Moist Adiabatic Lapse Rate Calculator

Moist Adiabatic Lapse Rate Equation:

\[ MALR = \frac{g (1 + \frac{H_v r}{R_{sd} T})}{C_p + \frac{H_v^2 r}{R_v T^2}} \]

Gravitational Acceleration (g):

m/s²

Latent Heat of Vaporization (Hv):

J/kg

Mixing Ratio (r):

kg/kg

Specific Gas Constant for Dry Air (Rsd):

J/kg/K

Temperature (T):

Specific Heat Capacity at Constant Pressure (Cp):

J/kg/K

Specific Gas Constant for Water Vapor (Rv):

J/kg/K

Moist Adiabatic Lapse Rate (MALR):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Moist Adiabatic Lapse Rate?

The Moist Adiabatic Lapse Rate (MALR) is the rate at which a saturated parcel of air cools as it rises in the atmosphere. It's slower than the dry adiabatic lapse rate due to the release of latent heat during condensation.

2. How Does the Calculator Work?

The calculator uses the MALR equation:

\[ MALR = \frac{g (1 + \frac{H_v r}{R_{sd} T})}{C_p + \frac{H_v^2 r}{R_v T^2}} \]

Where:

\( g \) — Gravitational acceleration (9.8 m/s²)
\( H_v \) — Latent heat of vaporization (J/kg)
\( r \) — Mixing ratio (kg/kg)
\( R_{sd} \) — Specific gas constant for dry air (287.05 J/kg/K)
\( T \) — Temperature (K)
\( C_p \) — Specific heat capacity at constant pressure (1005 J/kg/K)
\( R_v \) — Specific gas constant for water vapor (461.5 J/kg/K)

Explanation: The equation accounts for both the expansion cooling of rising air and the heating from condensation.

3. Importance of MALR Calculation

Details: MALR is crucial in meteorology for understanding cloud formation, atmospheric stability, and weather forecasting. It helps predict thunderstorm development and precipitation patterns.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Typical values are pre-filled for Earth's atmosphere at sea level. Temperature must be in Kelvin.

5. Frequently Asked Questions (FAQ)

Q1: How does MALR differ from DALR?
A: The Dry Adiabatic Lapse Rate (DALR) is about 9.8°C/km, while MALR is typically 4-9°C/km depending on temperature and humidity.

Q2: Why does MALR vary with temperature?
A: Warmer air can hold more water vapor, so more latent heat is released during condensation, resulting in a slower lapse rate.

Q3: What's a typical MALR value?
A: In Earth's troposphere, MALR averages about 6°C/km but can range from 4°C/km in warm, moist air to near 9°C/km in cold, dry air.

Q4: How does MALR affect weather?
A: When environmental lapse rate exceeds MALR, the atmosphere becomes conditionally unstable, potentially leading to thunderstorms.

Q5: Can MALR be negative?
A: No, MALR is always positive but can approach zero in extremely warm, moist conditions.