= Thermal filtering of daily and annual temperature oscillations
{title2=$\delta_Y/\delta_D=\sqrt{\omega_D/\omega_Y}$}
The <thermal penetration depth> of a harmonic <ground temperature> disturbance scales as the inverse square root of its <angular frequency>. For yearly and daily forcing, a 365-day year gives $\delta_Y/\delta_D=\sqrt{365}\simeq19.1$. At ten daily penetration depths the daily component is attenuated by $e^{-10}$, whereas the annual one retains about $59.2\%$ of its surface amplitude. At ten annual penetration depths, even the annual component is attenuated by $e^{-10}$. These are consequences of the linear <thermal diffusion wave> model, with homogeneous constant <thermal diffusivity>.
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