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LaTeX Math Inline
bodyt

Local Calendar Time

LaTeX Math Inline
body\delta T_A

Annual average surface temperature variation based on weather reports

LaTeX Math Inline
bodyz(l)

LaTeX Math Inline
bodyA_T

Period of annual temperature variation cycle:

LaTeX Math Inline
body--uriencoded--A_T = 1 \, %7B\rm year%7D

LaTeX Math Inline
bodyj_z

True vertical component of regional Earth's Heat Flux

LaTeX Math Inline
body\delta t_A

Time shift of annual highest temperature with respect to January 1

LaTeX Math Inline
bodyT_s

Local annual average surface temperature based on weather reports

LaTeX Math Inline
body\delta T_D

Daily average surface temperature variation based on weather reports

LaTeX Math Inline
body--uriencoded--a_e%7Ben%7D

Local average Thermal diffusivity of the soil between Earth's surface and NTL

LaTeX Math Inline
bodyD_T

Period of daily temperature variation cycle:

LaTeX Math Inline
body--uriencoded--A_D = 1 \, %7B\rm day%7D


LaTeX Math Inline
body\lambda_re(z)
Subsurface Thermal Conductivity profile as function of TVDss

LaTeX Math Inline
body\delta t_D

Time shift of daily highest temperature with respect to Midnight 00:00



LaTeX Math Inline
body--uriencoded--\delta T_%7B\rm cut%7D

Temperature measurement threshold (usually

LaTeX Math Inline
body--uriencoded--\delta T_%7B\rm cut%7D = 0.01 \, %7B\rm °C%7D

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LaTeX Math Block
anchorT_z
alignmentleft
T(t, z) = T_s + \int_{z_s}^z G_T(z) dz + T_Y(t, z) + T_D(t, z)




LaTeX Math Block
anchorG_T
alignmentleft
G_T(z) = \frac{j_z}{\lambda_r(z)}



LaTeX Math Block
anchorT_z
alignmentleft
T_Y(t,z) = \delta T_A \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e{en} \, A_T}} \, \right] \, \cos \left[  \, 2 \pi \frac{t - \delta t_A}{A_T} + (z_s -z) \sqrt {\frac{\pi}{a_e{en} \, A_T}} \, \right]



LaTeX Math Block
anchorT_z
alignmentleft
T_D(t,z) = \delta T_D \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e{en} \, D_T}} \, \right] \, \cos \left[  \, 2 \pi \frac{t - \delta t_D}{D_T} + (z_s -z) \sqrt {\frac{\pi}{a_e{en} \, D_T}} \, \right]


Neutral Layer


LaTeX Math Block
anchorz_N
alignmentleft
z_n = z_s + H_n



LaTeX Math Block
anchorH_N
alignmentleft
H_n = \sqrt{\frac{a_e{en} \, A_T }{\pi}} \, \ln \frac{\delta T_A }{\delta T_{\rm cut} }


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