Cloud Parcel Modelling - Part 5: Cloud Droplet Size Distribution Evolution and Precipitation Onset
Droplet Size Distribution Evolution
In earlier parts, we've treated cloud droplets as individual particles growing by condensation. While this is useful for understanding the physics of a single droplet, cloud microphysics at scale requires us to treat droplets as a population — a size distribution — which evolves dynamically during the cloud lifetime.
🔄 Why Track a Size Distribution?
- Real clouds contain billions of droplets of different sizes
- Vapor competition causes size divergence
- Collision–coalescence and evaporation affect size shape
- Radiative and optical properties depend on DSD shape
📈 Initial Shape After Activation
After CCN activate (typically at supersaturation ~0.1–1%), the initial droplet size distribution (DSD) is narrow and centered near the critical radius (~0.1–0.2 μm). Its shape depends on the CCN size spectrum and can often be approximated as lognormal.
⏳ During Condensational Growth
Condensational growth is faster for smaller droplets initially (because of higher supersaturation excess), but as vapor is consumed, growth slows and the DSD broadens. The shape may transition to a gamma distribution:
n(r) = N₀ · rα · exp(−βr)
where:
n(r): number of droplets per radius binα: shape parameterβ: width parameter
📊 What Happens to DSD?
Condensational growth: modest broadening
Collision–Coalescence: large tail growth
Evaporation (entrainment): narrows or skews toward smaller droplets
🌧️ Precipitation-Scale Growth
Once some droplets grow beyond ~20 μm, collision–coalescence dominates. This process rapidly broadens the DSD and generates a tail extending into raindrop sizes (>100 μm). Eventually, a bimodal distribution may emerge: cloud droplets + raindrops.
🧠 Microphysics Process Summary
| Process | Effect on DSD | Scale |
|---|---|---|
| Activation | Narrow lognormal | Microscale |
| Condensation | Slight broadening, skewed | Micro |
| Collision–Coalescence | Rapid broadening, bimodal | Meso |
| Evaporation | Removal of smallest droplets | Micro |
| Giant CCN | Large tail from beginning | Micro–Meso |
📌 When to Use Droplet vs Distribution Approach
- Single Droplet: Ideal for theory, Köhler curve, κ derivation
- Distribution: Required for energy, radiation, precipitation, and cloud optical properties
- Cloud parcel models: Often use bins or moments to simulate DSD evolution
🔍 Summary
- Cloud droplet size distribution starts narrow, becomes broader
- Collisions lead to precipitation and bimodal shapes
- Evaporation, entrainment, or turbulence can reshape the DSD
- Tracking DSD is essential to connect microphysics with cloud radiative and rainfall properties
Collision–Coalescence & Precipitation Onset 💧➡️☔
Status: 🚫 Not yet implemented in this model
This part is not simulated in cloud parcel model, but this is the mechanism that turns cloud into rain.
This process becomes critical once cloud droplets grow large enough to begin colliding and merging (coalescing), leading to precipitation.
Condensational growth alone is too slow to produce raindrops. To model rain formation realistically, cloud parcel models must include this collision–coalescence mechanism.
Key Concepts
- Collision Kernel: Describes the rate of collisions between droplets of different sizes.
- Onset Threshold: Coalescence becomes efficient when droplet radius exceeds ~20 µm.
- Enhancing Factors:
- High number concentration (more frequent encounters)
- Turbulence (increases relative motion and collision rate)
- Droplet size variability (differential fall speeds)
📌 Without this process, the model can simulate cloud formation but not rainfall production.
Future versions of the parcel model may include stochastic collection equations or Monte Carlo methods to approximate this process.
✅ So, is it Correct to Say "Collision–Coalescence Happens in Clouds but Not Simulated in Cloud Parcel Modeling"?
Yes — that’s accurate and commonly stated in cloud microphysics literature.
✅ Collision–Coalescence:
- Physically occurs in real clouds.
- It's the dominant process responsible for the formation of drizzle and rain, especially in warm (non-ice) clouds.
🚫 Cloud Parcel Models (Basic Ones):
- Typically do not simulate collision–coalescence directly.
- Focus mainly on:
- Condensational growth (vapor condensing onto droplets)
- Activation of droplets based on supersaturation
- Assume a Lagrangian air parcel with no mixing, falling raindrops, or collection processes.
🧪 Why It’s Omitted:
- Collision–coalescence is a stochastic, nonlinear process involving complex interactions between droplets of varying sizes.
- Requires solving the stochastic collection equation, or using Monte Carlo particle tracking — which adds a lot of complexity.
- So, basic parcel models stop at droplet growth by condensation and may indicate a precipitation onset threshold (like r > 20 µm) but don’t simulate it further.
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