Journal Pre-proof

Quality control of eddy covariance fluxes of two ecosystem types
with local flux-variance similarity functions in West Africa

Ossénatou Mamadou, Miriam Hounsinou, Djidjoho Renaud Roméo Koukoui, Jean-Martial Cohard, Simon Afouda, Romain Biron, Jean Kempf, Théodore Ouani, Basile Kounouhewa

PII: S0169-8095(24)00557-X

DOI: https://doi.org/10.1016/j.atmosres.2024.107775

Reference: ATMOS 107775

To appear in: *Atmospheric Research*

Received date: 24 April 2024

Revised date: 15 October 2024

Accepted date: 6 November 2024

Please cite this article as: O. Mamadou, M. Hounsinou, D.R.R. Koukoui, et al., Quality control of eddy covariance fluxes of two ecosystem types with local flux-variance similarity functions in West Africa, *Atmospheric Research* (2024), https://doi.org/10.1016/j.atmosres.2024.107775

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<figure><img src="image_1.png" /></figure>
# Quality control of eddy covariance fluxes of two ecosystem types with local flux-variance similarity functions in West Africa

Ossénatou Mamadou<sup>a,b,*</sup>, Miriam Hounsinou<sup>a,b,*</sup>, Djidjoho Renaud Roméo Koukoui<sup>a,b</sup>, Jean-Martial Cohard<sup>c</sup>, Simon Afouda<sup>d</sup>, Romain Biron<sup>c</sup>, Jean Kempf<sup>c</sup>, Théodore Ouani<sup>d</sup> and Basile Kounouhewa<sup>b</sup>

a) Institut de Mathématiques et de Sciences Physiques, Université d'Abomey-Calavi, BP 613 Dangbo, Bénin

b) Laboratoire de Physique du Rayonnement, Faculté des Sciences et Techniques, Université d'Abomey-Calavi, Bénin

c) Institut des Géosciences de l'Environnement, Univ. Grenoble Alpes, CNRS, IRD, INPG, Grenoble, France

d) Institut de Recherche pour le Développement, 08 BP841 Cotonou, Bénin

e) Centre d'Ecologie Fonctionnelle et Evolutive, Univ. Montpellier, CNRS, Montpellier, France

* Corresponding authors: Ossénatou Mamadou (ossenatou.mamadou@imsp-uac.org) and Miriam Hounsinou (miriam.hounsinou@imsp-uac.org)

## Highlights

* Eddy covariance data Quality Control (QC) depends on the similarity functions used.

* Turbulence development test on the vertical wind speed only is not sufficient.

* Turbulence development test on T, q and c based on local similarity functions improved the QC.

* Considering the interdependence of H, LE and Fc improves the QC of these fluxes.

## Abstract

Ecosystem capacity studies for carbon sequestration and water extraction are largely conditioned by Eddy Covariance (EC) measurement availability and quality. Our study aims at evaluating several procedures of EC data qualification. Indeed, quality control of EC data is generally ensured by stationarity and well-developed turbulence tests. The latter is based on
integral turbulence characteristic (ITC) models. In this study, we revisited the quality control
procedure using locally established ITC models for wind speed components and atmospheric
scalsars (temperature, humidity and carbon dioxide molar densities) in unstable and stable
conditions. We also considered the interdependence of flux qualities because of the
corrections applied to fluxes during their preprocessing. The analyses were carried out using
one year of data collected above a woodland forest and mixed crop sites, both situated in
Northern Benin, West Africa. From these analyzes we note that the quality flags vary
depending on the use of local or existing ITC models. Also, the test of turbulence
development on atmospheric scalars, previously neglected, is of great importance in the
quality control of data. Thus, taking into account the ITC models associated with the
atmospheric scalars established locally in the well-developed turbulence test as well as taking
into account the interdependence of the flux quality have considerably improved the standard
quality control procedure used in effectively filtering unrealistic flux data while keeping a
considerable percentage of good and medium quality data.

**Key words:** Eddy Covariance data, Integral Turbulence Characteristics, Quality control, Benin, West Africa

**1. Introduction**

Quality assurance (QA) and quality control (QC) procedures are essential for all
meteorological measurements (Foken et al., 2012). Those concerning the Eddy Covariance
(EC) measurements, are essential given the complex computational procedure and particularly
the underlying theoretical assumptions behind the EC method (Foken et al., 2012; Wutzler et
al., 2018). The required assumptions concern the stationarity conditions and the well-
developed turbulence (Aubinet et al., 2012), which must be verified during post-processing of
the EC data. Indeed, violation of these may induce systematic errors in the eddy flux
calculation from EC data (Richardson et al., 2012; Mauder et al., 2013). Dedicated tests have
been designed to filter out processed data that doesn't fulfill these assumptions (Aubinet et al.,
2012). These quality control tests are to be applied to inform on the data quality before
analyzing it for specific studies such as turbulent fluxes, ecosystem and land surface
interactions modeling, or annual water and carbon dioxide budgets.

