Standard sea level pressure is approx 1013.25 hPa.
Enter height to calculate the final temperature at that altitude.
Wet Adiabatic Lapse Rate:–
Comparison to Dry Rate:–
Temp at Altitude:–
Understanding Wet Adiabatic Lapse Rate
The Wet Adiabatic Lapse Rate (WALR), also known as the Saturated Adiabatic Lapse Rate (SALR), is a critical concept in meteorology and atmospheric thermodynamics. It represents the rate at which a parcel of saturated air (100% relative humidity) cools as it rises in the atmosphere.
Unlike dry air, which cools at a relatively constant rate (the Dry Adiabatic Lapse Rate, approx. 9.8°C/km), saturated air cools more slowly. This is due to the release of latent heat during the condensation process. As water vapor turns into liquid droplets (cloud formation), energy is released, warming the air parcel and offsetting some of the cooling caused by expansion.
How It Is Calculated
The WALR is not a constant value. It depends heavily on the temperature and pressure of the air parcel. In warm, tropical air near the surface, the WALR can be as low as 4°C/km because the air holds a lot of moisture, releasing significant latent heat. In very cold, upper-atmosphere air, the moisture content is low, and the WALR approaches the Dry Adiabatic Lapse Rate.
The formula implemented in this calculator is derived from the first law of thermodynamics and the Clausius-Clapeyron relation:
Lv: Latent heat of vaporization (varies with Temp)
rs: Saturation mixing ratio
Rd: Specific gas constant for dry air (287 J/kg·K)
T: Temperature in Kelvin
Cpd: Specific heat of dry air (1005 J/kg·K)
Why is this Important?
The difference between the environmental lapse rate (the actual temperature profile of the atmosphere) and the wet adiabatic lapse rate determines atmospheric stability:
Unstable Atmosphere: If the environment cools faster than the WALR, a rising saturated air parcel will remain warmer than its surroundings and continue to rise, leading to tall cumulonimbus clouds and thunderstorms.
Stable Atmosphere: If the environment cools slower than the WALR, the rising parcel becomes colder than its surroundings and sinks back down, suppressing cloud formation.
Dry vs. Wet Adiabatic Lapse Rates
While the Dry Adiabatic Lapse Rate (DALR) is fixed at roughly 9.8°C per kilometer, the Wet Adiabatic Lapse Rate typically ranges between 4°C/km and 9°C/km. This calculator helps meteorologists, pilots, and hikers estimate temperature changes in cloud layers and assess the potential for storm development.
function calculateWALR() {
// 1. Get Inputs
var tempC = parseFloat(document.getElementById('airTemp').value);
var pressureHPa = parseFloat(document.getElementById('airPressure').value);
var altChange = parseFloat(document.getElementById('altitudeChange').value);
// 2. Validate Inputs
if (isNaN(tempC) || isNaN(pressureHPa)) {
alert("Please enter valid numbers for Temperature and Pressure.");
return;
}
if (pressureHPa <= 0) {
alert("Pressure must be greater than 0.");
return;
}
// 3. Define Constants
var g = 9.8076; // Gravity (m/s^2)
var Rd = 287.0; // Gas constant dry air (J/kgK)
var Rv = 461.5; // Gas constant water vapor (J/kgK)
var epsilon = Rd / Rv; // Ratio of gas constants (~0.622)
var Cpd = 1005.0; // Specific heat of dry air (J/kgK)
// 4. Intermediate Calculations
var tempK = tempC + 273.15; // Kelvin
// Calculate Saturation Vapor Pressure (es) using Tetens Formula
// es in hPa
var es = 6.112 * Math.exp((17.67 * tempC) / (tempC + 243.5));
// Calculate Saturation Mixing Ratio (rs)
// rs is dimensionless (kg/kg)
// Formula: rs = epsilon * (es / (P – es))
var rs = epsilon * (es / (pressureHPa – es));
// Calculate Latent Heat of Vaporization (Lv)
// Lv varies slightly with T. Approximation: Lv = 2.501e6 – 2370*Tc (J/kg)
var Lv = (2501000 – (2370 * tempC));
// 5. Calculate WALR (Gamma_w)
// Numerator = 1 + (Lv * rs) / (Rd * T)
var numerator = 1 + ((Lv * rs) / (Rd * tempK));
// Denominator = Cpd + (Lv^2 * rs * epsilon) / (Rd * T^2)
var denominator = Cpd + ((Math.pow(Lv, 2) * rs * epsilon) / (Rd * Math.pow(tempK, 2)));
// Result in Kelvin per meter (K/m) or Celsius per meter
var lapseRatePerMeter = g * (numerator / denominator);
// Convert to Celsius per Kilometer (C/km)
var lapseRatePerKm = lapseRatePerMeter * 1000;
// 6. Display Results
var resultDiv = document.getElementById('result-area');
var walrDisplay = document.getElementById('walrResult');
var ratioDisplay = document.getElementById('ratioResult');
var finalTempRow = document.getElementById('finalTempRow');
var finalTempDisplay = document.getElementById('finalTempResult');
resultDiv.style.display = 'block';
walrDisplay.innerHTML = lapseRatePerKm.toFixed(2) + " °C/km";
// Compare to Dry Rate (approx 9.8)
var dryRate = 9.8;
var percentageOfDry = (lapseRatePerKm / dryRate) * 100;
ratioDisplay.innerHTML = percentageOfDry.toFixed(1) + "% of Dry Rate";
// Handle Altitude Change Logic
if (!isNaN(altChange) && altChange !== 0) {
// Temperature decreases as we go up
var tempDrop = lapseRatePerKm * altChange;
var finalTemp = tempC – tempDrop;
finalTempRow.style.display = 'flex';
finalTempDisplay.innerHTML = finalTemp.toFixed(1) + " °C";
} else {
finalTempRow.style.display = 'none';
}
}