Eddy covariance



The eddy covariance (also known as eddy correlation and eddy flux) is a key atmospheric measurement technique to measure and calculate vertical turbulent fluxes within atmospheric boundary layers. The method analyses high-frequency
wind Wind is the natural movement of atmosphere of Earth, air or other gases relative to a planetary surface, planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating ...
and scalar atmospheric data series, gas, energy, and momentum, which yields values of
flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...
es of these properties. It is a
statistical Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
method used in
meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
and other applications ( micrometeorology, oceanography, hydrology, agricultural sciences, industrial and regulatory applications, etc.) to determine exchange rates of trace gases over natural ecosystems and agricultural fields, and to quantify gas emissions rates from other land and water areas. It is frequently used to estimate
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the Multiplication, product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a dire ...
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
, water vapour, carbon dioxide and methane fluxes.Burba, G., 2013. Eddy Covariance Method for Scientific, Industrial, Agricultural and Regulatory Applications: a Field Book on Measuring Ecosystem Gas Exchange and Areal Emission Rates. LI-COR Biosciences, Lincoln, USA, 331 pp. The technique is also used extensively for verification and tuning of
global climate model A general circulation model (GCM) is a type of climate model Numerical climate models use quantitative methods to simulate the interactions of the important drivers of climate, including Earth's atmosphere, atmosphere, oceans, land surfa ...
s, mesoscale and weather models, complex biogeochemical and ecological models, and remote sensing estimates from satellites and aircraft. The technique is mathematically complex, and requires significant care in setting up and processing data. To date, there is no uniform terminology or a single methodology for the eddy covariance technique, but much effort is being made by flux measurement networks (e.g., FluxNet
to unify the various approaches. The technique has additionally proven applicable under water to the
benthic zone The benthic zone is the ecological region at the lowest level of a body of water such as an ocean, lake, or stream, including the sediment surface and some sub-surface layers. The name comes from ancient Greek, βένθος (bénthos), meaning "t ...
for measuring oxygen fluxes between the sea floor and overlying water. In these environments, the technique is generally known as the eddy correlation technique, or just eddy correlation. Oxygen fluxes are extracted from raw measurements largely following the same principles as used in the atmosphere, and they are typically used as a proxy for carbon exchange, which is important for local and global carbon budgets. For most benthic ecosystems, eddy correlation is the most accurate technique for measuring ''in-situ'' fluxes. The technique's development and its applications under water remains a fruitful area of research.

General principles

Representation of the air flow in the atmospheric boundary layer

Air flow can be imagined as a horizontal flow of numerous rotating eddies, that is, turbulent vortices of various sizes, with each eddy having horizontal and vertical components. The situation looks chaotic, but vertical movement of the components can be measured from the tower.

Physical meaning

At one physical point on the tower, at time 1, eddy 1 moves parcel of air c1 down at speed w_1. Then, at time 2, eddy 2 moves parcel c2 up at speed w_2. Each parcel has gas concentration, pressure, temperature, and humidity. If these factors, along with the speed are known, we can determine the flux. For example, if one knew how many molecules of water went down with eddies at time 1, and how many molecules went up with eddies at time 2, at the same point, one could calculate the vertical flux of water at this point over this time. So, vertical flux can be presented as a covariance of the vertical wind velocity and the concentration of the entity of interest.


The 3D wind and another variable (usually gas concentration, temperature or momentum) are decomposed into
mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude (mathematics), magnitude and sign (mathematics), sign) of a gi ...
and fluctuating components. The covariance is calculated between the fluctuating component of the vertical wind and the fluctuating component of gas concentration. The measured flux is proportional to the covariance. The area from which the detected eddies originate is described probabilistically and called a flux footprint. The flux footprint area is dynamic in size and shape, changing with wind direction, thermal stability and measurements height, and has a gradual border. The effect of sensor separation, finite sampling length, sonic path averaging, as well as other instrumental limitations, affect frequency response of the measurement system and may need a co-spectral correction, especially noticeable with closed-path instruments and at low heights below 1 to 1.5 m.

Mathematical foundation

In mathematical terms, "eddy flux" is computed as a
covariance In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the les ...
between instantaneous deviation in vertical wind speed (w') from the mean value (\bar) and instantaneous deviation in gas concentration, mixing ratio (s'), from its mean value (\bar), multiplied by mean air density (\rho_a). Several mathematical operations and assumptions, including Reynolds decomposition, are involved in getting from physically complete equations of the turbulent flow to practical equations for computing "eddy flux," as shown below.

