function updateLabels() {
var unit = document.getElementById('unitSystem').value;
if (unit === 'metric') {
document.getElementById('labelTemp').innerText = 'Starting Surface Temperature (°C)';
document.getElementById('labelStartAlt').innerText = 'Starting Altitude (Meters)';
document.getElementById('labelEndAlt').innerText = 'Target Altitude (Meters)';
document.getElementById('startTemp').placeholder = 'e.g. 25';
document.getElementById('endAlt').placeholder = 'e.g. 2000';
} else {
document.getElementById('labelTemp').innerText = 'Starting Surface Temperature (°F)';
document.getElementById('labelStartAlt').innerText = 'Starting Altitude (Feet)';
document.getElementById('labelEndAlt').innerText = 'Target Altitude (Feet)';
document.getElementById('startTemp').placeholder = 'e.g. 75';
document.getElementById('endAlt').placeholder = 'e.g. 5000';
}
}
function calculateDALR() {
// Inputs
var unit = document.getElementById('unitSystem').value;
var tStart = parseFloat(document.getElementById('startTemp').value);
var altStart = parseFloat(document.getElementById('startAlt').value);
var altEnd = parseFloat(document.getElementById('endAlt').value);
// Validation
if (isNaN(tStart) || isNaN(altStart) || isNaN(altEnd)) {
alert("Please enter valid numerical values for temperature and altitude.");
return;
}
// Constants
// Metric: 9.8°C per 1000m (0.0098°C/m)
// Imperial: 5.5°F per 1000ft (0.0055°F/ft)
var lapseRate;
var unitSym;
var distSym;
if (unit === 'metric') {
lapseRate = 0.0098; // Degrees Celsius per Meter
unitSym = "°C";
distSym = "m";
} else {
lapseRate = 0.0055; // Degrees Fahrenheit per Foot
unitSym = "°F";
distSym = "ft";
}
// Logic
var altDiff = altEnd – altStart;
var tempChange = altDiff * lapseRate;
// If rising (positive altDiff), temp decreases.
// Formula: T_final = T_start – (Rate * Delta_Z)
var tFinal = tStart – tempChange;
// Display Formatting
var resultDiv = document.getElementById('result-area');
var resultVal = document.getElementById('finalTempResult');
var infoText = document.getElementById('tempChangeInfo');
resultDiv.style.display = 'block';
resultVal.innerText = tFinal.toFixed(2) + " " + unitSym;
// Contextual explanation
var direction = (altDiff >= 0) ? "lifted" : "descended";
var changeType = (altDiff >= 0) ? "cooled" : "warmed";
infoText.innerHTML = "The air parcel was " + direction + " by " + Math.abs(altDiff) + " " + distSym + "." +
"Due to the Dry Adiabatic Lapse Rate, it " + changeType + " by " + Math.abs(tempChange).toFixed(2) + " " + unitSym + ".";
}
What is the Dry Adiabatic Lapse Rate?
The Dry Adiabatic Lapse Rate (DALR) describes how the temperature of an unsaturated air parcel changes as it moves vertically through the atmosphere. Unlike the environmental lapse rate, which is the actual temperature profile of the atmosphere, the DALR is a theoretical constant used to predict how air behaves when forced to rise or sink without exchanging heat with its surroundings.
This calculator helps meteorologists, pilots, and outdoor enthusiasts determine the temperature of dry air at different altitudes, which is crucial for predicting cloud formation, atmospheric instability, and thunderstorm potential.
The Physics of Adiabatic Cooling
When an air parcel rises, the atmospheric pressure surrounding it decreases. This allows the parcel to expand. Expansion requires work, and the energy for this work comes from the internal heat energy of the air parcel. As a result, the temperature drops. Conversely, when air sinks, it is compressed by higher pressure, leading to an increase in temperature.
The term "Dry" implies that the air has not reached 100% relative humidity (saturation) and no condensation is occurring. Once condensation begins, latent heat is released, and the cooling rate slows down (switching to the Moist Adiabatic Lapse Rate).
Standard Lapse Rate Constants
While local conditions can vary slightly due to gravity and composition, the standard constants used for DALR are:
Metric System: Approximately 9.8°C per 1,000 meters (often rounded to 10°C/km).
Imperial System: Approximately 5.5°F per 1,000 feet.
Calculation Formula
To calculate the final temperature of a dry air parcel, use the following formula:
Tfinal = Tinitial – ( Γd × Δz )
Where:
Tfinal = The final temperature of the parcel.
Tinitial = The starting temperature.
Γd = The Dry Adiabatic Lapse Rate (0.0098 °C/m or 0.0055 °F/ft).
Δz = The change in altitude (Final Altitude – Initial Altitude).
Example Calculation
Imagine a hiker at the base of a mountain measuring the temperature at 20°C. The base is at sea level (0m) and the peak is at 2,000m. Assuming the air is dry:
Temperature Drop: 2,000m × 0.0098°C/m = 19.6°C
Final Temperature: 20°C – 19.6°C = 0.4°C
The hiker should expect freezing or near-freezing conditions at the summit.
Why is DALR Important?
Cloud Base Prediction: By comparing the temperature and dew point convergence using the DALR, meteorologists can estimate the altitude where clouds will form (Lifting Condensation Level).
Atmospheric Stability: If the actual environmental air is cooling faster than the DALR, the atmosphere is unstable, promoting vertical motion and storms. If it cools slower (or warms), the atmosphere is stable.
Aviation Safety: Pilots use lapse rates to anticipate turbulence and icing conditions at different flight levels.