5.3: What are the requirements for forming a cloud drop?

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There are three requirements for forming a cloud drop:

Moisture
Aerosol
Cooling

If any one of these three is missing, a cloud cannot form. We have talked about moisture and aerosol and now need to consider ways that the air can be cooled. The air needs to be cooled so that the water vapor pressure initially equals and then exceeds the water saturation vapor pressure.

An easy way to remember these key ingredients is to think of a Big MAC.

屏幕快照 2019-08-14 13.24.24.png — A Big **MAC**. Hungry for some more? Credit: Cleaveland via flickr

Saturation occurs when e=e_s, w=w_s, and condensation = evaporation. At saturation, RH = e/e_s ~ w/w_s = 1, or in terms of percent, 100%. When we find the lifting condensation level (LCL) on a skew-T, we are finding the pressure level at which T (as determined from the dry adiabat) = T_d (as determined from the constant water vapor mixing ratio), or when w = w_s.

Let’s define two new variables that are useful in discussing the cloud drop formation.

Often we talk about the saturation ratio:

\[s= \dfrac{e}{e_{s}}\]

where e is the water vapor pressure and e_s is the saturation vapor pressure. S < 1 for a subsaturated environment, S = 1 for saturation (condensation = evaporation), and S > 1 for a supersaturated environment.

We also talk about supersaturation:

\[s=S-1=\dfrac{e}{e_{s}}-1\]

s = 0 at saturation; s < 0 for a subsaturated environment; s > 0 for a supersaturated environment. Note that s and S are both unitless.

This equation applies only for a flat surface of pure water. When we get into situations where we have curvature or a solute, we need to think about the supersaturation relative to the equilibrium value of e, e_eq, which can be different from e_s. So, depending on the circumstances, e_eq can be e_s (flat liquid water), e_i (flat ice), e_sc(curved liquid water), e_sol (curved solution), or some combination. We will see that a small supersaturation is actually needed to form clouds.

Exercise

The relative humidity is 85%. What is the saturation ratio? What is the supersaturation?

Answer

S = 0.85 and s = 0.85 - 1 = -0.15

The relative humidity is 102%. What is the saturation ratio? What is the supersaturation?

Exercise

The relative humidity is 102%. What is the saturation ratio? What is the supersaturation?

Answer: S = 1.02 and s = 0.02

Note that it is possible to have the relative humidity be greater than 100%, which makes the supersaturation positive. This condition can't last long because condensation will exceed evaporation until they become equal. But how can supersaturation happen?