# Eddy Covariance¶

## Algorithm for calculating flux densities of momentum, energy and scalars¶

### (I) **Some fundamentals**¶

In micrometeorology, the eddy covariance method is used to determine turbulent fluxes across a boundary layer interface, as for example, the land-atmosphere or the sea-atmosphere interface. The method is theoretically simple in concept, provided that fast response sensors (determining atmospheric parameters and scalars at high frequency) are available. It can directly determine flux densities of energy, momentum and gases or aerosol, in a semi-continuous manner. However, in dealing with a “complex system” such as the atmosphere, nothing is simple. A number of assumptions have to be taken into account and a number of pre calculation and post calculation data treatment procedures have to be carried out.

Firstly, as the name indicates, the method determines the co variation
of turbulent vertical motion of air and the vertical turbulent motion of
energy, or momentum, or mass. In describing turbulent motion one has to
deconvolute the mean value of the motion from the fluctuation of the
mean motion as can be described by the “Reynold’s deconvolution
principle”. The turbulent motion of air at any instant can be defined as
the mean value of its velocity vector (the vertical velocity in our
case) plus the value of its fluctuation from the mean. Of course the
choice of the ensemble of values to calculate this mean is described
later (in most of our cases it is 20-30 minutes as determined by the
calculated ogives, **vide infra**). Hence, for example, in eddy
covariance the product of the two means of the vertical wind velocity in
one hand (w) and the mean of a mass concentration of a scalar (s) can be
mathematically depicted as

F= \(\overline{w}.\overline{s} + \overline{w^{'}}.\overline{s^{'}} = \overline{w.s}\)

which means that the product of the two co-varying means is the mean of their products since the average of their variations are/or should always be zero (this is also a check for correctness of our calculations). Hence, the flux F of a scalar is defined as the mean of the product of the vertical wind velocity and the “value” of the scalar. The typical example here is:

**Flux of CO2 above a surface= mean of the vertical wind velocity in
meters per second times the mean concentration of CO2, in mg per cubic
meter, resulting in a flux density of**

**mg. m-2.s-1**

The convention here is that upward fluxes (from the interface) have a positive sign and downward fluxes (to the interface) have a negative sign. The flux density is conceptually the flow of mass from or to a unit area of the interface per unit time. In distinguishing the term “Flux density” from the term “Flux”, the latter is the flow of mass from a defined area for a specifically defined length of time, thus having units mass (flow) per area.

The assumptions for the above statistical calculations are numerous. The most important are discussed here. Flux calculations assume that the area under consideration has no horizontal gradient of the scalar, or otherwise, that there is a homogeneous horizontal concentration for the calculation of vertical flux. Secondly, that this assumption holds for the averaging period that we calculate flux density. Or again, otherwise, that there is no advection of scalar to this area. Thirdly, that the vertical wind velocity is determined at very high frequencies, together with scalar determination at the same high frequencies so that most of turbulent transport can be captured. This means expensive ultrasonic anemometer(s) and even more expensive dedicated sensors. Fourthly, that the sensors determine mass per unit volume or that corrections involving the “ideal gas equation” are made within the instrument or offline. Other data pretreatment and post calculations corrections are listed below:

Because of electronic and natural noise (e.g. insects interfere with the anemometer signal), data have to be “despiked”. This means that a datum peak, greater than 3 times the standard deviation of the mean ensemble value is deleted and replaced by the mean of its previous and next values. This is the simplest case.

Frequencies lower than the ones recorded and that appear in the time series, should be filtered out by a high pass filter. This means that only “high frequencies” of the co-spectra are considered because data of low frequency are due to large eddies and indicate advection. These large eddies should be filtered out. The high pass filter is initiated by the “block averaging” statistical treatment.

Planar rotation is a correction that may be needed to correct the leveling of the sonic anemometer to avoid vertical wind data contamination by horizontal wind.

