Atmospheric Genesis — BRKS01 · PSU Berks

I · First Principles

The State of the Air

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°C · Dry Bulb

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Every story begins here: the kinetic energy of molecules. Temperature is not heat — it is the mean translational velocity of air molecules, each vibrating at ~500 m/s. From this raw number and nothing more, we can summon physics.

T_K = T_C + 273.15
e_s = 6.112 · exp(17.67·T_C / (T_C+243.5)) [hPa]
Current e_s = — hPa | e = — hPa

Dewpoint: —°C · RH: —%

II · The Weight of the Sky

Pressure & Air Density

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hPa · MSLP

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kg/m³ · ρ

Ten tons of air pressing on every square meter. The ideal gas law in disguise:

ρ = P / (Rd · Tv) where Rd = 287.05 J/(kg·K)
Tv = T·(1 + w/ε)/(1+w) [virtual temperature]
ρ_now = — kg/m³ | Tv = — K

Moist air is lighter than dry air at the same T and P — water vapor displaces heavier N₂ and O₂. This single fact drives thunderstorm initiation, sea breezes, and monsoons.

III · The Conserved Quantities

Potential Temperature Family — the atmosphere's memory

θ · Pot. Temp

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K · adiabatic

θ_v · Virtual

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K · includes moisture

θ_e · Equiv.

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K · latent heat locked

θ_e − θ

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K · instability proxy

θ is the temperature a parcel would have if compressed (or expanded) dry-adiabatically to 1000 hPa — it is conserved during dry adiabatic ascent, the atmosphere's fingerprint.

θ = T·(P₀/P)^(Rd/cp) where P₀=1000 hPa, cp=1005.7 J/(kg·K)
θ_v = θ·(1+w/ε)/(1+w) [buoyancy-relevant]
θ_e = θ·exp((3.376/T_L − 0.00254)·w·(1+0.81w)) [Bolton 1980]
When θ_e−θ is large → moist instability, convective potential unleashed

At peak heating today, θ reached — K — the parcel rose 11 km before the lapse rate said stop.

IV · Moisture Transport

Mixing Ratio & the LCL

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g/kg · mixing ratio

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m · LCL height

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The Lifting Condensation Level — cloud base — the exact altitude where this parcel's vapor pressure equals saturation:

w = ε·e/(P−e) [kg/kg]
LCL ≈ 125·(T_C − Td_C) [m]
Sat ratio = w/w_s = —

▲ LCL tower: lower = moister = earlier cloud formation

V · The Vector Field

Wind — From Speed to Flux

FROM

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degrees

Speed becomes vector. U and V components are the building blocks of divergence, vorticity, and flux:

u = −|V|·sin(wd) [m/s · eastward]
v = −|V|·cos(wd) [m/s · northward]
u = — | v = — m/s
|V| = — m/s Gust: — mph

With a network of stations, ∂u/∂x + ∂v/∂y gives us divergence — positive = sinking air = clearing; negative = convergence = rising = storms.

VI · Energy Exchange

Sensible Heat Flux & Bowen Ratio

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W/m² · H flux

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W/m² · solar

The surface breathes energy into the atmosphere:

H = ρ·cp·CH·|V|·(Ts−Ta) [W/m²]
CH ≈ 0.01 [bulk transfer coeff]
Bowen Ratio B = H/LE ≈ (1−RH)/RH

Bowen Ratio: the split between sensible (warming) and latent (moistening) heat exchange:

WET

DRY

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VII · Convective Potential

CAPE Proxy & Buoyancy

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J/kg · ≈CAPE

CAPE — Convective Available Potential Energy — is the integral of buoyancy through the troposphere. This proxy uses θ_e − θ:

CAPE ≈ ∫ (g/T)·(T_parcel−T_env) dz
Proxy: (θ_e − θ)·g/θ·Δz_eff
CAPE_proxy = — J/kg
<500: stable · 500-1500: moderate · >2000: significant

Through this day you can watch buoyancy build with the solar forcing — the atmosphere storing energy like a coiled spring — and then relax as the sun descends, the molecules quieting their uprising urge.

VIII · The Grand Synthesis

All Variables, Live

Stand back far enough and you see it: a single weather station is a node in a tensor field. Temperature and humidity are scalars. Wind is a vector. Their spatial gradients — when you place stations around it — birth the tensor quantities: the strain rate of the wind field, the deformation tensor, the rate of vorticity generation. Each parcel of air at this station right now is a Lagrangian tracer of the broader flow. Its θ_e is its passport — it came from somewhere with that entropy, and it is bound for somewhere else, carrying that fingerprint into the next hour's sounding, the next county's sky.

The molecules don't know they are writing a narrative. But they are.