Quality control procedures of EC flux have been proposed firstly by Foken and Wichura
(1996) and Vickers and Mahrt (1997) for momentum, sensible heat, water vapor and CO2
fluxes. They remain the most widely used in the micrometeorologist's community (Pastorello et al., 2020) despite the recent work of Papale et al. (2006) and Wutzler et al. (2018), who proposed post-processing procedures but focusing only on the CO₂ flux. The QC procedure from Foken and Wichura involves steady state and integral turbulence characteristics (ITC), which allow detection of periods when the assumptions of EC theory are not satisfied (Mauder et al., 2006, 2013; Mauder and Foken, 2004; Rebmann et al., 2005; Foken et al., 2004; Aubinet et al., 2012; Foken and Wichura. 1996). Foken and Wichura's QC procedure are also able to detect, among other things, instrumental problems likely to introduce systematic errors into the data (Mauder and Foken, 2004). The combination of these two tests proposed by Foken and Wichura (1996) gives quality indicators to be assigned to each time average (generally half-hourly) flux data. Data are thus classified as good, moderate and low quality. Low-quality data are rejected and can be gap filled according to the targeted aim (Aubinet et al., 2012; Pastorello et al., 2020; Moffat et al., 2007; Lucas-Moffat et al., 2022; Zhu et al., 2022, 2023). However, Mauder et al. (2013) have demonstrated from four TERENO (Terrestrial Environmental Observatories) datasets and one CarboEurope-IP dataset that the quality control procedure proposed by Foken and Wichura (1996) didn't correctly classify data to low-quality. Similar results have been reported by Mamadou (2014) based on two contrasting ecosystems in Benin. Furthermore, Mauder et al. (2013) showed that taking into account the interdependence of fluxes and corrections applied along the preprocessing on flux improves the results of data quality control.

In our view, several reasons may explain why this QC procedure cannot accurately qualify data of certain ecosystems. The ITC test involves comparing the observed ITC with empirical ITC models that are assumed to be universal for ideal site and turbulence conditions. However, several authors have documented ITC models, but they all show some differences due to measurement uncertainty, ecosystem-specific characteristics, and variations in the footprint associated with wind speed, direction, and measurement height (Foken et al., 1991; Panofsky et al., 1977; Moraes et al., 2005; Martins et al., 2009; Fortuniak et al., 2013; Lieu et al., 2016; Hurdebise et al., 2017; Hounsinou et al., 2022, 2023). Seasonal dependencies of empirical ITC models have also been highlighted by Hounsinou et al. (2022, 2023) above two different ecosystems in Benin. Foken and Wichura (1996) chose indeed to use the empirical ITC models determined by Foken et al. (1991) in QC procedures; these models were re-analyzed by Mauder and Foken (2004) later. The use of models re-analyzed by Mauder and Foken (2004) or any other model could bias the assignment of a flag quality to
the EC data when these models are not adequate to the ecosystem studied, as already suggested by Fortuniak et al. (2013) and Aubinet et al. (2012). Another potential reason for the failure of Foken and Wichura's (1996) quality control could be related to the fact that ITC models associated to atmospheric scalars are not taken into account due to the lack of suitable models for these variables (Mauder et al., 2013). We posit that developing local ITC models for all variables used to calculate the flux, taking into account the specificities of each ecosystem might be interesting since it could provide a better quality control of flux data.

This work aims to assess EC data quality using the quality control procedure proposed by Foken and Wichura (1996) with locally established ITC models. Our analyses are carried out with data collected above a clear woodland forest (Bellefoungou) and a mixed crop (Nalohou). Both sites are located in northwest Benin, West Africa; a region under a Sudanian climate (~ 1200 mm/year). The questions we seek to answer in the remainder of this paper are: Will quality control of EC measurements using the approach developed by Foken and Wichura (1996) give more satisfactory results if it:

- uses locally pre-established ITC models to replace the models proposed by Foken and Wichura (1996)?

- takes into account the flux interdependency management proposed by Mauder et al. (2013)?

- takes into account ITC models associated with atmospheric scalars (T, q, c)?

To this end, the next part of this manuscript is organized as follows: in the first part, we list the data pre-processing steps and present the post-processing procedure used to ensure and control the quality of the EC data; the second part is focused on the analysis and comparison of the results from the various approaches carried out to answer each of the previous research questions; the final part draws a conclusion from all these results.

