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LaTeX Math Inline
body--uriencoded--%7B \bf j%7D(x,y,z) = \%7B 0, \, 0 , \, j_z = %7B\rm const%7D \%7D

LaTeX Math Inline
body\lambda_r(x,y,z) = \lambda_r(z)


Equations

}{delta T_{\rm cut} }Dright]
Neutral Layer


LaTeX Math Block
anchorT_z_N
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T(t, z) = T_ns =+ \int_{z_s}^z G_T(z) dz + H_nT_Y(t, z) + T_D(t, z)



LaTeX Math Block
anchorHG_NT
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H_nG_T(z) = \sqrt{\frac{a_e \, A_T }{\pi}} \, \ln \frac{d T_g}{d z}= \frac{j_z}{\lambda_r}


LaTeX Math Block
anchorT_z
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T_Y(t,z) = \delta T_A 
\
Below Neutral Temperature LayerAbove Neutral Temperature Layer

LaTeX Math Inline
bodyz > z_n

LaTeX Math Inline
bodyz < z_n

LaTeX Math Block
anchorT_g
alignmentleft
T_G(l) = T_s + \int_{z_s}^z G_T(z) dz
LaTeX Math Block
anchorT_z
alignmentleft
T(t, z) = T_0 + \frac{j_z}{\lambda_r(z)} (z-z_s) + T_Y(t, z) + T_D(t, z)
LaTeX Math Block
anchorG_T
alignmentleft
G_T(z) =\frac{d T_g}{d z}= \frac{j_z}{\lambda_r}
LaTeX Math Block
anchorT_z
alignmentleft
T_Y(t,z) = \delta T_A \, \exp \left[ \, {(z_s-z}) \sqrt, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e \, A_T}} \, \right] \, \cos \left[  \, 2 \pi \frac{t - \delta t_A}{A_T} + (z_s -z) \sqrt {\frac{\pi}{a_e \, A_T}} \, \right] \, \cos \left[  \,



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


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 \, 
A_T }{\pi}} \, \
ln \frac{\delta T_A }{\delta T_{\rm cut} }


where

LaTeX Math Inline
bodyz_s = z(l=0)

TVDss of the Earth's surface in a given location. In case the Earth's surface is at sea level then 

LaTeX Math Inline
bodyz_s = 0

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