Solution (source code)

= Solution

At the surface both attenuation factors are one and both lags vanish:
$$
\boxed{\Theta(0,t)=\Theta_0+A\cos(\omega_Yt)+B\cos(\omega_Dt).}
$$
The sketch is a rapid daily oscillation on a slowly varying annual background. The <amplitudes> cannot be inferred uniquely from the sampling intervals alone.