# 2. Eddy covariance data acquisition and processing procedure

## 2.1. Data acquisition and pre-processing

Data were acquired over a clear woodland forest and on a mosaic of crops and fallow with an eddy covariance system, each consisting of an open-path gas analyzer (Licor 7500), and a 3D sonic anemometer (CSAT3, Campbell) operating at 20Hz and low-frequency (15 minutes) sensors. The sonic anemometer was oriented perpendicular to the main wind
directions, which are the South-West and North-East winds observed during the West African Monsoon and Harmattan, respectively (Hounsinou et al., 2023), to prevent wind perturbation by the sensor. Data pre-processing involved applying the following corrections to the high-frequency measurements (see Aubinet et al. (2012) and Mamadou (2014) for details):

* Correction of the licor drift for water vapor and CO₂ measurements (Mamadou, 2014).

* 5σ outlier detection and replacement by linear interpolations (Aubinet et al., 2012).

* Double rotation of the sonic anemometer coordinate system before variance and flux calculations (Aubinet et al., 2012).

* Time lag correction (Aubinet et al., 2012).

* Conversion of fluctuations of sonic temperature into actual temperature (Schotanus et al., 1983).

* Webb correction (Webb et al., 1980).

* Frequency correction according to Van Dijk et al. (2004).

Fluxes are calculated in 30 min periods. It is the covariance between fluctuations in the vertical component of wind speed and the fluctuation in the variable x which represents u, T, q and c (the longitudinal component of wind speed, temperature, humidity and carbon dioxide molar densities) (Aubinet et al., 2012). The 15 min low frequency data are averaged at 30 min. Each of the analysed years represents the year which presented the fewest measurements missing in the available dataset. We retained as a 'year test', for the implementation of the developed methodology, the 2014- and 2015-year, respectively, at Bellefoungou and Nalohou. It is noteworthy to recall that data acquired between 2008 and 2013 at the forest site (Bellefoungou) and between 2007 and 2013 at the mixed crop site (Nalohou) have served to establish ITC models locally (Hounsinou et al., 2022, 2023). Site information is presented in Table 1 and additional details can be also found in Guyot et al. (2012), Ago et al. (2014, 2016), Mamadou et al. (2014, 2016) and Hounsinou et al. (2022, 2023).

<table><caption>**Table 1:** Geographical and measurement conditions of study sites</caption><thead><tr><td>Site</td><td>Geographical coordinates</td><td>Ecosystem type</td><td>Canopy height</td><td>Measurement height</td><td>Period used</td></tr></thead><tbody><tr><td>Bellefoungou</td><td>9.79° N, 1.72° E, 445 m</td><td>woodland</td><td>15 m</td><td>18 m</td><td>01/01/2014 – 31/12/2014</td></tr><tr><td>Nalohou</td><td>9.74° N, 1.60° E, 449 m</td><td>mixed crop</td><td>0 – 3 m</td><td>4.95 m</td><td>01/01/2015 – 07/11/2015</td></tr><tr><td></td><td></td><td></td><td></td><td>5.40 m</td><td>07/11/2015 – 31/12/2015</td></tr></tbody></table>
## 2.2. Post-processing of Eddy covariance data

### 2.2.1. Steady State and Integral Turbulence Characteristics test

The steady state test used in this paper is given by the following equation according to Foken and Wichura (1996):

$$S_{\overline{x'w'}} = 100 \left| \frac{\overline{x'w'}^{5 \text{ min}} - \overline{x'w'}^{30 \text{ min}}}{\overline{x'w'}^{30 \text{ min}}} \right| \quad (1)$$

It estimates the changes in covariance over the 30 min considered period from the 5 min covariance.

The developed turbulence test (Mauder and Foken, 2004) for a variable $x$ noted $DT_x$ is defined according to Eq.2 from the observed and modeled normalized standard deviations ($\sigma_x/x_*$).

$$DT_x = 100 \left| \frac{\left| \frac{\sigma_x}{x_*} \right|_{\text{modeled}} - \left| \frac{\sigma_x}{x_*} \right|_{\text{observed}}}{\left| \frac{\sigma_x}{x_*} \right|_{\text{modeled}}} \right| \quad (2)$$

The observed $\sigma_x/x_*$ are calculated for each half-hour $x$ data set as the ratio of the standard deviations ($\sigma_x$) to the appropriate scale parameter ($x_*$) using field data. The modeled $\sigma_x/x_*$ are calculated for each half-hour from ITC models which are flux-variance similarity functions depending only on the atmospheric stability parameter $\zeta = (z - d)/L$ ($z$ is the measurement height, $d$ the displacement height and $L$ is the Obukhov length) according to the Monin-Obukhov Similarity Theory (MOST) (Stull, 1988; Kaimal and Finnigan, 1994; Foken, 2017). The modeled $\sigma_x/x_*$ are then calculated from the stability parameter $\zeta$ derived from field observations. The ITC models we use in this study, for the two investigated sites, are those proposed by Foken and Wichura (1996) as updated by Mauder and Foken (2004) and those established locally by Hounsinou et al. (2022, 2023). It is important to note that this is not a question of challenging the models proposed by Mauder and Foken (2004) but of testing models that take into account site effects that impact the flux-variance similarity functions as shown by Katul et al. (2011, 2013). In the work of Hounsinou et al. (2022, 2023), site effects are taken into account by an analysis by season: that is, dry season, wet season and transition phases (moistening and drying). During these seasons, wind conditions are very contrasting, leading to changes in footprint and weather conditions. The ITC models of Hounsinou et al.
(2022, 2023) have been locally built for each season and for both stable and unstable atmospheric conditions on the clear woodland (Bellefoungou) and mixed crop (Nalohou) sites. The authors showed with the Wilcoxon test that the models obtained are significantly seasonal dependent mainly during stable conditions as they take into account the seasonally contrasted wind speed and directions and the associated footprint of each flux station (see Hounsinou et al. (2022, 2023) for more details). However, all these ITC models respect the MOST whatever the atmospheric stability and the seasons.

