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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!

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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

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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)

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EM Spectrum

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Base Electromagnetic equations Maxwell’s equations – Set of equations that relate the characteristics and propagation of magnetic and electrical fields

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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)

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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 = εσT 4, where ε = emissivity and σ = 5.67x10 -8 [W/m 2 K 4 ] Wien’s Displacement law: = 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

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Brightness Temperature Standard measurement for remote sensing signal More strictly correct is the spectral irradiance I(,T) obtained via Plank’s Law: (J·s -1 ·m -2 ·sr -1 ·Hz -1 ) But brightness temperature is easier: T b = εT where T b = brightness temperature (K), T = temperature of material (K), and ε = emissivity

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Simplify to Rayleigh-Jean law Bypass Plank’s law: estimate T b using the spectral brightness B (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

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Example of data collected

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Soil Thermal Properties Thermal conductivity : Heat transfer through a unit area of soil (J/s m K, or W/m K) Heat capacity c b : Change in unit volume’s heat content per unit change in temperature (J/m 3 K) Soil Thermal Inertia: From remote sensing: where G = variation in surface heat flux, T = T max – T min, and ω = 2 /86400s

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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

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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

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Left: Nighttime temperature over bare soil Right: Daytime temperature over bare soil Minacapilli and Blanda 2009

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(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

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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 ) Lu et al. (2009)

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Idso et al 1976

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Smits et al 2010

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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.

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