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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
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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
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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
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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)
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Jackson. 1973. SSSA Spec. Publ., 5, 37–55
Diurnal soil water content change5, 6, and 7 days after irrigation
Sunrise
Sunset
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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.
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Theory
KkTDDDKt
T
t TvTLmmv
)()(.21
))((. 321 LvoLm qqTTCTtt
T
Water Flow
Heat Transfer
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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
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Heat Pulse Probe
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40 mm
6 mm6 mm
1.3
StainlessStainlesssteel tubingsteel tubing
ThermocoupleThermocouple
ResistanceResistanceheaterheater
Sketch of a heat pulse sensor
Heat pulse probe
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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
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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
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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
( )
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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
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Thermal properties
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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)
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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
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Calculation of Volumetric Heat Capacity
wwsb ccc
This equation can be used to estimate soil b or with the heat-pulse technique.
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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
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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
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Upstream needle
Heater
Downstream needle
1 cm
Heat pulse measurements for estimating soil liquid Water Flux
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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)]
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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)
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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
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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
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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
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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
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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
)
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A Heat Pulse Technique for Estimating Soil Water
Evaporation
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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
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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
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Heat-pulse sensors arrangement. Six sensors were installed within the top 7 cm of the soil profile.
7cm
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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
)
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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)
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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
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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)
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Latent Heat in Soil Heat Flux Measurements
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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.
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Materials and MethodsSoil heat flux (G) measured via heat-pulse sensors installed at
3 depths: 1, 3, and 6 cm
G = -(T/z)
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cutaway view
soil surface
heat-pulse sensor
side view
1 cm
3 cm
6 cm
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Materials and MethodsEvaporation (LE) determined via microlysimeters (per 24 h)
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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
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‘G’ measured above the drying front isn’t really G – its G + LE.
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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
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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
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HP sensors installed in a corn field in 2009
Bare soil In-row
Between-rows with roots Between-rows without roots
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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
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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
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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
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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
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Liquid water flux at the 7.5 mm soil depth
from the model simulation.
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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.
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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.
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