It is relevant to mention also that high $DT_x$ values can result from non-developed turbulence conditions often observed during stable conditions, gravity wave occurrences, horizontal heterogeneity in the upwind direction, or instrumental problems (Mauder and Foken, 2004; Gash and Gulf, 1996; Pappaccogli et al., 2022; Falocchi et al., 2018; Stefanello et al., 2020). The $DT_x$ test is not applied to the atmospheric scalars $T$, $q$ and $c$ under quasi-neutral conditions when the absolute value of the thermal flux is less than 10 Wm$^{-2}$, since the ITC associated to atmospheric scalars are not well defined under these conditions (Hounsinou et al, 2022, 2023; Mauder and Foken, 2004). Beyond this condition, the test can be applied to both parameters used to determine covariance fluxes, but is often applied to:

* $\sigma_u/u_*$ and $\sigma_w/u_*$ for momentum flux.

* $\sigma_w/u_*$ and $\sigma_T/T_*$ for sensible heat flux.

* $\sigma_w/u_*$ only for latent heat and CO$_2$ fluxes.

Furthermore, at the CarboEurope meeting at Spoleto in 2004, it was decided to apply the turbulence development test to $\sigma_w/u_*$ alone, whatever the flux (Mauder and Foken, 2004), in the absence of suitable models available for atmospheric scalars (Mauder et al., 2013). As we have all the empirical ITC models previously established locally (Hounsinou et al., 2022, 2023), which are potentially suitable for testing turbulence developments, these models were implemented for two different years (2014, 2015) to examine their robustness for controlling quality of the EC data acquired over the two studied sites.

### 2.2.2. Quality flag

In this study, we use a simplified version of the quality flag attribution scheme proposed by Foken et al. (2004) issued from the CarboEurope-IP meeting, Spoleto, 2004 (Table 2). The unassigned flags due to measurement failures, filtering out the rainy data and the non-application of ITC tests under some conditions of atmospheric stratification, in particular
near-neutral conditions, are represented by Not Available ‘NA’. Post-processing of EC data consists of rejecting those whose flags were NA and 2.

<table><caption>**Table 2:** Overall Quality Flag System according CarboEurope-IP meeting, Spoleto, 2004 (Mauder and Foken, 2004)</caption><thead><tr><td>Data quality</td><td>Flag</td><td>S<sub>x'w'</sub></td><td>DT<sub>x</sub></td></tr></thead><tbody><tr><td>high quality data</td><td>0</td><td>&lt; 30</td><td>&lt; 30</td></tr><tr><td>moderate quality data</td><td>1</td><td>&lt; 100</td><td>&lt; 100</td></tr><tr><td>low data quality</td><td>2</td><td>&gt; 100</td><td>&gt; 100</td></tr></tbody></table>

Mauder et al. (2013) have shown that taking into account the interdependence of fluxes linked to the corrections of Schotanus et al. (1983) and Webb et al. (1980) in the assignment of flux quality indicators improves data quality control. These authors have proceeded as follows:

* the H flag is increased by +1, if the LE flag is equal to 2,

* the LE flag is increased by +1, if the H flag is equal to 2 and

* the Fc flag is increased by +1, if the H or LE flag is equal to 2.

Indeed, the interdependence of the fluxes is due to the fact that $w'q'$ is required to convert the buoyancy flux (associated with the sonic temperature) into sensible heat flux (associated with the real air temperature) according to Schotanus et al. (1983). Also, $w'T'$ is required to correct the H₂O and CO₂ fluxes (Webb et al., 1980).