The cumulative sum of the co-varying frequencies indicates at what time this sum reaches a steady value, whereby this is considered as the optimum time for ensemble averaging of the co-spectra. Such a process is called the “

**ogives representation”**.The foot print of the area that is “sampled” by the instrumentation placed above the turbulent roughness layer, is calculated after the fetch (the length of the field away from the placed sensors) is calculated. Fetch and footprint are horizontal wind velocity and atmospheric stability depended.

### (II) **Description of data input for algorithm Eddy Covariance Fluxes Calculations**¶

The input file to the algorithm should have the following format:

* Date-Time in the form: (2014-07-15 00:00:00)

* Ux (m/s): Horizontal wind velocity on the x axis, for the streamlines arriving at the directional

sonic anemometer

* Uy (m/s): Vertical to x axis horizontal wind velocity

* Uz (m/s): Vertical to the interface wind velocity

* Sonic temperature Ts (^{o}C): as measured by the sonic
anemometer and calibrated, in situ, by a hot

wire temperature sensor

* Wind Direction (deg): horizontal wind direction defined by the sonic anemometer

* Wind Speed (m/s): as determined by the sonic anemometer before deconvolution to Ux and Uy.

* Air Pressure (mbar): as measured by an in situ barometer.

* In the present examples the water vapour concentration variations are used to calculate Latent Heat flux densities.

* Scalar concentration in units of mass per unit volume e.g. mg.
m^{-3}: as measured by the fast scalar sensor, it being of the
open path (CORRECTIONS NEEDED), or of the closed path design.

*** All data should be separated by a comma.**

**An example of the ASCII file for the input of the 10Hz data is shown
below:**

2014-07-15 00:00:00,2.708,1.843,-0.093,25.33,253.4,4.551,1010,0.00177525696271233

2014-07-15 00:00:00.1,2.634,1.726,-0.149,25.35,253.4,4.36,1010,0.00177525696271233

2014-07-15 00:00:00.2,2.715,1.777,-0.198,25.36,253.4,4.492,1010,0.00177525696271233

2014-07-15 00:00:00.3,2.656,1.806,-0.225,25.38,253.4,4.462,1010,0.00177525696271233

2014-07-15 00:00:00.4,2.666,1.872,-0.296,25.45,253.4,4.538,1010,0.00177525696271233

2014-07-15 00:00:00.5,2.682,1.864,-0.293,25.33,253.4,4.546,1010,0.00177525696271233

2014-07-15 00:00:00.6,2.656,1.82,-0.121,25.33,253.4,4.476,1010,0.00177525696271233

**If one for the sake of understanding the input data, puts labels on
each column of the 10Hz data, this is depicted below. The last column
indicates the feasibility of the software to calculate flux densities of
a number of scalars. However, data input should be entered as above.**

*IMPORTANT:

1. When requested by the application, we insert numerical values in the following parameters:

a. Time period (default value in tenths of seconds: 18000 ==> Acceptable values: 3000 (5 minutes), 6000 (10 minutes), 9000 (15 minutes), 12000 (20 minutes), 15000 (25 minutes), 18000 (30 minutes). Time period depends on the values given by the ogive analysis.

b. Limit (default value): 3.5 times the standard deviation from the mean value of the ensemble. Ensemble is defined in point a. above.

c. Angle that the sonic faces the horizontal wind streamlines. For unidirectional ultrasonic anemometers this angle has to be user defined, with angle values up to 360 placed in both boxes. *CAUTION: ONLY for directional sonic anemometers an arc of 120 degrees should be considered. This means 60 degrees either side of the horizontal wind streamlines, whereby, the anemometer faces directly the streamlines. e.g. for wind coming from the north (0 degrees), arc should be from 300 degrees to 60 degrees. For wind coming from the south east (135 degrees), arc should be from 75 degrees to 195 degrees. This means that for the first example the value 300 should be placed in the first box and 60 in the second, etc. Values that are obtained beyond the 120 degrees horizontal wind streamlines arc, may give erroneous results.

d. For omnidirectional sonic anemometers values in both boxes should be the same and represent the horizontal wind direction streamlines.

2. NB: If we have a lot of empty values graphs 18 and 19 will not appear.