Dispersion parameters for Pasquill–Gifford stability class G (extremely stable) Gaussian plume models are often used to model atmospheric dispersion because they are simple and computationally efficient. When not constrained by the ground or by inversion layers, the Gaussian plume equation has the following form:
$$\chi=\frac1{2\cdot\pi\cdot\sigma_y(x)\cdot\sigma_z(x)\cdot u}\cdot\exp\left(-\frac{y^2}{2\cdot\sigma_y^2(x)}\right)\cdot\exp\left(-\frac{\left(z-h\right)^2}{2\cdot\sigma_z^2(x)}\right)$$
where $u$ is the mean wind speed and $h$ is the release height.
The dispersion parameters $\sigma_y$ and $\sigma_z$ correspond to the standard deviations of the normal crosswind and vertical concentration distributions. Their values depend on downwind distance $x$, release height, surface roughness, and especially on atmospheric stability class. They are usually calculated using power-law functions:
$$\sigma_y(x)=p_y\cdot x^{q_y}$$
$$\sigma_z(x)=p_z\cdot x^{q_z}$$
There are numerous parameterizations available in the literature for the Pasquill–Gifford stability classes A through F. However, I cannot find any parameter values for stability class G (extremely stable).
Where can I find a reference for dispersion parameters that include stability class G?
Or is there a principal reason why stability class G is not included in the literature?
 A: The original publications did not even have any class G. It was introduced later, as noted by M. Mohan, T.A. Siddiqui (1998) https://doi.org/10.1016/S1352-2310(98)00109-5 However, it is much older, e.g., Hanna (1983) https://doi.org/10.1175/1520-0450(1983)022%3C1424:LTIAPM%3E2.0.CO;2
Stability class G is extremely difficult to parametrize and use for prediction. It basically includes any stability up to those that almost laminarize even close to the surface. The Richardson number is very high. The above paper says Ri >= 0.18. The boundary layer height can be extremely small.
Vertical turbulence is very strongly suppressed. On the other hand, the plumes meander strongly in the horizontal direction. Even so that it might be hard to even define Gaussian dispersion because the meandering is governed by larger scale or even mesoscale phenomena (small temperature differences, drainage flows).
Hanna (1983) does not even list $\sigma_\theta$ for class G. However, he does list the correction factor for meandering for $\sigma_y$ from NRC Regulatory Guide 1.145 but also shows other approaches that are not class-based but most often work with the actual wind speed.
This regulatory guides state that for no meandering one can use $\sigma_y(G) = \frac{2}{3}\sigma_y(F)$. For $\sigma_z$ it proposes $\sigma_z(G) = \frac{3}{5} \sigma_y(G)$. With meandering one has $\Sigma_y = M \sigma_y$ for $x$ < 800 m and $\Sigma_y = (M-1) \sigma_{y,800\mathrm{m}} + \sigma_y$ for $x$ >= 800 m.
