# 6.6: Cloud Sizes

Cumuliform clouds typically have diameters roughly equal to their depths, as mentioned previously. For example, a fair weather cumulus cloud typically averages about 1 km in size, while a thunderstorm might be 10 km.

Not all clouds are created equal. At any given time the sky contains a spectrum of cloud sizes that has a lognormal distribution (Figure 6.10, eq. 6.6)

\ \begin{align} f(X)=\frac{\Delta X}{\sqrt{2 \pi} \cdot X \cdot S_{X}} \cdot \exp \left[-0.5 \cdot\left(\frac{\ln \left(X / L_{X}\right)}{S_{X}}\right)^{2}\right]\end{align} \label{6.6}

where $$X$$ is the cloud diameter or depth, $$∆X$$ is a small range of cloud sizes, $$f(X)$$ is the fraction of clouds of sizes between $$X–0.5∆X$$ and $$X+0.5∆X$$, $$L_x$$ is a location parameter, and $$S_x$$ is a dimensionless spread parameter. These parameters vary widely in time and location.

According to this distribution, there are many clouds of nearly the same size, but there also are a few clouds of much larger size. This causes a skewed distribution with a long tail to the right (Figure 6.10).

Sample Application

Use a spreadsheet to find and plot the fraction of clouds ranging from X = 50 to 4950 m width, given ∆X = 100 m, SX =0.5, and LX = 1000 m.