Chapter 8 - Soil Temperature - LAWR

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SSC 107, Fall 2001 – Chapter 8 Page 8-14 2K T 1 ⎡z ω = ω ⎢ ⎣ t 2 2 - z - t 1 ⎤ ⎥ ⎦ 1 2 K 1 ⎡ z2 - z = 2 ⎢ ω ⎣ t 2 - t T 1 ω 1 2 ⎤ ⎥ ⎦ K T 1 = 2 ⎡z ⎢ ⎣ t - z 2 1 ω 2 - t1 Thus, K T can be determined by measuring the time at which the maximum temperature is observed at two depths. K T is the diffusivity of the soil between two depths. 2 ⎤ ⎥ ⎦
SSC 107, Fall 2001 – Chapter 8 Page 8-15 Simultaneous Transport of Water and Heat • Temperature gradients affect soil-water potential which induces both liquid and vapor movement. • Soil-water potential gradients move water, which consequently carries heat. • Combined transport generally ignored in very wet systems and in very dry systems. Temp. gradient effect on water flow small in relation to soil-water potential grad. in wet range. Little water is moved in very dry range. • Two approaches • Mechanistic • Irreversible thermodynamics Mechanistic For water ∂ θ ∂t v ∂ ⎛ = ⎜ D ∂z ⎝ T ∂T ⎞ ∂ ⎛ ⎟ + ⎜D ∂z ⎠ ∂z ⎝ w ∂ θv ⎞ ∂K ⎟ - ∂z ⎠ ∂z For heat ∂T ∂ ⎛ C = ⎜λ ∂t ∂z ⎝ e ∂T ⎞ ∂ ⎛ ⎟ - L ⎜D ∂z ⎠ ∂z ⎝ w, v ∂θ ⎞ ⎟ ∂z ⎠ D T - water diffusivity under temperature gradient D w - water diffusivity under water potential gradient L - Latent heat of vaporization D w,v - Diffusivity for heat conveyed by water movement Problems with mechanistic approach - Difficult to measure or calculate diffusivities - Two flow mechanisms are not strictly additive since they interact
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Chapter 8 - Soil Temperature - LAWR

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