Heat Pulse Measurements to determine:

soil thermal propertiessoil water content

infiltrating liquid water fluxsensible heat flux in soil

latent heat flux (vaporization or fusion)upward liquid water flux

Agron 405/505

Soil heat and water dynamics

Impact biological, chemical, and physical,

processes

Modeling coupled heat and water dynamics is

difficult and requires many hard to measure

parameters

Measuring in situ coupled heat and water

dynamics has improved recently

Temperature with depth in Corn

15

20

25

30

242 243 244 245

DOY 2008

Tem

per

atu

re ℃

5 cm 10cm 17.5 cm 35 cm

15

20

25

30Below Right RowA

15

20

25

30

3525 cm From Right Row

B

15

20

25

30

35

40

45

50

55

60At CenterBetween

Rows

C

15

20

25

30

35

40

0 cm 5 cm20 cm

25 cm From Left Row

D

0 4 8 12 16 20 24

Time (hours)

Tem

per

atu

re (

°C)

Jackson. 1973. SSSA Spec. Publ., 5, 37–55

Diurnal soil water content change5, 6, and 7 days after irrigation

Sunrise

Sunset

Coupled Heat and Water Transfer

Thermal gradients cause water to move in unsaturated soil.

When water moves in soil, it carries heat.

Because heat transfer and water movement affect one another they are coupled.

Theory

KkTDDDKt

T

t TvTLmmv

)()(.21

))((. 321 LvoLm qqTTCTtt

T

Water Flow

Heat Transfer

Some heat pulse probe possibilities

Measure soil thermal properties

Measure soil water content

Measure infiltrating liquid water flux

Measure sensible heat flux in soil

Measure latent heat flux (vaporization or

fusion)

Measure upward liquid water flux

Heat Pulse Probe

40 mm

6 mm6 mm

1.3

StainlessStainlesssteel tubingsteel tubing

ThermocoupleThermocouple

ResistanceResistanceheaterheater

Sketch of a heat pulse sensor

Heat pulse probe

tt(s)(s)00 3030 6060 9090 120120 150150

TT ( (

oo C)C)

0.00.0

0.10.1

0.20.2

0.30.3

0.40.4

0.50.5((ttmm, , TTmm))A V

Datalogger

DC power

rr

Heat Pulse Method

For a cylindrical coordinate, heat conduction Eq. and solution:

c

q

t

T

rr

T

t

T

1

2

2

t

rEi

tt

rEi

qtrT

4)(44),(

2

0

2

Temperature response after applied t0=8 s heat pulse on the central heater needle

0

0. 3

0. 6

0. 9

1. 2

1. 5

0 20 40 60 80Time (s)

Tem

pera

ture

incr

ease

(K

) tm=30 s

ΔTm=1.23 K

Determining of soil thermal properties by heat pulse sensor

Determining of soil thermal properties by heat pulse sensor

Soil thermal conductivity (W/mC):C

Soil heat capacity C (J/m3C):

mTre

qtcC

20 '

Soil thermal diffusivity (J/m3C)

r

t t t

t

t tm m

m

m

2

0 04

1 1

( )ln

( )

Example of heat pulse data

By fitting a heat transfer model to the heat pulse data we determine the soil thermal properties.

Time (s)

10 20 30 40 50 60 70 80

Tem

pera

ture

incr

ease

(K

)

0.1

0.2

0.3

0.4

0.5

0.6

Time (s)

10 20 30 40 50 60 70 80

Tem

pera

ture

incr

ease

(K

)

0.1

0.2

0.3

0.4

0.5

0.6

C = 1.79 MJ m-3 K-1

= 0.84 W m-1 K-1

C = 2.51 MJ m-3 K-1

= 1.11 W m-1 K-1

Thermal properties

Soil thermal properties

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

(

10-6

m2 s

-1)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Sandy loamClay loamSilt loamSilty clay loam

(W

m-1

K-1

)

0.0

1.0

2.0

3.0C

(10

6 J m

-3 K

-1)

0.0

1.0

2.0

3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

m-3 m-3) vs (m-3 m-3) na (m

-3 m-3)

m-3 m-3) vs (m-3 m-3) na (m

-3 m-3)

Influences of soil texture, b and on

0.0

0.4

0.8

1.2

1.6

2.0

0 0.1 0.2 0.3 0.4 0.5

(m3 m-3)

(W

m-1

K-1

)

Loam 1.2

Loam 1.4

Sand 1.6

b

Calculation of Volumetric Heat Capacity

wwsb ccc

This equation can be used to estimate soil b or with the heat-pulse technique.

