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Remote Sensing and Soil Thermal Properties:. Conductivity, Heat Capacity, and Electromagnetics! OH MY!. Eric Russell 4/9/2010 Agron 577: Soil Physics. Outline. What is remote sensing? Microwave remote sensing Very basic electromagnetics

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remote sensing and soil thermal properties

Remote Sensing and Soil Thermal Properties:

Conductivity, Heat Capacity, and Electromagnetics! OH MY!

Eric Russell


Agron 577: Soil Physics

  • 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
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)
base electromagnetic equations
Base Electromagnetic equations
  • Maxwell’s equations
    • Set of equations that relate the characteristics and propagation of magnetic and electrical fields
  • 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 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
brightness temperature
Brightness Temperature
  • Standard measurement for remote sensing signal
  • More strictly correct is the spectral irradiance I(l,T) obtained via Plank’s Law:


  • But brightness temperature is easier: Tb = εT

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

simplify to rayleigh jean law
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
soil thermal properties
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

thermal inertia and soil moisture
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
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 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 θ

Right: Normalized soil thermal inertia Kp as a function of degree of saturation (normalized q)

Lu et al. (2009)

  • 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.