙𝑋𝑠𝑎𝑋𝑠𝑖

One uses (Cox et al., 1999)

𝑋𝑗 = 𝐶𝑗

𝑓𝑗 1−𝜃𝑠𝑎𝑡

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 𝜆𝑑𝑟𝑦,𝑚𝑖𝑛 = 0.19

Alternatively



THER

MA

L P

RO

PER

TIES

TH

EOR

Y



SATURATED THERMAL CONDUCTIVITY, 𝜆𝑠𝑎𝑡 • The saturated thermal conductivity

generally depends on the thermal conductivities of the solid soil material, 𝜆𝑠𝑜𝑖𝑙 , liquid soil water, 𝜆𝑙𝑖𝑞, and ice, 𝜆𝑖𝑐𝑒, sometimes on

𝜆𝑎𝑖𝑟.

One uses

Most LSMs use (from Johansen, 1975?):

Or

𝜆𝑠𝑎𝑡 = 𝜆𝑠𝑜𝑖𝑙1−𝜃𝑠𝑎𝑡𝜆𝑖𝑐𝑒

𝜃𝑠𝑎𝑡−𝜃𝑢𝜆𝑙𝑖𝑞𝜃𝑠𝑎𝑡𝑢

𝜆𝑠𝑎𝑡 =

1.58 𝜆𝑑𝑟𝑦 < 0.25

1.58 + 12.4 𝜆𝑑𝑟𝑦 − 0.25 0.25 < 𝜆𝑑𝑟𝑦 < 0.3

2.2 𝜆𝑑𝑟𝑦 > 0.3

𝜆𝑠𝑎𝑡 = 𝜆𝑑𝑟𝑦 𝜆𝑙𝑖𝑞𝜃𝑠𝑎𝑡𝑢

𝜆𝑖𝑐𝑒

𝜃𝑠𝑎𝑡𝑓

𝜆𝑎𝑖𝑟𝜃𝑠𝑎𝑡

Soil solid conductivity (see next slide)

THER

MA

L P

RO

PER

TIES

TH

EOR

Y

SOIL SOLID THERMAL CONDUCTIVITY, 𝜆𝑠𝑜𝑖𝑙 • The saturated thermal conductivity

generally depends on the thermal conductivities of the solid soil material, 𝜆𝑠𝑜𝑖𝑙 , liquid soil water, 𝜆𝑙𝑖𝑞, and ice, 𝜆𝑖𝑐𝑒, sometimes of

𝜆𝑎𝑖𝑟.

Some use:

In a number of LSMs, 𝜆𝑠𝑜𝑖𝑙 is assumed to be dependent only on the thermal conductivity of the mineral soil solids as given by (Johansen, 1975):

𝜆𝑠𝑜𝑖𝑙 = 𝜆𝑞𝑢𝑓𝑞𝑢𝜆𝑜

1−𝑓𝑞𝑢

𝜆𝑠𝑜𝑖𝑙 =𝜆𝑞𝑢𝑓𝑠𝑎𝑛𝑑 + 𝜆𝑐𝑙𝑎𝑦𝑓𝑐𝑙𝑎𝑦

𝑓𝑠𝑎𝑛𝑑 +𝑓𝑐𝑙𝑎𝑦

𝜆𝑞𝑢 the thermal conductivity of quartz, having a value of 8.8 or 7 W m-1 K-1

𝜆𝑜 is the thermal conductivity of other minerals, generally set to 2 or 3 W m-1 K-1

𝑓𝑞𝑢 = 0.038 + 0.0095𝑓𝑆𝐴

𝜆𝑠𝑜𝑖𝑙 = 7.0 𝜆𝑠𝑜𝑖𝑙 = 3.44



THER

MA

L P

RO

PER

TIES

TH

EOR

Y

SOIL HEAT CAPACITY, 𝐶ℎ • 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 (𝜌𝑖 ) and volume fractions (𝜙𝑖 ).

• Alternatively we can use the volumetric heat capacity

• Some models use a constant 𝐶ℎ(= 2.19×106; independent of soil type), i.e. its values remain unchanged despite changes in 𝜃, whereas others uses values ranging between 1.93 ×106 for sand to 2.48×106, for clay.

