Atmospheric Lapse Rate Calculator - Environmental
Calculate atmospheric lapse rate environmental with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Formula
ELR = -(T2 - T1) / (Z2 - Z1)
Where ELR is the environmental lapse rate in C/km, T1 and T2 are temperatures at lower and upper altitudes Z1 and Z2. Positive ELR means cooling with height. Compare to DALR (9.8) and MALR (~6) for stability.
Worked Examples
Example 1: Standard Conditionally Unstable Profile
Problem: Lower station: 25 C at 500 m. Upper station: 10 C at 2500 m. Dewpoint 15 C.
Solution: dT = 25-10 = 15 C, dZ = 2.0 km\nELR = 15/2.0 = 7.5 C/km\nDALR=9.8, MALR~6.0\nSince MALR < ELR < DALR: Conditionally Unstable\nLCL = 500 + 125*(25-15) = 1750 m
Result: ELR: 7.5 C/km | Conditionally Unstable | LCL: 1750 m
Example 2: Temperature Inversion Detection
Problem: Lower: 10 C at 200 m. Upper: 15 C at 800 m. Dewpoint 5 C.
Solution: dT = 10-15 = -5 C (warming with height)\nELR = -(-5)/0.6 = -8.3 C/km (inversion)\nAbsolutely Stable\nLCL = 200 + 125*5 = 825 m
Result: ELR: -8.3 C/km | Inversion | Absolutely Stable
Frequently Asked Questions
What is the environmental lapse rate?
The environmental lapse rate (ELR) is the actual rate at which air temperature decreases with increasing altitude in the atmosphere at a given time and place. Unlike the theoretical adiabatic lapse rates, the ELR varies constantly depending on weather conditions, time of day, season, and geographic location. It is measured directly by radiosondes (weather balloons) that record temperature at successive altitudes. The global average tropospheric lapse rate is approximately 6.5 C per kilometer, but local values can range from negative rates during temperature inversions to superadiabatic rates exceeding 10 C per kilometer near strongly heated surfaces. The ELR is the key determinant of atmospheric stability.
What is the dry adiabatic lapse rate and why is it constant?
The dry adiabatic lapse rate (DALR) of 9.8 C per kilometer describes how an unsaturated air parcel cools as it rises through the atmosphere. It is essentially constant because it depends only on the gravitational acceleration and the specific heat capacity of dry air at constant pressure. As a parcel rises it expands due to decreasing pressure, doing work on its surroundings and cooling in the process. No heat is exchanged with the environment in an adiabatic process. The DALR applies to any unsaturated parcel regardless of its initial temperature or the environmental conditions. Understanding the DALR is fundamental to determining whether the atmosphere will support or suppress vertical motion.
What is the moist adiabatic lapse rate and why does it vary?
The moist adiabatic lapse rate (MALR) describes how a saturated air parcel cools as it continues to rise above its condensation level. The MALR is always less than the DALR because condensation of water vapor releases latent heat that partially counteracts the cooling due to expansion. Typical MALR values range from about 4 C per kilometer in warm tropical air with high moisture content to nearly 9 C per kilometer in very cold polar air with little moisture. The MALR varies because warmer air holds more water vapor per degree of cooling and therefore releases more latent heat upon condensation. This variable rate is important for predicting cloud development and precipitation processes.
How does the lapse rate determine atmospheric stability?
Atmospheric stability is determined by comparing the environmental lapse rate to the adiabatic lapse rates. If the ELR exceeds the DALR (greater than 9.8 C/km), the atmosphere is absolutely unstable and any displacement will be amplified. If the ELR is between the MALR and DALR, the atmosphere is conditionally unstable, meaning instability occurs only if the air is saturated. If the ELR is less than the MALR, conditions are absolutely stable and vertical motion is suppressed. A negative ELR indicates a temperature inversion which represents extreme stability. Forecasters analyze these relationships on thermodynamic diagrams to assess the potential for convective weather development.
How do superadiabatic lapse rates develop near the surface?
Superadiabatic lapse rates, where the environmental lapse rate exceeds the DALR of 9.8 C per kilometer, develop in the lowest tens of meters above strongly heated surfaces. On hot sunny days, the ground surface temperature can exceed the air temperature by 20 C or more, creating an extremely steep temperature gradient in the surface layer. This condition is inherently unstable and drives vigorous thermal convection in the form of thermals, dust devils, and convective plumes. Superadiabatic conditions are most intense over dark dry surfaces like asphalt or plowed fields under strong solar heating with light winds. The condition is quickly erased by the turbulent mixing it generates.
How does the lapse rate change between the troposphere and stratosphere?
In the troposphere, which extends from the surface to about 8 to 16 km depending on latitude, the average lapse rate is approximately 6.5 C per kilometer due to convective mixing and radiative processes. At the tropopause, the lapse rate approaches zero, marking the boundary where convection ceases. Above the tropopause in the stratosphere, temperature actually increases with height due to absorption of ultraviolet radiation by the ozone layer, creating a strongly stable inversion that limits vertical exchange between these two atmospheric layers. This stability is why the stratosphere acts as a barrier that traps most weather phenomena in the troposphere below it.