Questions: Mixing Ratio and Saturation Mixing Ratio

Question 1

An unsaturated air parcel with a mixing ratio of 12 g/kg rises from 900 hPa to 700 hPa without reaching saturation. Which statement correctly describes the parcel's moisture properties at 700 hPa?

• A. The mixing ratio has decreased because the parcel expanded and the water vapor diluted
• B. The mixing ratio is still 12 g/kg, but the relative humidity has increased because the saturation mixing ratio decreased as the parcel cooled
• C. Both mixing ratio and relative humidity are unchanged because rising air conserves all moisture properties
• D. The mixing ratio increased because colder air can hold more water vapor per unit mass

Answer: (B)

Mixing ratio is conservative for an unsaturated parcel: no water has been added or removed, so the mass of vapor per kilogram of dry air stays at 12 g/kg. But as the parcel rises and cools, the *saturation* mixing ratio decreases (cold air has lower saturation capacity per Clausius-Clapeyron). Since relative humidity = (actual mixing ratio) / (saturation mixing ratio), RH rises even though no moisture was added. This is the key contrast: mixing ratio tracks actual moisture, relative humidity tracks proximity to saturation — they can change independently.

Question 2

A meteorologist needs to track whether two air parcels that have been lifted to different altitudes originally contained the same amount of water vapor. Which moisture variable should she compare?

• A. Relative humidity, because it is expressed as a percentage and is comparable across altitudes
• B. Dew point temperature, because it is independent of the parcel's current temperature
• C. Mixing ratio, because it is conserved during dry adiabatic lifting and directly measures vapor mass per unit dry air mass
• D. Specific humidity, which is always constant regardless of pressure and temperature changes

Answer: (C)

Mixing ratio is the right choice because it is conserved during dry adiabatic (unsaturated) ascent — it measures the actual mass of water vapor per unit dry air mass, which doesn't change when pressure or temperature change without condensation. Relative humidity is not conserved: it increases as the parcel cools, even with no moisture change. Dew point is useful but changes with pressure as well. Specific humidity is also approximately conservative, but mixing ratio is the most direct measure of absolute moisture content.

Question 3

When an unsaturated air parcel rises and cools, its relative humidity increases because moisture is being added to the parcel from the surrounding environment.

• T. True
• F. False

Answer: False

No moisture is exchanged with the environment during dry adiabatic lifting. Relative humidity increases solely because the parcel cools — its saturation mixing ratio (the denominator of the RH fraction) decreases with temperature, making the existing moisture a larger fraction of what the air could hold. This distinction is critical: it means RH alone cannot tell you whether a parcel gained or lost moisture. The mixing ratio, not RH, tells you whether actual moisture content changed.

Question 4

At the dew point temperature, an air parcel's actual mixing ratio equals its saturation mixing ratio, so relative humidity is 100%.

• T. True
• F. False

Answer: True

The dew point is defined as the temperature to which air must be cooled (at constant pressure and moisture content) to reach saturation. At that temperature, the saturation mixing ratio has decreased to exactly equal the actual mixing ratio. Since RH = (actual mixing ratio)/(saturation mixing ratio) × 100%, RH = 100% at the dew point. This is the thermodynamic definition connecting dew point, mixing ratio, and saturation mixing ratio in a single consistent framework.

Question 5

Explain why mixing ratio is more useful than relative humidity for tracking a parcel's moisture content as it rises through the atmosphere.

Model answer: Mixing ratio (mass of water vapor per kg of dry air) is conserved during unsaturated ascent — it doesn't change unless water actually condenses out or is added. Relative humidity, by contrast, rises as the parcel cools even with no change in actual water vapor, because the saturation capacity decreases with temperature. Using RH to track moisture as a parcel rises would give the false impression that moisture is increasing, when in reality only the temperature changed.

The practical implication is significant for sounding analysis: meteorologists plot mixing ratio on thermodynamic diagrams to identify where a parcel originated and how much moisture it carries, then compare to the saturation mixing ratio line at each level to find where clouds form (where the two values converge). Using RH instead would conflate the temperature effect with actual moisture changes, making the analysis ambiguous.