@wikipedia
Motivation
Outputs
Inputs
| Local Calendar Time | | Annual average surface temperature variation based on weather reports |
| | | Period of annual temperature variation cycle: | LaTeX Math Inline |
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| body | --uriencoded--A_T = 1 \, %7B\rm year%7D |
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| True vertical component of regional Earth's Heat Flux | | Time shift of annual highest temperature with respect to January 1 |
| Local annual average surface temperature based on weather reports | | Daily average surface temperature variation based on weather reports |
| LaTeX Math Inline |
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| body | --uriencoded--a_%7Ben%7D |
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| Local average Thermal diffusivity of the soil between Earth's surface and NTL | | Period of daily temperature variation cycle: | LaTeX Math Inline |
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| body | --uriencoded--A_D = 1 \, %7B\rm day%7D |
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| Subsurface Thermal Conductivity profile as function of TVDss | | Time shift of daily highest temperature with respect to Midnight 00:00 |
|
| | LaTeX Math Inline |
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| body | --uriencoded--\delta T_%7B\rm cut%7D |
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| Temperature measurement threshold (usually | LaTeX Math Inline |
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| body | --uriencoded--\delta T_%7B\rm cut%7D = 0.01 \, %7B\rm °C%7D |
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) |
where
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| TVDss of the Earth's surface in a given location. In case the Earth's surface is at sea level then |
Assumptions
Equations
| LaTeX Math Block |
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| T_G(t, {\bf r}) = T_{GS}({\bf r}) + T_Y(t, z) + T_D(t, z) |
| | LaTeX Math Block |
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| G_T(z) = \frac{j_z}{\lambda_r(z)} |
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| LaTeX Math Block |
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| \nabla T_{GS} = \lambda^{-1}({\bf r}) \cdot {\bf j} |
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| LaTeX Math Block |
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| T_{GS}(x, y, z = z_s) = T_s |
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| LaTeX Math Block |
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| T_Y(t,z) = \delta T_A \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_{en} \, A_T}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_A}{A_T} + (z_s -z) \sqrt {\frac{\pi}{a_{en} \, A_T}} \, \right] |
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| LaTeX Math Block |
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| T_D(t,z) = \delta T_D \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_{en} \, D_T}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_D}{D_T} + (z_s -z) \sqrt {\frac{\pi}{a_{en} \, D_T}} \, \right] |
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| Neutral Layer |
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| LaTeX Math Block |
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| z_n = z_s + H_n |
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| LaTeX Math Block |
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| H_n = \sqrt{\frac{a_{en} \, A_T }{\pi}} \, \ln \frac{\delta T_A }{\delta T_{\rm cut} } |
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See Also
...
Geology / Geothermal Temperature Field
...