In this study, we applied three approaches of quality control procedures, each using the empirical ITC models proposed by Foken and Wichura (1996) on the one hand, and the empirical ITC models pre-established locally by Hounsinou et al. (2022, 2023) on the other. These procedures consist in applying the Steady State (SS) test and:

(i) The Integral Turbulence Characteristics (ITC) test on $\sigma_w/u_*$ only as proposed at CarboEurope-IP meeting, Spoleto, 2004. This approach of QC procedure is noted SS ITC<sub>w</sub>(Fm) when the empirical $\sigma_w/u_*$ models proposed by Foken and Wichura (1996) are used in the ITC test, and SS ITC<sub>w</sub>(Lm) when the empirical $\sigma_w/u_*$ models established locally by Hounsinou et al. (2022, 2023) are used.
(ii) The ITC test on $\sigma_w/u_*$ only, then taking into account the interdependence of the H, LE and Fc fluxes proposed by Mauder et al. (2013). This approach is noted **SS ITCw(Fm) + IF** and **SS ITCw(Lm) + IF** when the empirical $\sigma_w/u_*$ models of Foken and Wichura (1996) and local models, respectively, are used in the ITC test.

(iii) The ITC test on the two variables used to calculate the flux covariance is followed by considering the interdependence of the H, LE and Fc fluxes. The latter approach is noted as **SS 2ITC(Fm)** and **SS 2ITC(Lm)** for $\tau$; **SS 2ITC(Fm) + IF** and **SS 2ITC(Lm) + IF** for the other fluxes, depending on whether the empirical models of Foken and Wichura (1996) and local models, respectively, are used.

The performance of each approach is evaluated by its ability to rule out outliers, which are supposed to be low quality data. In this study, we consider as outliers the values lower than the 5th percentile or higher than the 95th percentile of the considered flux data distribution. For each flux data distribution, the 5th and 95th percentiles are determined according to the time of day. In other words:

1. For each season the data are distributed according to the diurnal cycle.

2. For each 30min of this diurnal cycle, a distribution of observations is considered, which gives 48 distributions for each season.

3. For each of these distributions, the 5th and 95th percentiles are calculated.

4. Data that are outside of these 5th and 95th percentiles are considered as outliers.

Outliers are therefore identified according to the time of day.

# 3. Results and Discussion

## 3.1. Meteorological conditions

The covariance time series of $\overline{u'w'}$, $\overline{T'w'}$, $\overline{q'w'}$ and $\overline{c'w'}$ used to calculate the fluxes, as well as some meteorological variables including net radiation, wind speed, precipitation, air temperature and relative humidity are presented according to daytime and nighttime in Fig1. Before applying the QC procedure to flux data, it is important to examine periods with missing values due to instrument failures. They were 0.45% and 14.24% on average at Bellefoungou and Nalohou, respectively. We can note 50 days (i.e., from 06/06/2015 to 25/07/2015) of total lack of flux measurements at the Nalohou site. Following the West
African monsoon regime, during the years 2014 and 2015, where these observations were
collected, the dry season having started on December 05, 2013 and ended on January 20, 2014
and the 2015 dry season having lasted from December 19, 2014 to January 30, 2015. These
periods were characterized by northeasterly winds from the Sahara with speeds lower than 4
ms⁻¹ (Mamadou et al., 2014; Guyot et al., 2009). Each dry season is followed by a prolonged
moistening period during which the first rains occur, signaling the arrival of the wet season.
The wet season lasts about 6 months, from April 10 to October 19 in 2014 and from April 30
to October 31 in 2015, giving a total cumulative rainfall of 1244 mm at the Bellefoungou site
in 2014 and 1403 mm at the Nalohou site in 2015. At both sites, ~13 km separated, an
increase in daytime covariances *u'*w', *T'*w', *q'*w' and *c'*w' was observed before the wet
season. Indeed, increases in net radiation and air temperature, which can reach ~ 900 Wm⁻²
and 38°C, respectively (Fig1), favor the development of turbulence, leading to more efficient
mass and energy transfers in the atmosphere. During the wet season, the air is very humid,
especially at night, which explains the drop in air temperature that induces low values of
*T'*w'. Conversely, there is an increase in *q'*w' and *c'*w' associated with vegetation
development. Covariance outliers can be observed at both sites and for all fluxes.
<figure><img src="image_2.png" /><figcaption>**Fig.1** Time series of precipitation (P), wind speed (Ws), net radiation (Rnet), air temperature (T), air relative humidity (RH) and covariances *u'*w', *T'*w', *q'*w' and *c'*w'. The light blue and black circles represent daytime and nighttime observations, respectively. The dry season is delimited by the light grey dashed lines and the wet season by the light grey lines defined from daily absolute humidity values according to Mamadou et al. (2014).</figcaption></figure>

