How is Lapse Rate Calculated

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Atmospheric Lapse Rate Calculator

Calculate the environmental lapse rate based on temperature changes over altitude.

Meters (m) Feet (ft)
Celsius (°C) Fahrenheit (°F) Kelvin (K)
Meters (m) Feet (ft)
Celsius (°C) Fahrenheit (°F) Kelvin (K)
Calculated Lapse Rate (Metric): 6.5 °C/km
Calculated Lapse Rate (Imperial): 3.57 °F/1000ft
Status: Normal (Stable)

How Is Lapse Rate Calculated?

The lapse rate is a critical meteorological parameter that defines the rate at which atmospheric temperature decreases with an increase in altitude. Understanding how to calculate lapse rate is essential for weather forecasting, aviation safety, and understanding atmospheric stability.

The Lapse Rate Formula

To calculate the environmental lapse rate ($\Gamma$), you measure the temperature at two different altitudes. The formula essentially calculates the negative gradient of temperature with respect to height:

$\Gamma = – \frac{T_2 – T_1}{z_2 – z_1}$

Where:

  • $T_1, T_2$: Temperatures at the lower and higher points respectively.
  • $z_1, z_2$: Altitudes at the lower and higher points respectively.

A positive result indicates the temperature is dropping as you go up (which is standard). A negative result indicates a Temperature Inversion, where it gets warmer as you go higher.

Standard Lapse Rates

In atmospheric thermodynamics, there are distinct types of lapse rates used as benchmarks:

  • Dry Adiabatic Lapse Rate (DALR): Approximately 9.8 °C/km (or 5.4 °F/1000ft). This applies to unsaturated air parcels.
  • Saturated (Wet) Adiabatic Lapse Rate (SALR/MALR): Varies, but typically averages around 5 °C/km to 6 °C/km. This applies when the air is saturated with moisture (clouds).
  • Environmental Lapse Rate (ELR): The actual rate measured in the atmosphere at a specific time and place. The standard average is often cited as 6.5 °C/km.

Interpreting the Results

The stability of the atmosphere is determined by comparing your calculated Environmental Lapse Rate (ELR) to the Dry Adiabatic Lapse Rate (DALR):

  • Unstable (Superadiabatic): Rate > 9.8 °C/km. Air parcels rise rapidly, leading to storms and turbulence.
  • Conditionally Unstable: Rate between 5 °C/km and 9.8 °C/km. Stability depends on moisture content.
  • Stable: Rate < 5 °C/km. Vertical motion is suppressed.
  • Inversion: Negative Rate. Temperature increases with height, trapping pollutants and fog near the ground.
function calculateLapseRate() { // 1. Get Inputs var alt1 = parseFloat(document.getElementById('alt1').value); var unitAlt1 = document.getElementById('unitAlt1').value; var temp1 = parseFloat(document.getElementById('temp1').value); var unitTemp1 = document.getElementById('unitTemp1').value; var alt2 = parseFloat(document.getElementById('alt2').value); var unitAlt2 = document.getElementById('unitAlt2').value; var temp2 = parseFloat(document.getElementById('temp2').value); var unitTemp2 = document.getElementById('unitTemp2').value; // 2. Validation if (isNaN(alt1) || isNaN(temp1) || isNaN(alt2) || isNaN(temp2)) { alert("Please enter valid numbers for all fields."); return; } if (alt1 === alt2) { alert("Altitudes cannot be the same. There must be a vertical distance to calculate a rate."); return; } // 3. Normalize Data to Metric (Meters and Celsius) // Convert Altitudes to Meters var z1_m = (unitAlt1 === 'ft') ? alt1 * 0.3048 : alt1; var z2_m = (unitAlt2 === 'ft') ? alt2 * 0.3048 : alt2; // Ensure z2 is the higher altitude for standard calculation flow, // or just rely on the math. Standard formula: -(T_high – T_low) / (Z_high – Z_low). // If user puts higher altitude in box 1, we swap or just compute raw diff. // Let's compute delta T and delta Z based on input order. var dZ_km = (z2_m – z1_m) / 1000; // Change in height in km // Convert Temperatures to Celsius var t1_c = temp1; if (unitTemp1 === 'f') t1_c = (temp1 – 32) * 5/9; if (unitTemp1 === 'k') t1_c = temp1 – 273.15; var t2_c = temp2; if (unitTemp2 === 'f') t2_c = (temp2 – 32) * 5/9; if (unitTemp2 === 'k') t2_c = temp2 – 273.15; var dT_c = t2_c – t1_c; // Change in temp // 4. Calculate Lapse Rate // Definition: Rate of decrease. L = -dT/dZ // If T decreases (negative dT) as Z increases (positive dZ), result should be positive. var lapseRateMetric = – (dT_c / dZ_km); // Calculate Imperial (F per 1000ft) // 1 C/km = 0.5486 F/1000ft approx? // Let's calculate directly from converted values for precision. // dT in F = dT_c * 1.8. dZ in 1000ft = dZ_km * 3.28084. var lapseRateImperial = lapseRateMetric * 0.54864; // 5. Determine Stability Status var status = ""; var statusColor = "#333"; var bgColor = "#fff"; if (lapseRateMetric = 0 && lapseRateMetric = 6 && lapseRateMetric <= 9.8) { status = "Conditionally Unstable"; statusColor = "#f39c12"; // Orange bgColor = "#fdebd0"; } else { status = "Absolutely Unstable (Superadiabatic)"; statusColor = "#8e44ad"; // Purple bgColor = "#ebdef0"; } // 6. Output Results document.getElementById('resMetric').innerHTML = lapseRateMetric.toFixed(2) + " °C/km"; document.getElementById('resImperial').innerHTML = lapseRateImperial.toFixed(2) + " °F/1000ft"; var statusEl = document.getElementById('resStatus'); statusEl.innerHTML = "Atmospheric Condition: " + status; statusEl.style.color = statusColor; statusEl.style.backgroundColor = bgColor; document.getElementById('resultsArea').style.display = "block"; }

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