Heat Pulse Measurements
to determine:
soil thermal properties
soil water content
infiltrating liquid water flux
sensible 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
30
Temperature ℃
5 cm
10cm
17.5 cm
35 cm
25
20
15
242
243
244
DOY 2008
245
30
25
A
Below Right Row
B
25 cm From
Right Row
C
At Center
Between
Rows
20
15
35
30
25
20
Temperature (°C)
15
60
55
50
0 cm
5 cm
20 cm
45
40
35
30
25
20
15
40
35
30
25
20
15
25 cm From
Left Row
D
0
4
8
12
16
Time (hours)
20
24
Sun
rise
Sun
set
Diurnal soil water content change
5, 6, and 7 days after irrigation
Jackson. 1973. SSSA Spec. Publ., 5, 37–55
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
Water Flow

T
1
 2
 .( K  Dmv ) m  ( DTL  DTv )T  Kk 
t
t
Heat Transfer
T

1
 2
 .T   3 m  C L (T  To )( qv  qL )
t
t
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
Sketch of a heat pulse sensor
Stainless
steel tubing
40
mm
Thermocouple
Resistance
heater
1.3
6 mm
Heat pulse probe
6 mm
Heat Pulse Method
A
V
0.5
DC power
(tm, Tm)
0.4
0.3
0.2
0.1
Datalogger
r
0.0
0
30 60 90 120 150
t(s)
For a cylindrical coordinate, heat conduction Eq. and solution:
  2T 1 T  q
T
 
   2 
t

r
r

t

 c
  r 2 
q    r2 
  Ei

T (r , t ) 
 Ei
4   4 (t  t0 ) 
4

t


Determining of soil thermal properties by
heat pulse sensor
Temperature increase (K)
1.5
tm=30 s
1.2
0.9
0.6
ΔTm=1.23 K
0.3
0
0
20
40
Time (s)
60
80
Temperature response after applied t0=8 s heat
pulse on the central heater needle
Determining of soil thermal properties by
heat pulse sensor
Soil thermal diffusivity (J/m3C)
r2

4

 tm 
1
1
  ln 




(
t
t
)
t
(
t
t
)
 m 0
 m 0 
m
Soil heat capacity C (J/m3C):
t0 q '
C  c 
2
er Tm
Soil thermal conductivity  (W/mC):
  C
Example of heat pulse data
Temperatureincrease
increase(K)
(K)
Temperature
0.6
0.6
C = 1.79 MJ m-3 K-1
 = 0.84 W m-1 K-1
0.5
0.5
0.4
0.4
0.3
0.3
C = 2.51 MJ m-3 K-1
 = 1.11 W m-1 K-1
0.2
0.2
0.1
0.1
1010
2020
3030
4040 5050
Time
Time(s)
(s)
6060
7070
8080
By fitting a heat transfer model to the heat pulse
data we determine the soil thermal properties.
Thermal properties
Soil thermal properties
m-3 m-3)
na (m-3 m-3)
Sandy loam
Clay loam
Silt loam
Silty clay loam
-1
 (W m K )
3.0
vs (m-3 m-3)
-1
2.0
1.0
0.0
-3
2.0
6
-1
C (10 J m K )
3.0
1.0
0.0
-1
0.6
-6
0.8
2
 (10 m s )
1.0
0.4
0.2
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 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)
Influences of soil texture, b and  on 
2.0
1.2
b
 (W m
-1
K-1)
1.6
0.8
Loam 1.2
Loam 1.4
0.4
Sand 1.6
0.0
0
0.1
0.2
0.3
 (m3 m-3)
0.4
0.5
Calculation of Volumetric Heat Capacity
c  b cs   wcw
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
-3 -1
 c (MJ m K )
3.0
2.5
y = 3.50x + 1.26
2.0
y = 3.52x + 1.12
1.5
1.0
Sand
0.5
0.0
0.00
0.10
0.20
0.30
Loam
0.40
0.50
 (m 3 m -3)
For mineral soils, c increases linearly with 
Thermo-TDR Water Content
.6
-3
TDR  (m m )
.5
3
.4
Sand
Sandy loam
Silt loam
Silt loam (intact)
Clay loam
Silty clay loam
.3
.2
Y = -0.008 + 0.995X
(r = 0.934, Syx = 0.026)
.1
0.0
0.0
2
.1
.2
.3
.4
.5
Gravimetric  (m m )
3
-3
.6
Heat pulse measurements for estimating soil
liquid Water Flux
Upstream needle
Heater
Downstream needle
1 cm
Heat transfer equations
•The governing heat transfer equation is
  2T  2T 
T
T
   2  2  V
t
y 
x
 x
V  J ( c) l / c
where J is the water flux [volume / (time x area)]
A solution to heat transfer equation
(Ren et al., 2000)
t
 1
 ( xd  Vs) 2 
ds

 s exp 
4 s
Td


(t )  0t
;
2
Tu
 1
 ( xu  Vs) 
s
exp

 ds

4

s
0


0  t  t0
t

 ( xd  Vs) 2 
1
 ds
 s exp 
4

s
t  t 0


Td
(t )  t
;
2
Tu

 ( xu  Vs) 
1
s
exp

 ds

4

s
t  t 0


t  t0
The ratio of downstream and upstream
T increase
The relationship between water flux and the
temperature ratio is very simple (Wang et al., 2002)
 Td 