**3.2. Stationarity**

The results of the stationarity tests are shown in Fig.2. This figure shows, as expected under well-developed turbulence conditions, that all covariances are more stationary during the daytime (0630 – 1800 UTC) than at nighttime. In general, without distinguishing daytime from nighttime, around 77, 74, 68 and 71% of the measurements of *u'*w', *T'*w', *q'*w' and *c'*w', respectively, are stationary with $0 < S_{\overline{x'w'}} < 30$ at the Bellefoungou forest site. Following Spoleto's flag scheme (Table 2), some measurements have acceptable stationarities ($30 < S_{\overline{x'w'}} < 100$) and around 9, 9, 11 and 10% of measurements of *u'*w', *T'*w', *q'*w' and *c'*w', respectively, are non-stationary ($S_{\overline{x'w'}} > 100$). These lead to the rejection of $\tau$, H, LE and Fc
data, which are qualified as low quality whatever the flag scheme used (Foken et al., 2004;
Rebmann et al., 2005). Similar results were observed at the Nalohou mixed crop site, but the
percentage of stationary data obtained was relatively lower than that observed in the forest.
Indeed, 65, 69, 63 and 68% of the measurements of *u'*w', *T'*w', *q'*w' and *c'*w', respectively,
are stationary with $S_{x'w'} < 30$ and around 12, 10, 12 and 10% result in the rejection of the
corresponding flux data. This lower stationarity can be explained by a relative spatial
heterogeneity of this crop site (See the Footprint analysis in Mamadou et al. (2014) and
Hounsinou et al. (2023)).

<figure><img src="image_3.png" /><figcaption>**Fig.2a** Distribution of stationarity data by day and hour at Bellefoungou and Nalohou sites. Grey color indicates missing data. Green, orange and red colors indicate data whose stationarity test gave values between 0 - 30, 30 - 100 and >100%, respectively.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Fig.2b** Frequency densities for the stationarity of *x'*$w'$ covariance at the Bellefoungou (left) and Nalohou (right) sites during daytime (light blue) and nighttime (black).</figcaption></figure>

**3.3. Turbulence**
The distribution according to day and hour as well as density histograms of the test related to well-developed turbulence when using the re-analyzed empirical ITC models by Mauder and Foken (2004) and when using the local models at both sites are presented in Fig.3 a and b, respectively. One can see that when local models are used, as expected, the well-developed turbulence conditions are more frequent during the daytime than at nighttime at both sites for all variables (Fig. 3a). This is easily explained by the high solar irradiation during the daytime, which favors air buoyancy and high sensible heat fluxes (T'w' in Fig. 1). In addition, occurrence of relatively higher wind speeds during the daytime than the nighttime contributes to higher wind shear during the daytime. Buoyancy and shear are the main terms in the production of turbulence kinetic energy, so the atmosphere is generally turbulent and unstable during the daytime, while at nighttime the atmosphere is often stable, which is the case in the region (Mamadou et al., 2014). These results agree well with those of Hounsinou et al. (2023), who showed that the turbulent kinetic energy was higher during the daytime than at nighttime over the region. The ITC test used with the models re-analyzed by Mauder and Foken (2004) gave similar results as the local models for temperature on both sites, since these models are similar (Fig. 3a). However, each of the distributions of DTu (Fm) and DTw (Fm) observed during the daytime do not seem too different from what is observed at nighttime, particularly at the Nalohou site (Fig. 3a). It appears clearly from the latter that the characterization of atmospheric turbulence for the u and w components of wind speed is not well represented when using the models re-analyzed by Mauder and Foken (2004).

At the Bellefoungou site, the results obtained when using the locally established models indicated that 88, 99 and 71% of daytime data and 77, 85 and 60% of nighttime data were measured under well-developed turbulence conditions according to DTu, DTw and DTt, respectively, while the models re-analyzed by Mauder and Foken (2004) indicated lower percentages of 43, 88 and 66% of daytime data and 38, 69 and 41% of nighttime data measured under well-developed turbulence conditions according to DTu, DTw and DTt, respectively (Fig. 3b). On the other hand, at the Nalohou site, 78, 72 and 80% of daytime data and 42, 47 and 27% of nighttime data measured under well-developed turbulence conditions according to DTu, DTw and DTt, respectively, were recorded using local models. At this site, in contrast to the Bellefoungou site, higher percentages of 64, 63 and 37% of nighttime data are measured under well-developed turbulence conditions according to DTu, DTw and DTt, respectively, using the models re-analyzed by Mauder and Foken (2004). Indeed, these models indicate a higher percentage of data measured under well-developed turbulence
conditions at the Nalohou site during nighttime, compared to the locally established models (Fig. 3b). This resulted in more occurrences (based on existing data) of well-developed turbulence conditions at the Nalohou site than at the Bellefoungou site when using the models re-analyzed by Mauder and Foken (2004), despite these models showing a slightly lower percentage of measured data under well-developed turbulence conditions than local models during the daytime (Fig. 3b). Furthermore, when using local models, we observe higher occurrences of well-developed turbulence conditions at the Bellefoungou site compared to the Nalohou site, whatever the variable considered (including q and c), in agreement with the results of the stationarity test.

