Ergodicity test of the eddy-covariance technique

Chen, J.; Hu, Y.; Yu, Y.; Lü, S.

doi:https://doi.org/10.5194/acp-15-9929-2015

Articles | Volume 15, issue 17

https://doi.org/10.5194/acp-15-9929-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/acp-15-9929-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 15, issue 17

Research article

|

04 Sep 2015

Research article |

| 04 Sep 2015

Ergodicity test of the eddy-covariance technique

J. Chen, Y. Hu, Y. Yu, and S. Lü

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Final revised paper (published on 04 Sep 2015)
Preprint (discussion started on 10 Jul 2014)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC C5470: 'Comments on "Ergodicity Test of the Eddy Correlation Method"', Anonymous Referee #1, 30 Jul 2014
- AC C8164: 'Respond to referee #1', Jinbei Chen, 17 Oct 2014
RC C5833: 'Review', Anonymous Referee #2, 13 Aug 2014
- AC C8172: 'Respond to referee #2', Jinbei Chen, 17 Oct 2014
AC C8161: 'Our comment', Jinbei Chen, 17 Oct 2014

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Jinbei Chen on behalf of the Authors (17 Oct 2014) Author's response Manuscript

ED: Referee Nomination & Report Request started (21 Oct 2014) by Eric Pardyjak

RR by Anonymous Referee #1 (28 Oct 2014)

RR by Anonymous Referee #3 (05 Nov 2014)

Suggestions for revision or reasons for rejection

Review of the manuscript “Ergodicity test of the eddy correlation method” by Chen et al.

General remarks
This manuscript deals with the ergodicity hypothesis for turbulence data, an often forgotten assumption behind the eddy covariance method. This manuscript proposes three new data analysis methods to evaluate the ergodic theorem for observational time series. These methods are applied to data from a more or less typical flux tower site in Nagqu, China and from the CASES-99 field campaign, where multiple turbulence towers were closely collocated. I completely agree that it is actually very important to check a data set for the ergodicity assumption if possible. However, I don’t agree that this is usually not done at all. If turbulence is stationary and homogeneous, then it is also ergodic (Galanti and Tsinober 2004). At least for stationarity, there are some well-established test procedures available that are widely applied in the micrometeorological and eddy flux community (Foken and Wichura 1996; Vickers and Mahrt 1997). The homogeneity criterion plays and important role during the site selection process for eddy towers, hoping for as homogeneous turbulent conditions as possible. Nevertheless, it is well-known, that true homogeneity can hardly be met in the real world, and even for homogeneous surfaces the turbulence field can be inhomogeneous due to turbulent organized structures (Inagaki et al. 2006; Huang et al. 2008).
Although the manuscript certainly has scientific merit, it is hard to read because major problems with the English grammar. Particularly, the introduction section needs major revisions in order to improve the use of the English language. This section is also too long and lacks clarity. It could probably be trimmed to half of its current length by applying a more concise writing style and by avoiding unnecessary repetitions. Sometimes, almost identical text passages are repeated a few lines later (e.g. 71, 89 134 etc.). The following sections starting with “theories and methods” are much more readable. The figures and tables are instructive and the major conclusions are drawn correctly. In the discussion section, I would have liked to see that the authors relate their findings more to other studies from the literature with similar topics. In general, I would recommend that this manuscript can be accepted for publication in ACP after major revisions, particularly regarding the use of the English language (e.g. singular or plural forms, use of the article ‘the’, tenses, sentence structure), have been made.

Minor comments
L48-49: This sentence cannot be understood even when ignoring grammatical mistakes.
L51: recognized instead of was recognizing
L61: Do you perhaps mean spatial average instead of average square?
L61: The correct reference is Galanti and Tsinober (2004), and plural form should be used in the following sentences
L115, L367-368: In contrast to the authors’ statement, it is NOT common practice anymore to apply linear de-trending to a time series before calculation covariances. The high-pass filtering effect of such a procedure would cause an unwanted underestimation of the total flux (Finnigan et al. 2003; Moncrieff et al. 2004). The McMillen (1988) reference presented by the authors is outdated.
L208-209: please check this sentence for English grammar
L416: a positive buoyancy effect
L446: Such numbering of paragraphes is uncommon, maybe use third order headers, e.g. 4.1.1 Verifying average ergodic theorem of eddies in different scales etc.
Section 5, Discussion:
Could you please comment on the question to what extend an analysis of a time series alone (without spatial information), such as your “average ergodic function” and your “autocorrelation ergodic function” can really be useful to evaluate the ergodicity assumption. Can non-propagating structures (Mahrt 2010) be detected by the proposed test procedures?
It would interesting to see how the results of this ergodicity test relate to the steady state test of Foken and Wichura (1996) compares statistical moments of 5 min and 30 min averaging time, or the stationarity test by Vickers and Mahrt (1997), which looks at the trend of a time series?
L800: I complete agree that the eddy covariance method is based on the ergodic assumption. However, it does not make use of Monin-Obukhov similarity theory, as it directly measures the turbulent exchange of a scalar.
L830: I completely agree that a lack of ergodicity related to the presence of large-scale eddy transport can lead to a considerable error of a tower flux measurement. This has already been pointed out by Mauder et al. (2007) or Foken et al. (2011) for example. Particulary, airborne turbulence measurements can be quite useful to determine fluxes based on spatial averaging and compare them with tower-based flux estimates.
L840: Indeed, eddy fluxes based on multi-station observation data are more likely to fulfil the ergodic assumption and therefore are less prone to error. Obviously, such spatial data sets are rare because of the big expense and the large logistical effort of such a measurement campaign, but virtual tower setups in a large-eddy simulation model can be readily employed to generate such data. Steinfeld et al. (2007) have published such a study and they came to interesting finding about the minimum required number of towers to obtain a representative flux estimate for a certain spatial domain.