Major assumptions

* Measurements at a point can represent an upwind area * Measurements are done inside the boundary layer of interest * Fetch/ flux footprint is adequate – fluxes are measured only at area of interest * Flux is fully turbulent – most of the net vertical transfer is done by eddies * Terrain is horizontal and uniformed: average of fluctuations is zero; density fluctuations negligible; flow convergence & divergence negligible * Instruments can detect very small changes at high frequency, ranging from minimum of 5 Hz and to 40 Hz for tower-based measurements


As of 2011 there were many software programs to process eddy covariance data and derive quantities such as heat, momentum, and gas fluxes. The programs range significantly in complexity, flexibility, number of allowed instruments and variables, help system and user support. Some programs are
open-source software Open-source software (OSS) is Software, computer software that is released under a Open-source license, license in which the copyright holder grants users the rights to use, study, change, and Software distribution, distribute the software an ...
, while others are closed-source or proprietary. Examples include commercial software with free licence for non-commercial use such as
open-source free programs such a
free closed-source packages such a


Common uses: *
Greenhouse gas emissions Greenhouse gas emissions from human activities strengthen the greenhouse effect, contributing to climate change. Most is carbon dioxide from burning fossil fuels: coal, petroleum, oil, and natural gas. The top contributors to greenhouse gas emi ...
Carbon dioxide Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon Carbon () is a chemical element with the chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetraval ...
emission monitoring *
Methane emissions Increasing methane emissions are a major contributor to the rising concentration of greenhouse gases in Earth's atmosphere, and are responsible for up to one-third of near-term global heating. During 2019, about 60% (360 million tons) of methane r ...
monitoring *Measuring water loss,
evapotranspiration Evapotranspiration (ET) is the combined processes by which water moves from the earth’s surface into the Atmosphere of Earth, atmosphere. It covers both water evaporation (movement of water to the air directly from soil, Canopy interception, ...
*Instantaneous water use efficiency *Instantaneous radiation use efficiency Novel uses: *Precision
irrigation Irrigation (also referred to as watering) is the practice of applying controlled amounts of water to land to help grow Crop, crops, Landscape plant, landscape plants, and Lawn, lawns. Irrigation has been a key aspect of agriculture for over 5,00 ...
, precision agriculture *
Carbon sequestration Carbon sequestration is the process of storing carbon in a carbon pool. Carbon dioxide () is naturally captured from the atmosphere through biological, chemical, and physical processes. These changes can be accelerated through changes in land ...
and capture monitoring *
Landfill gas Landfill gas is a mix of different gases created by the action of microorganisms within a landfill as they decompose Biodegradable waste, organic waste, including for example, food waste and paper waste. Landfill gas is approximately forty to six ...
emissions into the atmosphere *Emissions of gases displaced by
hydraulic fracturing Fracking (also known as hydraulic fracturing, hydrofracturing, or hydrofracking) is a well stimulation technique involving the fracturing of bedrock Formation (geology), formations by a pressurized liquid. The process involves the high-pressure ...
into the atmosphere *Gas leak detection and location *Methane emission from permafrost regions *Biogenic VOCs emission * Reactive trace gas exchange flux measurement

Common applications


Remote sensing Remote sensing is the acquisition of information Information is an Abstraction, abstract concept that refers to that which has the power to Communication, inform. At the most fundamental level information pertains to the Interpretation ...
is an approach to modeling
evapotranspiration Evapotranspiration (ET) is the combined processes by which water moves from the earth’s surface into the Atmosphere of Earth, atmosphere. It covers both water evaporation (movement of water to the air directly from soil, Canopy interception, ...
using an energy balance and the latent heat flux to find evapotranspiration rates. Evapotranspiration (ET) is a part of the
water cycle The water cycle, also known as the hydrologic cycle or the hydrological cycle, is a biogeochemical cycle that describes the continuous movement of water on, above and below the surface of the Earth. The mass of water on Earth remains fairly const ...
, and accurate ET readings are important to local and global models to manage water resources. ET rates are an important part of research in hydrology related fields, as well as for farming practices. MOD16 is an example of a program which measures ET best for temperate climates.


Micrometeorology focuses climate study on the specific vegetation canopy scale, again with applications to hydrological and ecologic research. In this context, eddy covariance can be used to measure heat mass flux in the boundary surface layer, or in the boundary layer surrounding the vegetation canopy. The effects of turbulence may for example be of specific interest to climate modelers or those studying the local ecosystem. Wind speed, turbulence, and mass (heat) concentration are values that could be recorded in a flux tower. Through measurements related to eddy covariance properties such as roughness coefficients may be empirically calculated, with applications to modeling.

Wetland ecosystems

Wetland vegetation varies widely and varies from plant to plant ecologically. Primary plant existence in wetlands can be monitored by using eddy covariance technology in conjunction with nutrient supply information by monitoring net CO2 and H2O fluxes. Readings can be taken from flux towers over a number of years to determine water use efficiency among others.