Regarding the water vapor (q) and carbon dioxide (c) concentrations, the results of the turbulence development test gave relatively lower general percentages (daytime and nighttime combined) of data measured under well-developed turbulence conditions than the preceding variables (u, w, T): that is, 72% and 41% during the daytime and nighttime, respectively, for variable q (70% and 46% during the daytime and nighttime, respectively, for variable c) at the Bellefoungou site and 40% during the daytime and 30% at nighttime for DTq, and 58% during the daytime and 28% at night for DTc at the Nalohou site. It is important to highlight that the turbulence development test for q and c is performed using established local models only, in the absence of the empirical models proposed by Foken and Wichura (1996) for these variables.
Bellefoungou

<figure><img src="image_5.png" /></figure>

Nalohou

<figure><img src="image_6.png" /></figure>

**Fig.3a** Distribution according to day and hour of the results of the ITC test carried out with the models proposed by Mauder and Foken (2004) (Fm) and the local models (Lm) using data from Bellefoungou and Nalohou sites. Grey color indicates missing data. Green, orange and red colors indicate data whose ITC test gave values 0 - 30, 30 - 100 and >100%, respectively.
<figure><img src="image_7.png" /><figcaption>**Fig.3b** Histograms of density frequencies for the ITC tests at the Bellefoungou and Nalohou sites using similarity functions proposed by Foken and Wichura (1996) (Fm – blue for daytime dark grey for nighttime) superimposed on that established locally (Lm – light blue for daytime and black for nighttime) for horizontal and vertical velocities, temperature, water vapor and CO₂ concentrations.</figcaption></figure>

**3.4. Analysis of quality control procedures**
The diurnal cycles of the pre-processed momentum ($\tau$), sensible heat (H), latent heat (LE) and carbon dioxide (Fc) fluxes data are shown in Figs. 4 to 7 with indications of the data rejected by rainy conditions and by the three different quality control procedures. The cycles show that the precipitation filter, previously applied to all data prior to quality control, filtered most of the outliers, particularly for LE and Fc. This filter allows disposing of 3.88% and 3.45% of the data measured during the analyzed years at the Bellefoungou and Nalohou sites, respectively.

The quality control procedures (i) (see section 2.2.2 for appellation/definition), do not reject low-quality data whatever the $\tau$, H, LE and Fc flux at both study sites (Figs 4-7). The procedures (ii), including interdependences, filter out more outliers for H, LE and Fc fluxes compared to the preceding ones (Figs 5-7). Similar results were reported by Mauder et al. (2013) at five sites. However, at our two studied sites, several outliers persist in the data after filtering these data with the quality control procedures (ii). Most of these outliers are rejected using the procedures (iii) (Figs 4-7). These findings demonstrate, therefore, that taking into account the ITC models of atmospheric scalars is highly relevant and a decisive factor in the well qualification of fluxes.

Several other tests can be added to the quality control procedures proposed by Foken and Wichura (1996) in the post-processing of flux data measured by the Eddy covariance method, such as the filter following a threshold of the mean of the vertical wind speed component, skewness and kurtosis coefficients, etc., but these are not within the scope of this study.
<figure><img src="image_8.png" /><figcaption>**Fig. 4** Diurnal cycles of dry, moistening, wet and drying seasons of the momentum flux data. The grey dots represent the measured data before data post-processing. The blue circles indicate data rejected by rainy conditions. The red triangles pointing down indicate data rejected by QC procedures performed with the models re-analyzed by Mauder and Foken (2004) (Fm) and magenta triangles pointing up indicate data rejected by QC procedures performed with the models established locally by Hounsinou et al. (2022, 2023) (Lm). Black curves represent the 5th and 95th percentiles for each data set.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig.5 Same as Fig.4 for the sensible heat flux data.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig.6 Same as Fig.4 for the latent heat flux data.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig.7 Same as Fig.4 for the carbon dioxide flux data.</figcaption></figure>

