Atmospheric Science numericals in CSIR NET Earth Science draw from a fairly small set of core formulas, repeated across different question framings. This sheet collects the ones that show up most often, with the context for when to use each.
Thermodynamics and Stability
Dry Adiabatic Lapse Rate (DALR)
Γd ≈ 9.8℃/km (approximately 1℃ per 100 m)
Used whenever an unsaturated air parcel rises or sinks. Temperature change = lapse rate × change in altitude.
Moist (Saturated) Adiabatic Lapse Rate (SALR)
Γs ≈ 4–6℃/km (varies with temperature and moisture content, always less than the DALR)
Applies once a rising parcel becomes saturated and latent heat release slows the cooling rate.
Environmental Lapse Rate (ELR)
The actual observed rate of temperature decrease with height in the surrounding atmosphere, averaging about 6.5℃/km globally. Comparing ELR to DALR/SALR determines atmospheric stability:
- ELR < SALR — absolutely stable
- ELR between SALR and DALR — conditionally unstable
- ELR > DALR — absolutely unstable
Pressure and the Hydrostatic Equation
dp/dz = −ρg
Pressure decreases with height at a rate proportional to air density and gravitational acceleration. This underlies most “pressure at altitude” style questions.
Ideal Gas Law (Applied to Air)
p = ρRT
Where p is pressure, ρ is density, R is the specific gas constant for dry air (≈287 J/kg·K), and T is temperature in Kelvin. Combine with the hydrostatic equation for density/pressure/temperature relationship questions.
Potential Temperature
θ = T(p₀/p)R/cp
Where p₀ is a reference pressure (usually 1000 hPa) and R/cp ≈ 0.286 for dry air. Potential temperature is conserved for a dry adiabatic process, making it useful for comparing air parcels at different altitudes.
Coriolis Force and Geostrophic Wind
Coriolis parameter: f = 2Ωsinφ
Where Ω is Earth’s angular velocity and φ is latitude. The Coriolis force is zero at the equator and maximum at the poles — this single fact underlies many conceptual questions about tropical vs. mid-latitude weather systems.
Geostrophic wind: Vg = (1/fρ) × (Δp/Δn)
Geostrophic wind speed is inversely proportional to the Coriolis parameter — meaning for the same pressure gradient, geostrophic winds are stronger closer to the equator and weaker near the poles.
Relative Humidity
RH (%) = (actual vapor pressure / saturation vapor pressure) × 100
Saturation vapor pressure increases non-linearly with temperature (Clausius-Clapeyron relation) — you don’t need to derive this in the exam, but you should know that warmer air can hold more moisture, which explains why RH drops as temperature rises even with constant actual moisture content.
How to Use This Sheet
- Memorize the DALR and SALR values first — they appear in the widest variety of question types.
- Practice stability classification questions (comparing ELR to DALR/SALR) since these combine conceptual and numerical understanding.
- Work through 8–10 solved geostrophic wind and Coriolis problems — these are formula-heavy but formulaic once practiced.
Practice These Formulas in Context
Earthoholic Academy’s Atmospheric Science course applies these formulas across topic-wise practice questions. For the full textbook treatment these formulas are drawn from, see the Atmosphere by Tarbuck course.
Frequently Asked Questions
Do I need to memorize exact constants like R = 287 J/kg·K?
Yes for the most common ones (R for dry air, standard lapse rates) — CSIR NET numericals generally expect you to know these without them being provided.
Which formula appears most often in Part C?
Lapse rate and stability questions (DALR vs. SALR vs. ELR) are the most consistently recurring numerical/conceptual combination.
Is calculus required for any of these?
No — CSIR NET-level questions use these relationships algebraically, not through derivation.