Moist Adiabatic Lapse Rate Calculator
0.00 °C/km
9.8 °C/km
Understanding the Moist Adiabatic Lapse Rate (MALR)
The Moist Adiabatic Lapse Rate (MALR), also known as the Saturated Adiabatic Lapse Rate (SALR), is a critical concept in meteorology and atmospheric thermodynamics. It defines the rate at which a saturated parcel of air cools as it rises, or warms as it descends, assuming no heat exchange with the surroundings (adiabatic) other than the release of latent heat.
Unlike the Dry Adiabatic Lapse Rate (DALR), which is roughly constant at 9.8°C/km, the MALR is not constant. It varies significantly depending on the temperature and pressure of the air parcel. This calculator helps meteorologists, students, and aviation enthusiasts estimate the stability of the atmosphere by determining the specific lapse rate for given conditions.
How Calculation Works
The calculation of the MALR is complex because it involves the release of latent heat. As water vapor condenses into liquid water within a rising saturated air parcel, it releases heat. This heat offsets some of the cooling caused by expansion, making the MALR smaller (i.e., the air cools more slowly) than the dry adiabatic rate.
The physics behind this calculator relies on the thermodynamic equation:
Where:
- g: Acceleration due to gravity (9.81 m/s²)
- Hv: Latent heat of vaporization of water
- r: Saturation mixing ratio of water vapor
- Rsd: Specific gas constant for dry air
- T: Temperature in Kelvin
- Cpd: Specific heat of dry air at constant pressure
- ε: Ratio of gas constant of dry air to water vapor (~0.622)
Why Does It Vary?
The key factor causing variation in the MALR is the moisture content of the air, which is highly dependent on temperature:
- Warm Air: Holds more moisture. When it rises and cools, massive amounts of condensation occur, releasing significant latent heat. This results in a much lower lapse rate (often around 4°C/km to 5°C/km near the surface in the tropics).
- Cold Air: Holds very little moisture. The latent heat release is minimal, so the MALR approaches the Dry Adiabatic Lapse Rate (closer to 9°C/km in the upper troposphere or polar regions).
Atmospheric Stability
Comparing the actual environmental lapse rate (ELR) to the MALR and DALR helps determine atmospheric stability:
- Absolutely Stable: ELR < MALR (Air parcel is always cooler/denser than surroundings).
- Conditionally Unstable: MALR < ELR < DALR (Stability depends on whether the air is saturated).
- Absolutely Unstable: ELR > DALR (Air parcel is always warmer/lighter than surroundings).
Understanding these rates is essential for forecasting thunderstorms, cloud formation, and turbulence.