# Remote Sensing and Soil Thermal Properties:

Urban and Civil

Nov 16, 2013 (4 years and 7 months ago)

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Remote Sensing and Soil Thermal
Properties:

Eric Russell

4/9/2010

Agron

577: Soil Physics

Conductivity, Heat Capacity, and
Electromagnetics! OH MY!

Outline

What is remote sensing?

Microwave remote sensing

Very basic electromagnetics

-
Boltzmann
law, brightness temperature

Soil thermal properties

Combining the previous two (the OH MY! part)

Figures

What is remote sensing?

Taking measurements from a place when not
being in physical contact of that place.

LiDAR, camera

For this presentation: microwaves

Utilizes the electromagnetic spectrum (EM)

EM Spectrum

Base Electromagnetic equations

Maxwell’s equations

Set of equations that relate the characteristics and
propagation of magnetic and electrical fields

Blackbodies

Theoretical concept

Perfect absorber and emitter

Objects can exhibit blackbody
-
like
characteristics at certain temperatures

Preferentially emits at specific
wavelength/frequency

Can use as an approximation (usually pretty
good)

Temperature is defined as the average kinetic energy of
molecules in a substance

Anything that has a temperature radiates via the Stefan
-
Boltzmann law:

J =
εσ
T
4

, where
ε

= emissivity and
σ

= 5.67x10
-
8

[W/m
2
K
4
]

Wien’s Displacement law:

l
= wavelength, b = 2.8977685(51)
×
10
−3

m∙K

a

(absorbtivity) +
r

(reflectivity) +
t

(transmissivity)
= 1

Kirchoff’s Law: at thermal equilibrium, emissivity (
ε
) =
a

Higher the temperature, greater the radiation emitted

T
b

max
l
Brightness Temperature

Standard measurement for remote sensing
signal

More strictly correct is the spectral irradiance
I
(
l
,T
) obtained via Plank’s Law:

(J∙s
-
1
∙m
-
2
∙sr
-
1
∙Hz
-
1
)

But brightness temperature is easier:

T
b

=
ε
T

where
T
b

= brightness temperature (K),
T

=
temperature of material (K), and
ε

= emissivity

1
2
3
1
2
,

kT
h
e
c
h
T
I
l
l
l
Simplify to Rayleigh
-
Jean law

Bypass Plank’s law: estimate
T
b

using the
spectral brightness
B
l
(
T
)

from the Rayleigh
-
Jean law:

where
k

= Boltzmann constant,

c

= speed of light,
T
b

= brightness

temperature, and
λ
= wavelength.

Then back out the brightness temperature

4
2
l
l
b
ckT
T
B

Example of data collected

Soil Thermal Properties

Thermal conductivity
k
㨠䡥H琠tr慮af敲⁴桲潵杨o愠

Heat capacity
c
r
b
: Change in unit volume’s heat
content per unit change in temperature (J/m
3

K)

Soil Thermal Inertia:

From remote sensing:

where
D
G

= variation in surface heat flux,

D
T

= T
max

T
min
, and
ω

= 2
p
/86400s

T
G
P
D
D

2
b
sat
sat
c
P
r
k

Thermal Inertia and Soil Moisture

As discussed, thermal properties depend upon
many factors

Focus on soil moisture (because it’s awesome…
and where my research lies)

Can create relationships between
θ

and
thermal inertia (can’t separate the individual
properties through remote sensing)

We are now done with big scary equations
and models

Even more on this…

Can’t separate conductivity from capacity from just
remote sensing

Properties depend on too many variables

Can estimate thermal inertia
P

using model shown

Can estimate parameters in thermal inertia if know soil
type/texture/moisture content, etc.

Due to variable needs in approximation, need more
than one measurement

Can model heat flux through energy balance

Diurnal temperature changes are easy to get

Left: Nighttime temperature over bare soil

Right: Daytime temperature over bare soil

Minacapilli and Blanda 2009

(a)

Ground heat flux G ≡ Q(0, t) (W m
−2
), and
(b)

surface (skin)
temperature T
s

≡ T(0, t) (
°
C) measured at the Lucky Hill site in the
Walnut Gulch Watershed, 5

16 June 2008.

Wang et al 2010

Left:

Soil thermal inertia
P

as a function of
θ

Right:

Normalized soil thermal inertia
K
p

as a function of
degree of saturation (normalized
q
)

Lu et al. (2009)

Idso et al 1976

Idso et al1976

Smits et al 2010

References

Bachmann, J., R.
Horton
, T. Ren, and R R Van Der Ploeg. "Comparison of the Thermal Properties of
Four Wettable and Four Water
-
repellent Soils."
Soil Sci. Soc. Am. J.

65 (2001): 1675
-
679.

Campbell
, Gaylon S., and John M.
Norman
.
Introduction to Environmental Biophysics
. 2nd ed. New
York: Springer, 1998.

Hillel
, Daniel.
Introduction to Environmental Soil Physics

Idso, Sherwood B., Ray D. Jackson, and Robert J. Reginato. "Compensating for Environmental
Variability in the Thermal Inertia Approach to Remote Sensing of Soil Moisture."
Journal of
Applied Meteorology

15 (1976): 811
-
17.

Lu, Sen, Zhaoqiang Ju, Tusheng Ren, and Robert
Horton
. "A General Approach to Estimate Soil
Water Content from Thermal Inertia."
Agricultural and Forest Meteorology

149 (2009): 1693
-
698.

Lu, Xinrui, Tusheng Ren, and Yuanshi Gong. "Experimental Inverstigation of Thermal Dispersion in
Saturated Soils with One
-
Dimensional Water Flow."
Soil Sci. Soc. Am. J.

73 (2009): 1912
-
920.

Minacapilli, M., M. Iovino, and F. Blanda. "High Resolution Remote Estimation of Soil Surface
Water Content by a Thermal Inertia Approach."
Journal of Hydrology

379 (2009): 229
-
38.

Smits, Kathleen M., Toshihiro Sakaki, Anuchit Limsuwat, and Tissa H. Illangasekare. "Thermal
Conductivity of Sands under Varying Moisture and Porosity in Drainage
-
Wetting Cycles."
Zone J.

9 (2010): 1
-
9.

Wang, J., R. L. Bras, G. Sivandran, and R. G. Knox. "A Simple Method for the Estimation of Thermal
Inertia."
Geophysical Research Letters

37 (2010): L05404.