This plugin implements the linear model of orographic precipitation described in Smith and Barstad, "A linear theory of orographic precipitation", Journal of the Atmospheric Sciences 61, no. 12 (2004): 1377-1391.

The model consists of two steady-state advection equations, one for the vertically-integrated cloud water density (\(q_c\)) and one for the vertically-integrated hydrometeordensity (\(q_h\)).

Transforming into Fourier space, one gets the following equation relating the Fourier transform of the terrain \(\hat h\) to the transform of the precipitation field \(\hat P\).

\begin{equation*} \hat P(k, l) = \frac{C_w i \sigma \hat h(k, l)}{(1 - im H_w)(1 + i \sigma \tau_f)(1 + i \sigma\tau_c)}. \end{equation*}

Here the first factor in the denominator describes airflow dynamics, the second and third factors describe cloud delays and advection, and

\begin{equation*} m = \left[ \left( \frac{N_m^{2} - \sigma^2}{\sigma^2} \right) (k^2 + l^2) \right]^{1/2}. \end{equation*}

Notation
Symbol	Units	Description
\(P\)	mm / hour	Precipitation
\(C_w\)	kg / m³	Uplift sensitivity factor
\(h\)	m	Terrain elevation
\(H_w\)	m	Vapor scale height
\(N_m\)	1 / s	Moist stability frequency
\(\tau_f\)	s	Fallout time
\(\tau_c\)	s	Cloud conversion time
\(\sigma\)		intrinsic frequency