J 
ln

x0  c l  Tu 

When
xd  xu  x0 
Temperature ratio is constant
3.0
-5
J = 3.6 x 10 m s
-1
Td / Tu
2.5
2.0
1.5
1.0
0.5
0
10
20
30 40
Time (s)
50
60
70
Measured heat pulse signals
1.2
1.2
8.1 cm/hr
Temperature increase (C)
2.5 cm/hr
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
Upstream
Downstream
0.0
0
20
40
60
Time (s)
80
0.0
100
Sand
0
20
40
60
Time (s)
80
100
Heat pulse signals converted to Td/Tu
3.0
2.5
Td / Tu
2.0
1.5
Sand
1.0
0 cm/hr
0.5
2.5
8.1
23.3
0.5
0.0
0
20
40
60
Time (s)
80
100
Heat pulse flux estimates versus
imposed unsaturated fluxes
2
Estimated water flux (cm h-1)
10
1
10
0
10
-1
10
-2
10 -2
10
-1
0
1
10
10
10
Imposed water flux (cm h-1)
2
10
A Heat Pulse Technique for
Estimating Soil Water Evaporation
Basic theory of HP method:
Sensible heat balance provides a means to determine
latent heat (LE) used for evaporation.
LE = (H1 – H2) – S
 0 no evaporation
 0 evaporation
 0 condensation
LE
Sensible heat flux in, H1
Sensible heat
storage change S
Sensible heat flux out, H2
Determining the dynamic soil water evaporation
T1
dT/dz1, 1, C1, H1
1
S
T2
2
Soil layer
3
dT/dz2, 2, C2, H2
T3
Heat-pulse sensor
LE = (H1 – H2) – S
Sensible soil heat flux: H =-(dT/dz)
Change in sensible heat storage: ΔS = C (ΔZ) (dT/dt)
7cm
Heat-pulse sensors arrangement. Six sensors were installed
within the top 7 cm of the soil profile.
Temperature (T ); Heat capacity (C) and thermal
conductivity(λ)
80
T (C)
60
0mm
6mm
12mm
40
0
3
.
.
2
C
1.2

0.8
1
0.4
0
0
174
175
176
177
178
Day of year 2007
179
180
λ( W/ mC )
C (MJ/m3 C)
20
Heat fluxes at 3 and 9 mm (H1,H2); heat
storage change (∆S) at soil layer (3~9 mm)
H and ∆S (W/m2)
700
H1 (3mm)
H2 (9mm)
500
∆S (3~9mm)
300
100
-100
174
175
176
177
Day of year 2007
178
179
180
Evaporation (mm/hr)
Evaporation dynamics measured by heat pulse
method
0.8
0.6
0.4
3~9 mm
9~15 mm
15~21 mm
21~27 mm
1st depth
2nd
3rd
4th
0.2
0
-0.2
174
175
176
177
178
Day of year 2007
179
180
HP daily evaporation (mm)
Comparison of daily soil water evaporation (mm)
from heat pulse with micro-lysimeters and Bowen
ratio methods
4.0
Bowen ratio
Micro-lysimeters
3.2
2.4
y = 0.95 x + 0.07
1.6
R2 = 0.96
0.8
0.0
0.0
0.8
1.6
2.4
3.2
4.0
Micro-lysimeters daily evaporation (mm)
Latent Heat in Soil Heat
Flux Measurements
Better Energy Balance Closure
When 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 Methods
Soil heat flux (G) measured via heat-pulse sensors installed at
3 depths: 1, 3, and 6 cm
G = -(T/z)
side view
soil surface
1 cm
heat-pulse
sensor
3 cm
6 cm
cutaway view
Materials and Methods
Evaporation (LE) determined via microlysimeters (per 24 h)
Cumulative Soil Heat Flux at 1-cm Depth
Cum. Soil Heat Flux at 1-cm (MJ m-2)
40
gradient
from 3 cm gradient
from 6 cm gradient
35
30
25
20
15
10
5
0
151
153
155
157
Day of Year
159
161
‘G’ measured above the drying front isn’t really G
– its G + LE.
Accumulated Energy
Accumulated Energy Flux (MJ m -2)
25
LE
Difference, 1 and 3 cm G
Difference, 1 and 6 cm G
20
15
10
5
0
151
153
155
157
Day of Year
159
161
Conclusions
Shallow soil heat flux measurements may capture G + (soiloriginating) 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
Between-rows with roots
In-row
Between-rows without roots
Soil temperature at different locations
30
50
Temperature (˚C)
Bare
40
25
30
20
20
15
10
30
10
In rows
30
Between-rows with roots
25
25
20
20
15
15
10
10
240 242 244 246 248 250 252 254 256 258
Between-rows no roots
240 242 244 246 248 250 252 254 256 258
Day of year 2009
Soil water evaporation dynamics
0.3
0.3
In-row
Evaporation (mm)
Bare
0.2
0.2
0.1
0.1
0.0
0.0
-0.1
-0.1
0.3
0.3
0.2
Between-rows with roots
Between-row without roots
0.2
0.1
0.1
0.0
0.0
-0.1
-0.1
240 242 244 246 248 250 252 254 256 258
240 242 244 246 248 250 252 254 256 258
Day of year 2009
Cumulative Evaporation (mm)
Cumulative soil water evaporation at 3-mm soil depth
40
Bare
Between-rows
30
Between-rows no roots
In-row
20
10
0
240
242
244
246
248
250
252
Day of year 2009
254
256
258
Fu
E
Water storage
change S
Fd
E  Fd  Fu   S
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).
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.
References
Ren, T., G.J. Kluitenberg, and R. Horton. 2000. Determining soil water flux and
pore 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: 165171.
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).