𝐶ℎ = 𝜙𝑚𝑖𝑛𝜌𝑚𝑖𝑛𝑐𝑚𝑖𝑛 + 𝜙𝑜𝑟𝑔𝜌𝑜𝑟𝑔𝑐𝑜𝑟𝑔 + 𝜙𝑙𝑖𝑞𝜌𝑙𝑖𝑞𝑐𝑙𝑖𝑞 + 𝜙𝑖𝑐𝑒𝜌𝑖𝑐𝑒𝑐𝑖𝑐𝑒 + 𝜙𝑎𝑖𝑟𝜌𝑎𝑖𝑟𝑐𝑎𝑖𝑟

𝜙𝑚𝑖𝑛 = 1 − 𝜃𝑠𝑎𝑡 𝜙𝑙𝑖𝑞 = 𝜃 𝜙𝑚𝑖𝑛 + 𝜙𝑜𝑟𝑔 + 𝜙𝑙𝑖𝑞 + 𝜙𝑖𝑐𝑒 + 𝜙𝑎𝑖𝑟 = 1.0

𝐶ℎ = 𝜙𝑚𝑖𝑛𝐶𝑚𝑖𝑛 + 𝜙𝑜𝑟𝑔𝐶𝑜𝑟𝑔 + 𝜙𝑙𝑖𝑞𝐶𝑙𝑖𝑞 + 𝜙𝑖𝑐𝑒𝐶𝑖𝑐𝑒 + 𝜙𝑎𝑖𝑟𝐶𝑎𝑖𝑟



THER

MA

L P

RO

PER

TIES

TH

EOR

Y

CALCULATION OF MINERAL HEAT CAPACITY, 𝑐𝑚𝑖𝑛 OR 𝐶𝑚𝑖𝑛 • The main PTF for heat capacity relates to the way 𝑐𝑚𝑖𝑛 or 𝐶𝑚𝑖𝑛 is calculated.

There are a number of options used in the LSMs: • (i) Employ the same value for all soil types • (ii) Use different values (tabulated) for each soil class, • (iii) Use different values per soil class, calculated as a function of texture:

(i) One uses 𝐶𝑚𝑖𝑛= 1.942×106 (Johansen, 1975), as one of its options. Others use 𝐶𝑚𝑖𝑛= 2.0×106; 𝑐𝑚𝑖𝑛 = 850 J kg-1 K-1, or 𝑐𝑚𝑖𝑛 = 733 J kg-1 K-1

(ii) Two LSMs use the same values for 𝐶𝑚𝑖𝑛 = 𝜌𝑚𝑖𝑛𝑐𝑚𝑖𝑛 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. :

𝐶𝑚𝑖𝑛 = 𝑓𝑐𝑙𝑎𝑦𝐶𝑐𝑙𝑎𝑦 + 𝑓𝑠𝑎𝑛𝑑𝐶𝑠𝑎𝑛𝑑 + 𝑓𝑠𝑖𝑙𝑡𝐶𝑠𝑖𝑙𝑡

𝐶𝑚𝑖𝑛 = (𝑓𝑠𝑎𝑛𝑑𝐶𝑠𝑎𝑛𝑑 + 𝑓𝑐𝑙𝑎𝑦𝐶𝑐𝑙𝑎𝑦 ) ( 𝑓𝑠𝑎𝑛𝑑 + 𝑓𝑐𝑙𝑎𝑦



RES

ULT

S: T

HER

MA

L C

ON

DU

CTI

VIT

Y

RESULTS, thermal conductivity

• Per soil type: large difference in 𝜆 between models

• 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]


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]


Jules1

Jules2

OLAM_BC

OLAM_VG

ISBA

CLM

JSBACH

CABLE

ORCHI DEE

NOAH

SSiB

Tessel

Sand



RES

ULT

S: H

EAT

CA

PAC

ITY

RESULTS, HEAT CAPACITY

• Per soil type: considerable difference in Ch between models

• 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

]


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

]


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

]


Jules1

Jules2

OLAM_BC

OLAM_VG

ISBA

CLM

JSBACH

CABLE

ORCHI DEE

NOAH

SSiB

CABLE_SLI

Tessel

Clay



CO

MPA

RIS

ON

USI

NG

HYD

RU

S M

OD

EL

MODEL RUNS, USING MODEL-SPECIFIC THERMAL (& hydraulic) properties

• Runs with Hydrus 1-D for 14 years (2001-2014) of half-hourly data from Avignon, model outputs are hourly

• 2 LSMs are compared in the next slides

• Bare soil, soil profile of 50 cm, no vapour flow, free drainage

• Sand, Loam, clay

• LSM thermal equations have been implemented into Hydrus-1D

• Effects on energy- and water balance have been investigated

• Effect on soil (surface) temperature and soil moisture content



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

NC

LUSI

ON

S

CONCLUSIONS

• Very different shapes for 𝜆(𝜃) curve, and considerable differences in 𝐶ℎ(𝜃), between LSM models

• Some LSM models have errors in their basic equations; some model teams have now corrected these

• PTFs for parameters in these thermal property functions vary considerably between models.

• They include a hydraulic PFT for porosity

• PFTs depend on soil texture and porosity/dry bulk density, as well as quartz content

CO

NC

LUSI

ON

S

CONCLUSIONS, C’ED

• The combined effect of the choice of thermal and hydraulic equations on the energy and water balance is large

• When only the thermal properties differ, the main effect is on deeper soil temperatures

• This has implications for modelling of permafrost regions or soil respiration, for example

CO

NC

LUSI

ON

S

NEXT STEPS

• Assess influence for vegetated surfaces (reduced)

• Use measured thermal properties to test validity of models

• Select preferred and/or adjust equations/PTFs

• Make recommendations to LS and Hydrological modellers

Documents

Equations and PFTs for soil thermal properties in LSMs ......= 733 J kg-1 K-1 (ii) Two LSMs use the same values for 𝐶 =𝜌 𝑐 for 11 USDA soil type as given in Pielke (2002)