Atmosphere and Weather Exam Cheat Sheet — Key Formulas & Tips

Posted on Feb 4, 2026 in Mathematics

Atmosphere & Weather Exam Cheat Sheet (Super Simple)

Exam-Style Questions — How to Answer (with steps)

1. Temperature Questions

Q: Convert Celsius ↔ Kelvin

How to answer:

  1. If going from °C → K: add 273.15 (K = °C + 273.15).
  2. If going from K → °C: subtract 273.15 (°C = K − 273.15).

2. Insolation / Energy Questions

Q: Why is this day warmer/colder?

How to answer:

  1. Look at the irradiance graph.
  2. Higher irradiance = more sunlight.
  3. More sunlight usually = warmer temperatures.

3. Relative Humidity (RH) Questions

Q: Find RH using a table/graph

How to answer:

  1. Find the maximum vapor at the given temperature from the table/graph.
  2. Take the actual vapor value given in the question.
  3. Use the formula: RH = (actual / maximum) × 100.

4. Dew Point Questions

Q: Find the dew point temperature

How to answer:

  1. Find the actual vapor value provided.
  2. Scan the saturation table to find which temperature’s maximum vapor matches the actual vapor.
  3. That temperature is the dew point.

5. Saturation / Condensation Questions

Q: Is the air saturated? Will condensation happen?

How to answer:

  • If T = Tdew, the air is saturated → condensation will occur → cloud or dew formation.

6. LCL (Cloud Base Height)

Q: Find cloud base height

How to answer:

  1. Compute T − Tdew (temperature minus dew point).
  2. Divide the result by 10 °C per km (approximate): LCL (km) = (T − Tdew) / 10.
  3. The result is the cloud base height in kilometers.

Example: T = 20 °C, Tdew = 10 °C → (20 − 10) = 10 → 10 / 10 = 1 km.

7. Terminal Velocity & Fall Time

Q: How long does a raindrop take to fall?

How to answer:

  1. Identify drop size → approximate terminal speed:
    • Small: 1 m/s
    • Medium: 5 m/s
    • Large: 9 m/s
  2. Use the formula: time = height / speed.

Example: 1500 m / 5 m/s = 300 s.

8. Irradiance & Temperature Graph Questions

Q: When was it warmest/coldest?

How to answer: Look for the highest or lowest point on the temperature graph.

Q: Was it cloudy?

How to answer:

  • Flat or consistently low irradiance = cloudy conditions.
  • A large midday peak in irradiance = sunny conditions.

9. FWHM

Q: What is the FWHM?

How to answer:

  1. Find the peak of the curve.
  2. Find the value halfway down from the peak.
  3. Measure the width of the curve at that half-peak height; that is the FWHM.

Practice Questions (Match Your Exam Style)

Practice 1: RH

Temp = 20 °C. Maximum vapor = 14 g/m³. Actual vapor = 7 g/m³.
Find RH.

Practice 2: Dew Point

Actual vapor = 10 g/m³. Table shows saturation at 15 °C = 10 g/m³.
Find dew point.

Practice 3: LCL

T = 18 °C, Dew point = 12 °C.
Find LCL height.

Practice 4: Fall Time

Drop speed = 5 m/s, height = 800 m.
Find time.

Practice 5: Cloud or No Cloud?

T = 12 °C, Tdew = 12 °C.
Will clouds form?

If you want, I can add answers to the practice questions too!

What you MUST know:

  • °C → K: add 273.15.
  • K → °C: subtract 273.15.
  • If sun angle is higher → warmer.
  • Alpha statement example: “A is 5 °C warmer than B.”

2. Energy (Bare Minimum)

  • More sunlight = more warming.
  • Hotter objects emit more energy.

3. Water & Condensation (Core Ideas)

  • Condensation happens when air cools to the dew point.
  • Dew point = temperature where the air becomes saturated with water vapor.
  • RH increases when temperature decreases (for fixed actual vapor).
  • RH decreases when temperature increases (for fixed actual vapor).

4. EXACT Calculations You May Need

A) Relative Humidity (RH)

You will be given a table/graph. Steps:

  1. Find the maximum vapor at the current temperature.
  2. Take the actual vapor value given.
  3. Calculate: RH = (actual / maximum) × 100.

B) Dew Point (Tdew)

Using the same table:

  1. Find the actual vapor value provided.
  2. Find which temperature’s saturation vapor equals that value.
  3. That temperature is the dew point.

C) LCL (Cloud Base Height)

Steps:

  1. Find Temperature − Dew Point.
  2. Divide by 10 °C/km (approximate) to get LCL in km.

Example: T = 20 °C, Dew point = 10 °C → difference = 10 °C → 10 / 10 = 1 km LCL.

5. Clouds & CCN

  • Clouds form when air cools to the dew point and cloud condensation nuclei (CCN) are present.

6. Terminal Velocity & Fall Time (Simple Numbers)

  • Small drop: 1 m/s
  • Medium drop: 5 m/s
  • Large drop: 9 m/s

Fall time formula:

time = height / terminal velocity

Example: 1000 m / 5 m/s = 200 s.

7. EMOS: Temperature & Irradiance

  • Temperature graph shows how warm or cold the day was.
  • Irradiance graph shows sunlight intensity.
    • High midday peak = sunny.
    • Low or flat curve = cloudy.

8. DVM Model (Daily Temperature Pattern)

  • Coldest: just before sunrise.
  • Warmest: afternoon (~3–4 pm).

9. FWHM (Keep Super Simple)

  • The width of a curve measured at half its peak height.

10. How to Answer Any Graph Question Fast

  1. Find the highest point.
  2. Find the lowest point.
  3. Compare and make an alpha statement (clear comparison statement).

11. Quick Problem Checklist

  • Convert temperature if needed (°C ↔ K).
  • Is T = Tdew? → saturated / clouds likely.
  • RH = (actual / maximum) × 100.
  • Find dew point from the saturation table.
  • Cloud base: ΔT / 10 (km).
  • Fall time: height / speed.
  • Use alpha statements for comparisons.