Solution to the problem of non-vanishing $\bar{w}$ in TEA

This repository contains data and scripts needed to reproduce the figures of Emad and Siebicke (2023)

True eddy accumulation - Part 1: Solutions to the problem of non-vanishing mean vertical wind velocity

The publication version is archived on zenodo

Abstract

The true eddy accumulation method (TEA) provides direct measurements of ecosystem-level turbulent fluxes for a wide range of atmospheric constituents. TEA utilizes conditional sampling to overcome the requirement for a fast sensor response demanded by the state-of-the-art eddy covariance method (EC). The TEA method is formulated under the assumption of ideal conditions with a zero mean vertical wind velocity during the averaging interval.
However, this idealization is rarely met under field conditions.
Additionally, unlike in EC, this assumption can not be imposed in post processing due to the real-time nature of sampling and the absence of high-frequency measurements of the scalar. Consequently, fluxes measured with the TEA method are biased with a non-turbulent advective term that scales with the scalar mean concentration.

Here, we explore the magnitude of this biased advective term and potential ways to minimize or remove it. We propose a new formulation to calculate TEA fluxes that minimizes the bias term. The new formulation shows that the magnitude of the error is constrained to $\bar{w}/{\overline{|w|}}$ when the stationarity criterion is fulfilled. Here, $w$ is the vertical wind velocity, and the overbar denotes time averaging. The error is shown to be dependent on the asymmetry of atmospheric transport, represented by the coefficient $\alpha_{c}$. Two methods of estimating the coefficient $\alpha_{c}$ are proposed, a probabilistic treatment of turbulent transport, and a method utilizing the assumption of scalar similarity. We show how other formulas for calculating the TEA flux are linked to the new formulation and explore the different corrections in a numerical simulation.

The new formulation avoids the direct dependence of the bias term on the scalar background concentration. This result increases the confidence in applying the TEA method to measuring fluxes of atmospheric constituents. This is particularly relevant to scalars with a large background concentration and a small flux. This paper is part one of a two-part series on true eddy accumulation.

Data format

Data are provided under the directory data in two different formats:

• rds: native R serialization format, convenient and recommended for loading the data into R.
• csv: for intolerability, a copy of the data is provided in csv format.

How to reproduce

Run scripts/03-create-plots.R which will call the dependency scripts and save the resulting figures in figures directory.

Metadata

Metadata for all files is stored under data/metadata. The metadata contains information about variables description and units.

Requirements

The font Carrois Gothic is required for the figures.

R packges in scripts/00-deps.R are needed. Below is a full R session info.

R session info

sessionInfo()

> sessionInfo()
  R version 4.2.1 (2022-06-23)
  Platform: x86_64-pc-linux-gnu (64-bit)
  Running under: Manjaro Linux
  
  Matrix products: default
  BLAS/LAPACK: /opt/intel/oneapi/mkl/2022.1.0/lib/intel64/libmkl_gf_lp64.so.2
  
  locale:
   [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C               LC_TIME=de_DE.UTF-8       
   [4] LC_COLLATE=en_US.UTF-8     LC_MONETARY=de_DE.UTF-8    LC_MESSAGES=en_US.UTF-8   
   [7] LC_PAPER=de_DE.UTF-8       LC_NAME=C                  LC_ADDRESS=C              
  [10] LC_TELEPHONE=C             LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C       
  
  attached base packages:
  [1] stats     graphics  grDevices utils     datasets  methods   base     
  
  other attached packages:
  [1] patchwork_1.1.1   latex2exp_0.9.4   lubridate_1.8.0   lmodel2_1.7-3     data.table_1.14.2
  [6] ggplot2_3.3.6     nvimcom_0.9-132   colorout_1.2-2   
  
  loaded via a namespace (and not attached):
   [1] magrittr_2.0.3   tidyselect_1.1.2 munsell_0.5.0    colorspace_2.0-3 R6_2.5.1        
   [6] rlang_1.0.4      fansi_1.0.3      stringr_1.4.0    dplyr_1.0.9      tools_4.2.1     
  [11] grid_4.2.1       gtable_0.3.0     utf8_1.2.2       cli_3.3.0        DBI_1.1.3       
  [16] withr_2.5.0      digest_0.6.29    assertthat_0.2.1 tibble_3.1.8     lifecycle_1.0.1 
  [21] farver_2.1.1     purrr_0.3.4      vctrs_0.4.1      glue_1.6.2       labeling_0.4.2  
  [26] stringi_1.7.8    compiler_4.2.1   pillar_1.8.0     generics_0.1.3   scales_1.2.0    
  [31] pkgconfig_2.0.3