Remote Sensing and Soil Thermal Properties:

Eric Russell4/9/2010

Agron 577: Soil Physics

Conductivity, Heat Capacity, and Electromagnetics! OH MY!

Outline

• What is remote sensing?– Microwave remote sensing

• Very basic electromagnetics– Blackbody radiation, Wien’s law, Stefan-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.

• Satellites, MRI’s, IR thermometers, RADAR, 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 and Radiation• 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 = εσT4 , where ε = emissivity and σ = 5.67x10-8 [W/m2K4]

• 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

bmax

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: Tb = εTwhere Tb = brightness temperature (K), T = temperature of material (K), and ε = emissivity

1

2

3

12

,

kT

h

ec

hTI

Simplify to Rayleigh-Jean law• Bypass Plank’s law: estimate Tb using the

spectral brightness Bl(T) from the Rayleigh-Jean law:

where k = Boltzmann constant, c = speed of light, Tb = brightness

temperature, and λ= wavelength.• Then back out the brightness temperature

4

2

bckT

TB

Example of data collected

Soil Thermal Properties• Thermal conductivity k: Heat transfer through a

unit area of soil (J/s m K, or W/m K)

• Heat capacity crb: Change in unit volume’s heat content per unit change in temperature (J/m3 K)

• Soil Thermal Inertia: • From remote sensing:

where DG = variation in surface heat flux, DT = Tmax – Tmin, and ω = 2p/86400s

T

GP

2

bsatsatcP

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

Figure Blitzkrieg!!!!

Left: Nighttime temperature over bare soilRight: 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 Ts ≡ 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 θRight: Normalized soil thermal inertia Kp 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. Amsterdam: Elsevier Academic, 2004. • 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." Vadose 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.

Questions? Comments?