Factors Influencing Soil c

Soil heat capacity as affected by water content

y = 3.50x + 1.26

y = 3.52x + 1.12

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00 0.10 0.20 0.30 0.40 0.50

(m3 m-3)

c (

MJ

m-3

K-1

)

Sand Loam

For mineral soils, c increases linearly with

Gravimetric (m3 m-3)

0.0 .1 .2 .3 .4 .5 .6

TD

R

(m

3 m-3

)

0.0

.1

.2

.3

.4

.5

.6

Y = -0.008 + 0.995X(r2 = 0.934, Syx = 0.026)

Silty clay loam

Silt loam

Sand

Clay loam

Sandy loam

Silt loam (intact)

Thermo-TDR Water Content

Upstream needle

Heater

Downstream needle

1 cm

Heat pulse measurements for estimating soil liquid Water Flux

Heat transfer equations

2

2

2

2

x

TV

y

T

x

T

t

T

ccJVl /)(

•The governing heat transfer equation is

where J is the water flux [volume / (time x area)]

02

u1

2d1

u

d

0

0

2u1

0

2d1

u

d

;

4

)(exp

4

)(exp

)(

0;

4

)(exp

4

)(exp

)(

0

0 tt

dss

Vsxs

dss

Vsxs

tT

T

tt

dss

Vsxs

dss

Vsxs

tT

T

t

tt

t

tt

t

t

A solution to heat transfer equation (Ren et al., 2000)

The relationship between water flux and the temperature ratio is very simple (Wang et al., 2002)

u

d

l T

T

cxJ ln

0

The ratio of downstream and upstream T increase

When 0xxx ud

Temperature ratio is constant

Time (s)

0 10 20 30 40 50 60 70

Td

/ T

u

0.5

1.0

1.5

2.0

2.5

3.0J = 3.6 x 10-5 m s-1

2.5 cm/hr

Time (s)

0 20 40 60 80 100

Te

mp

era

ture

incre

ase

(C

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

UpstreamDownstream

8.1 cm/hr

Time (s)

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

Sand

Measured heat pulse signals

Time (s)

0 20 40 60 80 100

Td

/ Tu

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 cm/hr0.52.58.123.3

Sand

Heat pulse signals converted to Td/Tu

Heat pulse flux estimates versus imposed unsaturated fluxes

10-2

10-1

100

101

102

10-2

10-1

100

101

102

Imposed water flux (cm h-1)

Est

imat

ed w

ater

flux

(cm

h-1

)

A Heat Pulse Technique for Estimating Soil Water

Evaporation

Basic theory of HP method:Basic theory of HP method:

Sensible heat balance provides a means to determine latent Sensible heat balance provides a means to determine latent heat (heat (LELE) used for evaporation.) used for evaporation.

LE =LE = ((HH11 – – HH22) –) – SS condensation

nevaporatio

nevaporationo

0

0

0

LELE

Sensible heat flux out, Sensible heat flux out, HH22

Sensible heat flux in, Sensible heat flux in, HH11

Sensible heat Sensible heat

storage change storage change SS

Determining the dynamic soil water evaporation

H1

H2

Sensible soil heat flux: H =-(dT/dz)

1, C1,

2, C2,

dT/dz1,

dT/dz2,

LE = (H1 – H2) – S

T3

T2

T1

Soil layer

S

Change in sensible heat storage: ΔS = C (ΔZ) (dT/dt)

Heat-pulse sensor

11

22

33

Heat-pulse sensors arrangement. Six sensors were installed within the top 7 cm of the soil profile.

7cm

Temperature (T ); Heat capacity (C) and thermal conductivity(λ)

0

20

40

60

800mm6mm12mm

C (

MJ/

m3

C)

0

1

2

3

174 175 176 177 178 179 180

0

0.4

0.8

1.2.

.

T (C

)

C

Day of year 2007

λ(

W/

mC

)

Heat fluxes at 3 and 9 mm (H1,H2); heat storage change (∆S) at soil layer (3~9 mm)

Day of year 2007

H a

nd

∆S

(W

/m2

)

-100

100

300

500

700

174 175 176 177 178 179 180

H1 (3mm)

H2 (9mm)

∆S (3~9mm)

Evaporation dynamics measured by heat pulse method

Eva

po

rati

on

(m

m/h

r)

Day of year 2007

-0.2

0

0.2

0.4

0.6

0.8

3~9 mm 1st depth 9~15 mm 2nd 15~21 mm 3rd21~27 mm 4th

174 175 176 177 178 179 180

y = 0.95 x + 0.07

R2 = 0.96

0.0

0.8

1.6

2.4

3.2

4.0

0.0 0.8 1.6 2.4 3.2 4.0

Bowen ratioMicro-lysimeters

Comparison of daily soil water evaporation (mm) from heat pulse with micro-lysimeters and Bowen ratio methods

HP

dai

ly e

vap

ora

tio

n

(mm

)

Micro-lysimeters daily evaporation (mm)

Latent Heat in Soil Heat Flux Measurements

Better Energy Balance ClosureWhen the latent heat flux (LE) includes evaporation from soil,

the depth at which we measure soil heat flux (G) is critical to accurately representing the surface energy balance.