References

Finnigan JJ, Clement R, Malhi Y, Leuning R, Cleugh HA: A re-evaluation of long-term flux measurement techniques, Part I: Averaging and coordinate rotation. Boundary-Layer Meteorol 107: 1-48, 2003.
Foken T, Wichura B: Tools for quality assessment of surface-based flux measurements. Agric For Meteorol 78: 83-105, 1996.
Foken T, Aubinet M, Finnigan JJ, Leclerc MY, Mauder M, Paw U KT: Results of a panel discussion about the energy balance closure correction for trace gases. Bull Amer Meteorol Soc 92: ES13-ES18, 2011.
Galanti B, Tsinober A: Is turbulence ergodic? Physics Letters A 330: 173-180, 2004.
Huang J, Lee X, Patton EG: A modelling study of flux imbalance and the influence of entrainment in the convective boundary layer. Boundary-Layer Meteorol 127: 273-292, 2008.
Inagaki A, Letzel MO, Raasch S, Kanda M: Impact of surface heterogeneity on energy imbalance. J Meteorol Soc Japan 84: 187-198, 2006.
Mahrt L: Computing turbulent fluxes near the surface: Needed improvements. Agric For Meteorol 150: 501-509, 2010.
Mauder M, Desjardins RL, MacPherson JI: Scale analysis of airborne flux measurements over heterogeneous terrain in a boreal ecosystem. J Geophys Res 112: D13112, doi:10.1029/2006JD0081332007.
Moncrieff J, Clement R, Finnigan JJ, Meyers TP: Averaging, detrending, and filtering of eddy covariance time series. In: Lee X, Massman W, Law B (eds) Handbook of Micrometeorology. A Guide for Surface flux Measurement and Analysis. Kluwer Academic Publishers, Dordrecht, pp 7-31, 2004.
Steinfeld G, Letzel MO, Raasch S, Kanda M, Inagaki A: Spatial representativeness of single tower measurements on the imbalance problem with eddy-covariance fluxes: results of a large-eddy simulation study. Boundary-Layer Meteorol 123: 77-98, 2007.
Vickers D, Mahrt L: Quality control and flux sampling problems for tower and aircraft data. J Atmos Oceanic Technol 14: 512-526, 1997.

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ED: Reconsider after major revisions (18 Nov 2014) by Eric Pardyjak

AR by Yinqiao Hu on behalf of the Authors (29 Dec 2014) Author's response Manuscript

ED: Referee Nomination & Report Request started (13 Jan 2015) by Eric Pardyjak

RR by Anonymous Referee #3 (20 Jan 2015)

RR by Anonymous Referee #1 (23 Jan 2015)

ED: Reconsider after minor revisions (Editor review) (23 Feb 2015) by Eric Pardyjak

AR by Yinqiao Hu on behalf of the Authors (05 Mar 2015) Author's response Manuscript

ED: Reconsider after minor revisions (Editor review) (16 Mar 2015) by Eric Pardyjak

AR by Yinqiao Hu on behalf of the Authors (26 Mar 2015) Author's response Manuscript

ED: Reconsider after minor revisions (Editor review) (09 Apr 2015) by Eric Pardyjak

AR by Yinqiao Hu on behalf of the Authors (16 Apr 2015)

ED: Publish subject to technical corrections (07 Aug 2015) by Rolf Sander

AR by Yinqiao Hu on behalf of the Authors (13 Aug 2015) Manuscript

Short summary

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 is relative not only to the atmospheric stratification but also to the eddy scale of atmospheric turbulence.