Greenhouse gasses and their warming effect

Fluxes of
greenhouse gasses A greenhouse gas (GHG or GhG) is a gas that Absorption (electromagnetic radiation), absorbs and Emission (electromagnetic radiation), emits radiant energy within the thermal infrared range, causing the greenhouse effect. The primary greenhouse ...
from vegetation and agricultural fields can be measured by eddy covariance as referenced in micrometeorology section above. By measuring vertical turbulent flux of gas states of H2O, CO2, heat, and CH4 among other
volatile organic compounds Volatile organic compounds (VOCs) are organic compound In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon chemical bond, bonds. Due to carbon's ability to Catenation, catenate (for ...
monitoring equipment can be used to infer canopy interaction. Landscape wide interpretations can be then inferred using the above data. High operational cost, weather limitations (some equipment is better suited for certain climates), and their resulting technical limitations may limit measurement accuracy.

Vegetation production in terrestrial ecosystems

Vegetation production models require accurate ground observations, in this context from eddy covariant flux measurement. Eddy covariance is used to measure the net primary production, and gross primary productions of plant populations. Advancements in technology have allowed for minor fluctuations resulting in a scale of 100-2000 meter measurements of air mass and energy readings. Study of the
carbon cycle The carbon cycle is the biogeochemical cycle by which carbon is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and Earth's atmosphere, atmosphere of the Earth. Carbon is the main component of biological compounds as well as ...
on vegetated growth and production is vitally important to both growers and scientists. Using such information carbon flux between ecosystems and the atmosphere can be observed, with applications ranging from climate change to weather models.

Related methods

Eddy accumulation

True eddy accumulation

The true eddy accumulation technique can be used to measure fluxes of trace gases for which there are no fast enough analysers available, thus where the eddy covariance technique is unsuitable. The basic idea is that upwards moving air parcels (updrafts) and downwards moving air parcels (downdrafts) are sampled proportionally to their velocity into separate reservoirs. A slow response gas analyser can then be used to quantify the average gas concentrations in both updraft and downdraft reservoirs.

Relaxed eddy accumulation

The main difference between the true and the relaxed eddy accumulation technique is that the latter samples air with a constant flow rate that is not proportional to the vertical wind speed.

See also

Eddy (fluid dynamics) In fluid dynamics, an eddy is the swirling of a fluid and the reverse current (water), current created when the fluid is in a Turbulence, turbulent flow regime. The moving fluid creates a space devoid of downstream-flowing fluid on the downstream ...
Ecosystem respiration Ecosystem respiration is the sum of all cellular respiration, respiration occurring by the living organisms in a specific ecosystem. The two main processes that contribute to ecosystem respiration are photosynthesis and cellular respiration. Photo ...
Evaporation Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase. High concentration of the evaporating substance in the surrounding gas significantly slows down evaporation, such as when h ...
Evapotranspiration Evapotranspiration (ET) is the combined processes by which water moves from the earth’s surface into the Atmosphere of Earth, atmosphere. It covers both water evaporation (movement of water to the air directly from soil, Canopy interception, ...
Greenhouse gas emissions Greenhouse gas emissions from human activities strengthen the greenhouse effect, contributing to climate change. Most is carbon dioxide from burning fossil fuels: coal, petroleum, oil, and natural gas. The top contributors to greenhouse gas emi ...
Heat flux Heat flux or thermal flux, sometimes also referred to as ''heat flux density'', heat-flow density or ''heat flow rate intensity'' is a flow of energy per unit area per unit time (physics), time. In SI its units are watts per square metre (W/m2). ...
* FluxNet *
Latent heat flux Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a Phase transition#Modern classifications, first-order phase ...
Transpiration Transpiration is the process of water movement through a plant and its evaporation from aerial parts, such as leaf, leaves, Plant stem, stems and flowers. Water is necessary for plants but only a small amount of water taken up by the roots is ...


Further reading

* Burba, G., 2013
Eddy Covariance Method for Scientific, Industrial, Agricultural and Regulatory Applications: a Field Book on Measuring Ecosystem Gas Exchange and Areal Emission Rates.
LI-COR Biosciences, Lincoln, USA, 331 pp. * Aubinet, M., T. Vesala, D. Papale (Eds.), 2012
Eddy Covariance: A Practical Guide to Measurement and Data Analysis.
Springer Atmospheric Sciences, Springer Verlag, 438 pp. * Foken, T., 2008. Micrometeorology, Springer-Verlag, Berlin, Germany, 308 pp. * Lee, X., W. Massman, and B. Law, 2004. Handbook of Micrometeorology. Kluwer Academic Publishers, The Netherlands, 250 pp. * Rosenberg, N. J., B. L. Blad, and S. B. Verma, 1983. Microclimate: The Biological Environment, Wiley-Interscience, 580 pp.

External links

{{Webarchive, url=https://web.archive.org/web/20160331043243/https://www.licor.com/env/products/eddy_covariance/ec_book.html , date=2016-03-31
Inter-comparison of Eddy Covariance Software

Textbooks on Eddy Covariance from Google Books
Covariance and correlation Boundary layer meteorology