Analysis of the surface temperature distribution at Badain Jaran … · Badain Jaran Desert using fully coupled hydro-thermal method Haijun Hu, Teodolina Lopez, Yujun Cui, Raphaël

Analysis of the surface temperature distribution at Badain Jaran Desert using fully coupled hydro-

thermal method

Haijun Hu, Teodolina Lopez, Yujun Cui, Raphaël Antoine, Ni An, Weikang Song

1. Introduction

Contents

4. Discussion

2. Materials and methods

3. Results

5. Conclusions

Badain Jaran Desert site

Surface Temperature at the site

Nighttime

Daytime

31st August 2008

(MODIS TERRA)

Motivation

Water table depth /m

0.5

…

32

…

165

Surface temperature Ts ?

Meteorological Data

2008/1

/1

2008/2

/1

2008/3

/1

2008/4

/1

2008/5

/1

2008/6

/1

2008/7

/1

2008/8

/1

2008/9

/1

2008/1

0/1

2008/1

1/1

2008/1

2/1

-30

-20

-10

0

10

20

30

40

Date

Air

Tem

pera

ture

(℃

)

2008/1

/1

2008/2

/1

2008/3

/1

2008/4

/1

2008/5

/1

2008/6

/1

2008/7

/1

2008/8

/1

2008/9

/1

2008/1

0/1

2008/1

1/1

2008/1

2/1

0

5

10

DateW

ind s

pee

d (

m/s

)

Air temperature Wind speed

Minqin station

2008/1

/1

2008/2

/1

2008/3

/1

2008/4

/1

2008/5

/1

2008/6

/1

2008/7

/1

2008/8

/1

2008/9

/1

2008/1

0/1

2008/1

1/1

2008/1

2/1

0.0

1.0x10-7

2.0x10-7

3.0x10-7

4.0x10-7

Date

Rai

nfa

ll (

m/s

)

Meteorological Data – Cont’d

Rainfall

2008/1

/1

2008/2

/1

2008/3

/1

2008/4

/1

2008/5

/1

2008/6

/1

2008/7

/1

2008/8

/1

2008/9

/1

2008/1

0/1

2008/1

1/1

2008/1

2/1

0

50

100

Date

Hu

mid

ity

(%

)

2008/1

/1

2008/2

/1

2008/3

/1

2008/4

/1

2008/5

/1

2008/6

/1

2008/7

/1

2008/8

/1

2008/9

/1

2008/1

0/1

2008/1

1/1

2008/1

2/1

0

5

10

15

20

Date

S

unsh

ine

durt

ion (

h)

Humidity Sunshine duration

0.0 0.1 0.2 0.3 0.420

15

10

5

0

The depth to water table

0.7m (Zhou 2015)

5m (Gates et al. 2008)




Volumetric water content (%)

Dep

th (

m)

Gates et al. (2008); Zhou (2015)Ma and Eumunds

（2006）Zhao et al.（2011）

Surface: dry layer 35cm

w<0.5% ≈ 0.01%

Volumetric water content

Dong et al.（2015）

0 30 60 90 120 150 180 210 240 270 300 330 360

-10

0

10

20

30

40

Measured temperature of lake water

Fitted line

DOY

Tem

per

atu

re (

℃)

5 4 sin(DOY/44 ) DOY 44

5 25 sin[(DOY-44)/322 ) 44 DOY 366T

− =

+

Lake water temperature

Fully-coupled numerical method

The governing equation of liquid and vapor water mass flow can be expressed as:

T T l w

TC C K K T K

t t

+ = + +

(A1)

+=

+

TTTT KTK

tC

t

TC

The governing equation of heat flow can be expressed as:

The fully coupled hydro-thermal method developed by Anni et al. (2017)

Initial and boundary conditions(A1)

Initial temperature: 5℃ Initial suction: hydrostatic equilibrium line

Heat &water

transportHeat &water

transport

Top

× ×

Bottom

Bottom boundary condition:(A1)

0 30 60 90 120 150 180 210 240 270 300 330 360

-10

0

10

20

30

40

Measured temperature of lake water

Fitted line

DOY

Tem

per

atu

re (

℃)

5 4 sin(DOY/44 ) DOY 44

5 25 sin[(DOY-44)/322 ) 44 DOY 366T

− =

+

(2) Suction at bottom

(1) Temperature at bottom

φ = 0

(A1)

Heat flux at the top boundary

- + +htop n Eq R H L=LERn H

(A1)

The net solar radiation

SW 0.25 0.5 sa

nR

N

= +

SW SW=

4LW a aT=

4LW s surfT=

The net solar radiation

(A1)

Sensible heat and latent heat

( )a pa s a

a

C T TH

r

−=

1000E v aL L E=

The latent heat

The sensible heat

as

a

p

a

ee

ee

E

E

−

−= 0

( )( )-310

10086400

p aE a bu h= + − Song （2015）

(A1)

Water flux at the top boundary

-( - )wtop a offq E P R=P

Roff

Ea

Hydraulic property(A1)

1 10 100 10000.0

0.1

0.2

0.3

0.4

Arya and Paris（1981） Mearused value

Suction/kPa

Vo

lum

etri

c w

ater

conte

nt

Water retention curve

Parameter value

a(cm) 88.3

θs 0.382

θr 0.0237

n 2.87

ks (m/s) 1.06×10-4

( )=

1 ( )

s rr m

n

a

−+ +

VG model

0.5 1/ 2= [1 (1 ) ]m m

sk k − −

Thermal property

0.330.18+3.61 =

0.0 0.1 0.2 0.3 0.40

1

2

3

4 De Vries method (Wilson,1990)

Chung and Horton（1987） Coté and Konrad （2005） Fited line for Ottawa sand (Zhang et al. 2015)

Volumetric water content

T

her

mal

co

nd

uct

ivit

y

(Wm

-1K

-1)

Heat conductivity

Calculation vs measurement at about 1 m depth

Soil temperature at about 1m depth

0 30 60 90 120 150 180 210 240 270 300 330 360

-40-30-20-10

0102030405060

Ts at depth 1m

Ts at depth 1.1m measured (Hu et al.2015)

Tw

DOY

Tem

per

ature

(℃

)

0 30 60 90 120 150 180 210 240 270 300 330 360

-30-20-10

0102030405060

Temperature at day

Temperature at night

DOY

Tem

per

ature

(℃

)

Calculated and measured temperatures (B1)

Surface temperature difference between different WTB depths

Surface temperature difference for different water table depth (WTD)

0 30 60 90 120 150 180 210 240 270 300 330 360

-10-8-6-4-202468

10 T

s at WTD 32m-T

s at WTD 0.5m

DOY

Tem

per

ature

(℃

)

0 30 60 90 120 150 180 210 240 270 300 330 360

-2

-1

0

1

2

Ts at WTD 165m-T

s at WTD 32m

DOY

Tem

per

atu

re (

℃)

Conclusions

(1) The numerical approach can be used to correctly determine the soil surface

temperature changes with varying water table depth.

(2) The hydraulic and thermal parameters need to be refined to increase the

calculation quality.

(3) Slope direction seems to be important to be accounted for because it can greatly

affect the solar radiation, wind speed etc.

Documents

Analysis of the surface temperature distribution at Badain Jaran … · Badain Jaran Desert using fully coupled hydro-thermal method Haijun Hu, Teodolina Lopez, Yujun Cui, Raphaël