Objective: Characterize variations in G with depth near the soil surface.

Materials and MethodsSoil heat flux (G) measured via heat-pulse sensors installed at

3 depths: 1, 3, and 6 cm

G = -(T/z)

cutaway view

soil surface

heat-pulse sensor

side view

1 cm

3 cm

6 cm

Materials and MethodsEvaporation (LE) determined via microlysimeters (per 24 h)

Cumulative Soil Heat Flux at 1-cm Depth

0

5

10

15

20

25

30

35

40

151 153 155 157 159 161

Cum

. Soi

l Hea

t Flu

x at

1-c

m (M

J m-2

)

Day of Year

gradientfrom 3 cm gradientfrom 6 cm gradient

‘G’ measured above the drying front isn’t really G – its G + LE.

Accumulated Energy

0

5

10

15

20

25

151 153 155 157 159 161

Acc

umul

ated

Ene

rgy

Flux

(MJ m

-2)

Day of Year

LEDifference, 1 and 3 cm GDifference, 1 and 6 cm G

ConclusionsShallow soil heat flux measurements may capture G + (soil-

originating) LE

Leads to ‘double accounting’ for LE in energy balance closure based on above-ground measurements

Recommendation: G must be measured at a depth below the expected penetration of the drying front (here, possibly as deep as 6 cm) in order to treat the surface energy balance as

Rn – G = LE + H

HP sensors installed in a corn field in 2009

Bare soil In-row

Between-rows with roots Between-rows without roots

Soil temperature at different locationsT

emp

erat

ure

(˚C

)

Day of year 2009

240 242 244 246 248 250 252 254 256 258

Bare

10

20

30

40

50

In rows

10

15

20

25

30

Between-rows with roots

10

15

20

25

30

240 242 244 246 248 250 252 254 256 258

Between-rows no roots

10

15

20

25

30

Eva

po

rati

on

(m

m)

Day of year 2009

Soil water evaporation dynamics

Bare

-0.1

0.0

0.1

0.2

0.3

240 242 244 246 248 250 252 254 256 258 240 242 244 246 248 250 252 254 256 258

Between-rows with roots

-0.1

0.0

0.1

0.2

0.3

In-row

-0.1

0.0

0.1

0.2

0.3

Between-row without roots

-0.1

0.0

0.1

0.2

0.3

Day of year 2009

Cumulative soil water evaporation at 3-mm soil depthC

um

ula

tive

Eva

po

rati

on

(m

m)

0

10

20

30

40

240 242 244 246 248 250 252 254 256 258

Bare

Between-rows

Between-rows no roots

In-row

SFFE ud

For a soil layer, ΔE is the evaporation rate (cm/h), Ft and Fb are the liquid water flux (cm/h) at top and bottom boundaries, and ΔS is the change in water storage (cm/h).

EE

Water storage Water storage change change SS

Fd

Fu

Liquid water flux at the 7.5 mm soil depth

from the model simulation.

Conclusions

The heat pulse method is able to provide a wide range of soil heat and water measurements.

This is an important time period to advance coupled heat and water experiments and models.

ReferencesRen, T., G.J. Kluitenberg, and R. Horton. 2000. Determining soil water flux and por

e water velocity by a heat pulse technique. Soil Sci. Soc. Am. J. 64:552–560.

Wang, Q., T.E. Ochsner, and R. Horton. 2002. Mathematical analysis of heat pulse signals for soil water fl ux determination. Water Resour. Res. 38,DOI 10.1029/2001WR001089.

Heitman, J.L., R. Horton, T.J. Sauer, and T.M. DeSutter, 2008. Sensible heat observations reveal soil water evaporation dynamics, J. Hydrometeor., 9: 165-171.

Heitman, J.L., X. Xiao, R. Horton, and T. J. Sauer, 2008. Sensible heat measurements indicating depth and magnitude of subsurface soil water evaporation. Water Resour. Res., 44, W00D05, doi:10.1029/2008WR006961.

Xiao X., R. Horton, T.J. Sauer, J.L. Heitman and T. Ren, 2011. Cumulative soil water evaporation as a function of depth and time. Vadose Zone J. (in press).