Saturated Adiabatic Lapse Rate Calculator Equation

Saturated Adiabatic Lapse Rate (SALR) Equation:

\[ \Gamma_s = \Gamma_d \left( \frac{1 + \frac{L_v r_s}{R_d T}}{1 + \frac{L_v^2 r_s}{c_p R_v T^2}} \right) \]

Saturated Adiabatic Lapse Rate (SALR):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Saturated Adiabatic Lapse Rate?

The Saturated Adiabatic Lapse Rate (SALR) is the rate at which saturated air cools as it rises and expands. It ranges from 4.5 to 9°C per kilometer depending on moisture content and temperature. Unlike the dry adiabatic lapse rate, SALR varies because latent heat is released as water vapor condenses.

2. How Does the Calculator Work?

The calculator uses the SALR equation:

\[ \Gamma_s = \Gamma_d \left( \frac{1 + \frac{L_v r_s}{R_d T}}{1 + \frac{L_v^2 r_s}{c_p R_v T^2}} \right) \]

Where:

\( \Gamma_s \) — Saturated adiabatic lapse rate (°C/km)
\( \Gamma_d \) — Dry adiabatic lapse rate (9.8°C/km)
\( L_v \) — Latent heat of vaporization (2.5×10⁶ J/kg)
\( r_s \) — Saturation mixing ratio (kg/kg)
\( R_d \) — Gas constant for dry air (287.05 J/kg·K)
\( R_v \) — Gas constant for water vapor (461.495 J/kg·K)
\( c_p \) — Specific heat capacity (1005 J/kg·K)
\( T \) — Temperature (K)

Explanation: The equation accounts for the release of latent heat during condensation, which reduces the cooling rate compared to dry air.

3. Importance of SALR Calculation

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

4. Using the Calculator

Tips: Enter moisture content in g/kg, temperature in °C, and pressure in hPa. Typical values range from 4.5°C/km (very moist air) to 9°C/km (dry air).

5. Frequently Asked Questions (FAQ)

Q1: Why does SALR vary with temperature?
A: Warmer air can hold more moisture, so more latent heat is released during condensation, resulting in a lower lapse rate.

Q2: How does SALR differ from DALR?
A: Dry Adiabatic Lapse Rate (DALR) is constant at 9.8°C/km, while SALR varies and is always less than DALR due to latent heat release.

Q3: What's the typical SALR value?
A: In the troposphere, SALR averages about 6°C/km but ranges from 4.5°C/km in warm, moist air to nearly 9°C/km in cold, dry air.

Q4: How does pressure affect SALR?
A: Higher pressure increases air density, which affects the heat capacity and thus the lapse rate, though the effect is secondary to temperature and moisture.

Q5: Why is SALR important for aviation?
A: Pilots use SALR to predict cloud bases, icing conditions, and turbulence associated with convective activity.