Ergodicity test of the eddy-covariance technique
The ergodic hypothesis is a basic hypothesis typically invoked in atmospheric surface layer (ASL) experiments. The ergodic theorem of stationary random processes is introduced to analyse and verify the ergodicity of atmospheric turbulence measured using the eddy-covariance technique with two sets of...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2015-09-01
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| Series: | Atmospheric Chemistry and Physics |
| Online Access: | http://www.atmos-chem-phys.net/15/9929/2015/acp-15-9929-2015.pdf |
| Summary: | The ergodic hypothesis is a basic hypothesis typically invoked in
atmospheric surface layer (ASL) experiments. The ergodic theorem of
stationary random processes is introduced to analyse and verify the
ergodicity of atmospheric turbulence measured using the eddy-covariance
technique with two sets of field observational data. The results show that
the ergodicity of atmospheric turbulence in atmospheric boundary layer (ABL) is relative not only to the
atmospheric stratification but also to the eddy scale of atmospheric
turbulence. The eddies of atmospheric turbulence, of which the scale is
smaller than the scale of the ABL (i.e. the
spatial scale is less than 1000 m and temporal scale is shorter than 10
min), effectively satisfy the ergodic theorems. Under these restrictions, a
finite time average can be used as a substitute for the ensemble average of
atmospheric turbulence, whereas eddies that are larger than ABL scale
dissatisfy the mean ergodic theorem. Consequently, when a finite time
average is used to substitute for the ensemble average, the eddy-covariance
technique incurs large errors due to the loss of low-frequency information
associated with larger eddies. A multi-station observation is compared with
a single-station observation, and then the scope that satisfies the ergodic theorem is
extended from scales smaller than the ABL, approximately 1000 m to scales
greater than about 2000 m. Therefore, substituting the finite time average
for the ensemble average of atmospheric turbulence is more faithfully approximate
the actual values.
Regardless of vertical velocity or temperature, the variance of eddies at
different scales follows Monin–Obukhov similarity theory (MOST) better if
the ergodic theorem can be satisfied; if not it deviates from MOST. The
exploration of ergodicity in atmospheric turbulence is doubtlessly helpful
in understanding the issues in atmospheric turbulent observations and
provides a theoretical basis for overcoming related difficulties. |
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| ISSN: | 1680-7316 1680-7324 |