Lapse rate
The lapse rate is the rate of change of an atmospheric variable, typically temperature, with increasing altitude in the Earth's atmosphere, where a positive value indicates a decrease in temperature with height.[1] This concept is fundamental in meteorology for assessing atmospheric stability and vertical motion of air parcels.[2] There are several key types of lapse rates, each describing different processes. The environmental lapse rate (ELR) represents the actual observed temperature decrease with altitude in the surrounding atmosphere, often measured using radiosondes and varying by location and time.[3] In contrast, the dry adiabatic lapse rate (DALR) is the theoretical rate at which a parcel of unsaturated air cools during adiabatic ascent, fixed at approximately 9.8°C per kilometer (or 5.5°F per 1,000 feet) due to expansion without heat exchange.[4] The moist adiabatic lapse rate (MALR) applies to saturated air parcels, where cooling is moderated by latent heat release from condensation, resulting in a lower and variable rate of about 6°C per kilometer in the lower troposphere.[2] Additionally, the standard lapse rate in the International Standard Atmosphere (ISA), used for aviation and instrument calibration, assumes a uniform decrease of 2°C per 1,000 feet (or 6.5°C per kilometer) up to 36,000 feet.[5] Lapse rates play a critical role in determining atmospheric stability, which influences weather patterns such as convection, cloud formation, and thunderstorm development.[2] The atmosphere is absolutely unstable when the ELR exceeds the DALR, promoting strong updrafts; conditionally unstable when the ELR lies between the MALR and DALR; and stable when the ELR is less than the MALR, suppressing vertical motion.[2] In aviation, deviations from the standard lapse rate affect aircraft performance, density altitude, and safety calculations.[5] These rates also inform forecasts of phenomena like inversions, where temperature increases with height, leading to stable layers that trap pollutants or fog.[1]Fundamental Concepts
Definition and Measurement
The lapse rate is defined as the negative rate of change of temperature with respect to altitude in a fluid medium such as the atmosphere, mathematically expressed as \Gamma = -\frac{dT}{dz}, where T is temperature and z is height above a reference level; a positive \Gamma indicates a decrease in temperature with increasing height.[6] This quantity is fundamental in meteorology for characterizing vertical temperature profiles and is typically expressed in units of °C/km or K/km.[2] While lapse rates encompass both the environmental lapse rate of the surrounding atmosphere and adiabatic lapse rates associated with rising air parcels, the general concept applies to any vertical temperature gradient in a stable fluid layer.[7] The term "lapse rate" originated in meteorology during the 19th century to describe atmospheric temperature variations with height, building on earlier observations.[8] Pioneering measurements were made by Horace-Bénédict de Saussure in 1783 during ascents of Mont Blanc, where he documented the first quantitative decrease in temperature with elevation.[8] In the mid-19th century, William Ferrel advanced the understanding by incorporating lapse rate effects into calculations of barometric pressure reduction to sea level, aiding in the analysis of atmospheric circulation patterns.[9] Atmospheric lapse rates are measured using a variety of in situ and remote sensing techniques to obtain vertical temperature profiles. Radiosondes, deployed via weather balloons, provide direct measurements by carrying calibrated thermistors or thermocouples that sense temperature at multiple altitudes up to about 30 km; these sensors are pre-launch calibrated in controlled chambers against reference temperatures and pressures to correct for instrumental biases and altitude-induced effects like solar heating.[10] Aircraft equipped with similar sensors offer targeted profiles during flights, often validating radiosonde data.[11] Satellite-based infrared sounders, such as those on geostationary or polar-orbiting platforms, infer temperature profiles indirectly from radiative emissions in specific spectral bands, with retrieval algorithms calibrated against radiosonde observations to achieve vertical resolution of 1-2 km.[12] Ground-based lidar systems, including Raman and differential absorption lidars, measure temperature via backscattered laser signals from atmospheric molecules, with calibration typically performed by aligning profiles to coincident radiosonde data for absolute accuracy.[13] From collected data, lapse rates are calculated using finite difference approximations for discrete measurements, such as \Gamma \approx -\frac{T_2 - T_1}{z_2 - z_1} between two altitude levels, which provides a local average gradient and is suitable for radiosonde or aircraft soundings with irregular spacing.[14] For continuous profiles from satellites or high-resolution lidars, the lapse rate can be derived by fitting a functional form (e.g., linear or polynomial) to the temperature-height data and differentiating, yielding a spatially varying \frac{dT}{dz} that captures fine-scale variations.[13] These methods ensure the computed lapse rate reflects the actual vertical structure while minimizing errors from measurement noise or sparse sampling.Types of Lapse Rates
