NWP | Microphysics | Convert moisture variables q's into rainfall

Atmospheric models convert moisture variables (\(q_v, q_c, q_r, q_i, q_s, q_g\)) into rainfall and precipitation through microphysics parameterizations that simulate microphysical phase changes and droplet growth mechanics.

The Microphysical Variables Explained

• \(q_v\) (Water Vapor Mixing Ratio): Gas-phase water molecules suspended in the air.
• \(q_c\) (Cloud Water Mixing Ratio): Liquid droplets so small (<20 μm) they have negligible fall velocity.
• \(q_r\) (Rain Water Mixing Ratio): Large liquid drops (>100 μm) heavy enough to fall to the surface.
• \(q_i\) (Cloud Ice), \(q_s\) (Snow), \(q_g\) (Graupel): Solid-phase microphysical species (frozen precipitation).

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The Conversion Pathway to Surface Precipitation

The conversion of vapor to surface rainfall follows a distinct chain of physical processes.

  [ qv: Water Vapor ]
          │
          ▼ (Condensation / Deposition)
  [ qc: Cloud Water ] ──(Freezing)──> [ qi / qs / qg: Ice/Snow/Graupel ]
          │                                      │
          ▼ (Autoconversion / Accretion)         ▼ (Melting)
  [ qr: Rain Water ] <───────────────────────────┘
          │
          ▼ (Sedimentation / Fall out)
[ Surface Precipitation ]

1. Condensation (\(q_v \rightarrow q_c\))

When air becomes supersaturated (RH > 100%), excess water vapor (\(q_v\)) condenses onto cloud condensation nuclei (CCN) to form cloud liquid water (\(q_c\)). If temperatures are below freezing (T < 0°C), \(q_v\) transforms directly into cloud ice (\(q_i\)) via vapor deposition.

2. Autoconversion (\(q_c \rightarrow q_r\))

Cloud droplets (\(q_c\)) are too small to fall. As they collide and merge (coalescence), they grow in size. Once they cross a critical size threshold (typically around 20 μm in radius), they are mathematically reclassified from cloud water (\(q_c\)) to rainwater (\(q_r\)).

3. Accretion (\(q_c + q_r \rightarrow q_r\))

Once rainwater (\(q_r\)) drops exist, they fall much faster than small cloud droplets (\(q_c\)). As a raindrop falls through a cloud layer, it sweeps up and absorbs the smaller cloud droplets in its path, rapidly increasing the rainwater volume (\(q_r\)).

4. The Cold-Rain Pathway (\(q_i \rightarrow q_s \rightarrow q_g \rightarrow q_r\))

In many mid-latitude and convective clouds, rain starts as ice:

• Vapor deposits onto cloud ice (\(q_i\)), growing it into snow (\(q_s\)).
• Snow collects supercooled cloud water, freezing it instantly to form dense graupel (\(q_g\)).
• As \(q_s\) and \(q_g\) fall below the freezing level (T > 0°C), they melt into liquid rainwater (\(q_r\)).

5. Sedimentation and Evaporation (\(q_r \rightarrow \text{Rainfall}\))

Rainwater drops fall toward the ground due to gravity, a process called sedimentation. As they fall through sub-saturated air layers beneath the cloud base, a portion of the rainwater evaporates back into vapor (\(q_r \rightarrow q_v\)). The remaining rainwater mass that successfully strikes the ground is measured as surface precipitation.