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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 air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few ...
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 ...
es of these properties. It is a
statistical Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industr ...
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 no ...
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 product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...
,
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 ...
, 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. It employs a mathematical model of the general circulation of a planetary atmosphere or ocean. It uses the Navier–Stokes equations on a rotating sphere with thermodynamic terms ...
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
AmerifluxICOSCarboEuropeOzFluxNEON
an
iLEAPS
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 " ...
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.

## Summary

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 and sign) of a given data set. For a data set, the '' ar ...
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 le ...
between instantaneous deviation in vertical wind speed ($w\text{'}$) from the mean value ($\bar$) and instantaneous deviation in gas concentration, mixing ratio ($s\text{'}$), 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

# Software

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 computer software that is released under a license in which the copyright holder grants users the rights to use, study, change, and distribute the software and its source code to anyone and for any purpose. ...
, while others are closed-source or
proprietary {{Short pages monitor