In atmospheric science, lapse rates are categorized primarily into the environmental lapse rate and adiabatic lapse rates, with the latter subdivided based on air moisture content. The environmental lapse rate represents the actual observed temperature gradient in the atmosphere at a specific location and time, varying due to factors such as solar heating, surface conditions, and large-scale weather patterns.[2] In contrast, adiabatic lapse rates describe the theoretical temperature change of an air parcel undergoing vertical displacement without heat exchange with its surroundings; these include the dry adiabatic lapse rate for unsaturated air, which is constant, and the moist (or saturated) adiabatic lapse rate for saturated air, which varies because of latent heat release during condensation.[15] Conditional lapse rates refer to scenarios where stability depends on whether air parcels become saturated, leading to conditional instability when the environmental lapse rate falls between dry and moist adiabatic values.[16] These categories form the foundation for assessing atmospheric stability by comparing the environmental lapse rate to adiabatic rates: a subadiabatic environmental rate (less steep than dry adiabatic) indicates stability, preventing significant vertical motion, while a superadiabatic rate (steeper than dry adiabatic) promotes instability and convection.[17] Neutral stability occurs when the environmental rate matches the dry adiabatic rate for unsaturated conditions.[2] Other minor types include the potential lapse rate, which adjusts the observed temperature profile for adiabatic compression or expansion to reflect changes in potential temperature—a conserved quantity in dry adiabatic processes—and is useful for evaluating stability in non-uniform pressure environments.[18] In oceanography, analogous concepts apply to fluid dynamics, such as potential temperature gradients or adiabatic lapse rates in seawater, which account for compressibility and salinity effects to assess oceanic stability and mixing.[19]Environmental Lapse Rate
Observed Variations
The environmental lapse rate (ELR) in the troposphere averages approximately 6.5 K/km globally, as established by the International Standard Atmosphere (ISA) model used for aviation and meteorological reference.[20] This value represents a long-term mean derived from extensive radiosonde and satellite observations, reflecting the balance between radiative cooling aloft and convective mixing.[21] Vertically, the ELR profile varies significantly, often steeper near the surface within the planetary boundary layer where values can reach up to 10 K/km due to intense daytime heating and turbulence.[22] Aloft in the free troposphere, the rate typically decreases to around 5-6 K/km as convection weakens, though temperature inversions—where the lapse rate becomes negative and temperature increases with height—frequently occur, particularly in subsidence regions or at night, stabilizing the atmosphere.[23] These inversions can persist for hours or days, trapping pollutants and altering local weather patterns. Spatially, the ELR is higher in tropical regions, often ranging from 8-10 K/km near the surface due to strong solar heating and deep convection, compared to lower values of 4-6 K/km in polar areas where frequent inversions and cold surface conditions reduce the gradient.[24] Temporally, seasonal changes show steeper rates in summer (up to 7-8 K/km on average) from enhanced surface warming, while winter values are shallower (around 4-5 K/km) due to reduced insolation and stronger stability.[25] Diurnal cycles further amplify this, with lapse rates steepening during the day from solar-induced surface heating and relaxing at night toward neutral or inverted profiles.[26] Key influencing factors include surface type, with arid deserts exhibiting steeper ELRs (often exceeding 8 K/km) from rapid daytime heating compared to oceans where marine layers maintain shallower gradients (around 5 K/km) via evaporative cooling.[27] Topography enhances variability in mountainous regions, where orographic lifting can steepen near-surface rates to 7-9 K/km through adiabatic cooling on slopes.[28] Pollution and urban heat islands tend to flatten the ELR near the ground (reducing it to 3-5 K/km) by elevating surface temperatures and promoting low-level stability via anthropogenic heat and aerosols.[29] These observed ELR variations are primarily documented through long-term reanalysis datasets such as ERA5 from the European Centre for Medium-Range Weather Forecasts, which integrates global observations into a consistent 0.25° grid for deriving average profiles, and NCEP/NCAR Reanalysis 1, providing similar vertically resolved data since 1948 for assessing spatial and temporal trends.[21][30] Such datasets reveal that deviations from the adiabatic lapse rates determine atmospheric stability, with ELR exceeding dry adiabatic values indicating potential for convection.[26]Standard Atmosphere Profile
The International Standard Atmosphere (ISA) is a hypothetical atmospheric model that establishes a standardized vertical profile of temperature, pressure, and density based on average conditions at mean sea level, serving as a reference for aviation and engineering calculations. It defines sea-level values of 15°C (288.15 K) temperature, 1013.25 hPa pressure, and 1.225 kg/m³ density, assuming a dry, motionless atmosphere without turbulence or moisture.[31] In the troposphere, from sea level to 11 km altitude, the ISA incorporates a constant environmental lapse rate of 6.5 K/km, resulting in a linear temperature decrease described by the equationT = 288.15 - 0.0065 h
where T is temperature in Kelvin and h is altitude in meters. At the tropopause (11 km), temperature stabilizes at 216.65 K (-56.5°C) and remains isothermal up to 20 km in the lower stratosphere. Pressure in the troposphere follows
p = 101325 \left( 1 - \frac{0.0065 h}{288.15} \right)^{5.256}
in pascals, while density is computed via the ideal gas law
\rho = \frac{p}{R T}
with R = 287 J/(kg·K); above the tropopause, pressure decays exponentially as
p = 22632 \exp\left( -0.0001577 (h - 11000) \right)
for h in meters.[31][32] Adopted by the International Civil Aviation Organization (ICAO) in 1954 through its Manual of the ICAO Standard Atmosphere (Document 7488), the ISA provides a uniform benchmark for aircraft performance evaluations, pressure altimeter settings, and instrument calibrations in flight operations. It enables consistent global comparisons between real-world conditions and this idealized profile, supporting safety and efficiency in aviation design and planning.[31][33] The ISA approximates a global mean but overlooks extremes such as polar cold or tropical heat, as well as diurnal or seasonal fluctuations. An extension, the US Standard Atmosphere of 1976, aligns identically with the ISA up to 32 km while providing data to higher altitudes for broader aerospace applications.[34][33]