Cloud Parcel Model – Part 0: Introduction and Context (B)

 

🌫️ How Cloud Parcel Models Simulate Height Without z(t) — And Why Precipitation Needs More Than One Parcel

Cloud parcel models are powerful tools in atmospheric science. They help us understand how supersaturation evolves, how droplets activate, and how latent heat feeds back into rising air. But there’s something subtle and important: most parcel models don’t explicitly simulate height (z) — and yet they simulate altitude-dependent processes quite well.

So how does this work? And how far can a single parcel model take us?

---

🔹 Vertical Motion: Implicit, Not Explicit

In the code you’re working with, the parcel’s vertical position z(t) is not integrated as a separate ODE. Instead, the model uses a fixed updraft speed w (e.g. 0.5 m/s), and time becomes a proxy for height:

$$\frac{dz}{dt} = w \quad \Rightarrow \quad z(t) = w \cdot t$$

So after 1800 seconds (30 minutes):

$$z = 0.5 \times 1800 = 900\ \text{meters}$$

This is never explicitly solved in the script, but it underlies the system. All changes in temperature, supersaturation, and droplet radius evolve as if the parcel is rising through the atmosphere.

💡 All changes in supersaturation (S), droplet radius (r), and temperature (T) over time are due to the parcel ascending into cooler, lower-pressure air and undergoing condensation and latent heating.

---

🎈 Are All Particles Always Brought to Higher Altitudes?

Yes — in this type of 1-parcel model:

• All initial aerosol particles are entrained in the parcel.

• They are exposed to the same thermodynamic path.

• Their growth depends only on their size/κ and the evolving supersaturation S(t).

The model assumes:

✔️ No gravitational settling,
✔️ No mixing or dispersion,
✔️ No vertical variability within the parcel.

So to answer the question:

"Are all of the bulk initial particles always brought up to higher distance?"
✅ Yes — all of them rise together with the parcel.

---

☁️ What Is a Parcel vs. a Cloud?

Let’s clarify terminology:

Concept	Description
Parcel	A small, idealized volume of air that rises with its own identity. No internal gradients. No mixing.
Cloud	A large, turbulent system of many such parcels, with variability in motion, thermodynamics, and droplet properties.

🧪 In your parcel model:

• One rising parcel

• One initial aerosol distribution

• One vertical trajectory (z = w·t)

• One temperature and vapor path

🌩️ In a real cloud:

• Many interacting parcels

• Different updrafts

• Variable humidity and aerosol content

• Turbulence, entrainment, and mixing

• Complex droplet and ice dynamics

❌ A cloud is not a single parcel
✅ A cloud is a volume composed of many parcels interacting over time and space

---

🌧️ Is One Parcel Enough to Form Precipitation?

No — a single parcel can show droplet formation, but not precipitation.

Here’s why:

🧊 1. Warm Rain (Collision–Coalescence)

Droplets must collide and merge to form raindrops. But this requires:

• Turbulent motion

• Broad size spectrum

• Asymmetric growth conditions

Single parcel models do not include turbulence or collisions.

❄️ 2. Ice Processes (Cold Rain / Snow)

Involve:

• Ice nucleation

• Riming

• Aggregation

• Bergeron–Findeisen processes

Again, these rely on spatial gradients and interaction across multiple parcels.

---

🔬 Models That Simulate Precipitation

Model Type	Captures Precipitation?	Features
Parcel Model	❌ No	Single trajectory, no mixing or collisions
Multi-parcel (Ensemble)	⛅ Some	Statistical spread of parcels
Bulk Microphysics (1D/3D)	✅ Yes	Mass budget in grid cells
Bin Microphysics (SBM)	✅✅ Yes	Resolves size spectra, collisions
Large Eddy Simulation (LES)	✅✅✅ Yes	3D turbulence + microphysics
Cloud-Resolving Model (CRM)	✅✅✅ Yes	Regional-scale cloud evolution

---

🔍 If You Want More Complexity...

To go beyond the limits of a basic parcel model:

Feature	What It Adds
Multiple parcel layers	Simulate vertical stratification
Turbulent entrainment	Add mixing with ambient air
Differential activation	Track particles with different κ or sizes
Gravitational settling	Allow droplets to fall through parcel layers

But, in a study that investigate black carbon (BC) heating effects on droplet activation, for example — the single-parcel framework is both physically consistent and insightful.

---

📌 Summary

Question	Answer
Does the model simulate z(t)?	Implicitly, via z = w·t
Are all particles lifted?	Yes — the whole aerosol population rises
Is one parcel a full cloud?	No — clouds consist of many interacting parcels
Can a parcel model form precipitation?	No — it lacks collisions, mixing, and variability
What models simulate rain?	LES, CRM, bin microphysics

---

🧠 Final Thoughts

Parcel models are like controlled experiments inside a rising balloon. They’re great for testing:

• Activation theory

• Droplet growth

• Latent heat feedback

• Supersaturation dynamics

But precipitation? That’s a story of collective behavior, requiring interaction, turbulence, and multidimensionality.

Understanding this distinction is the key to using parcel models wisely — and seeing their elegant simplicity as both a strength and a boundary.