<table><caption>**Table 3:** Percentage of “outliers” data and “not outliers” data rejected by each controlling approach</caption><thead><tr><th rowspan="2">Sites</th><th rowspan="2">Procedures</th><th colspan="4">outliers</th><th colspan="4">not outliers</th></tr><tr><th>τ</th><th>H</th><th>LE</th><th>Fc</th><th>τ</th><th>H</th><th>LE</th><th>Fc</th></tr></thead><tbody><tr><td rowspan="6">Bellefoungou</td><td>(i)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>SS ITC<sub>w</sub>(Fm)</td><td>2.27</td><td>1.99</td><td>1.95</td><td>1.66</td><td>6.3</td><td>6.67</td><td>8.68</td><td>8.43</td></tr><tr><td>SS ITC<sub>w</sub>(Lm)</td><td>2.25</td><td>1.96</td><td>1.93</td><td>1.64</td><td>6.32</td><td>6.25</td><td>8.3</td><td>8.05</td></tr><tr><td>(ii)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>SS ITC<sub>w</sub>(Fm) + IF</td><td>-</td><td>2.49</td><td>2.71</td><td>2.88</td><td>-</td><td>10.07</td><td>11.01</td><td>12.96</td></tr><tr><td>SS ITC<sub>w</sub>(Lm) + IF</td><td>-</td><td>2.47</td><td>2.73</td><td>2.89</td><td>-</td><td>9.2</td><td>10.64</td><td>12.28</td></tr><tr><td>(iii)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Nalohou</td><td>(i)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>SS ITC<sub>w</sub>(Fm)</td><td>2.76</td><td>3.32</td><td>4.69</td><td>3.85</td><td>10.96</td><td>10.13</td><td>10.99</td><td>9.98</td></tr><tr><td></td><td>SS ITC<sub>w</sub>(Lm)</td><td>2.89</td><td>3.26</td><td>4.53</td><td>3.62</td><td>11.33</td><td>8.78</td><td>9.75</td><td>8.86</td></tr><tr><td></td><td>(ii)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>SS ITC<sub>w</sub>(Fm) + IF</td><td>-</td><td>4.13</td><td>5.15</td><td>4.83</td><td>-</td><td>13.32</td><td>13.7</td><td>14.96</td></tr><tr><td></td><td>SS ITC<sub>w</sub>(Lm) + IF</td><td>-</td><td>4.05</td><td>5.01</td><td>4.61</td><td>-</td><td>11.77</td><td>12.57</td><td>13.6</td></tr></tbody></table>
<table><tr><td>(iii)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>SS 2ITC(Fm) + IF</td><td>2.83</td><td>6.84</td><td>5.96</td><td>5.55</td><td>12.39</td><td>33.91</td><td>15.51</td><td>16.44</td></tr><tr><td>SS 2ITC(Lm) + IF</td><td>3.11</td><td>5.67</td><td>7.27</td><td>6.86</td><td>14.23</td><td>21.58</td><td>24.79</td><td>26.84</td></tr></table>

For $\tau$, procedures (iii) are always named SS 2ITC(Fm) + IF and SS 2ITC(Lm) + IF to conform to the other fluxes.

### 3.5. Analysis of empirical ITC models used for quality control procedures

Table 3 presents the percentage of rejected data for the different procedures and for the different sites. Considering the two procedures (i & ii), the quantity of rejected data is not too different if we use the models re-analyzed by Mauder and Foken (2004) or the local models, but the half-hourly data rejected by these two different models are not exactly the same, as can be seen on Figs.4-7. It is important to note that local models generally filter out a bit less data than the Mauder and Foken (2004) for procedures (i) and (ii) (Table 3). The results of the procedure (iii) are highly dependent on the empirical models used (Table 3, Figs. 4-7). Considering the percentages of rejected outlier data whatever the models (local or otherwise), the results from the procedure (iii) showed more satisfactory results than the other ones analyzed in this study.

The final flags from these quality control procedures (iii) (SS 2ITC(Fm) + IF and SS 2ITC(Lm) + IF) are shown in Fig.8. The most striking result is that the use of local functions give more 0 and 1 flags than the use of general functions, especially for the Bellefoungou site. For the Nalohou site, the 2 flags are always less for the use of local functions than the use of the general function, but the distribution between the 0 and 1 flags is equivalent for both functions. It is noteworthy that the percentage of flag 2 data is higher at nighttime than during the daytime for all fluxes measured at the two sites, regardless of the empirical models used. This finding can be explained by the fact that stationarity and well-developed turbulence regimes are less frequent at nighttime than during the daytime, as can be seen in Figs.2 and 3.

For the momentum flux ($\tau$), there is no issue of taking into account the interdependence of the fluxes (Table 3). The results of the SS 2ITC(Lm) and SS 2ITC(Fm) quality control procedures show that the number of flag 0 and 1 data depends on the empirical ITC models used, particularly at the Bellefoungou site (Fig.8). However, the percentages of flag 2 data obtained from the SS 2ITC(Fm) and local SS 2ITC(Lm) approaches for both daytime and nighttime data were 10.96% and 9.54%, respectively, at the Bellefoungou site, and 15.35% and 13.17%, respectively, at the Nalohou site. This means that the SS 2ITC(Lm) approach
filters out around 1% (and 2%) more of the τ data measured at the Bellefoungou (and Nalohou) site than the SS 2ITC(Fm) procedure.

For sensible heat flux, the SS 2ITC(Fm) + IF approach filters out 10.91 and 13.50% more H data than the SS 2ITC(Lm) + IF approach at the Bellefoungou and Nalohou sites, respectively. However, Fig. 5 shows some H outliers filtered out by the SS 2ITC(Lm) + IF approach and not the SS 2ITC(Lm) + IF approach, and some other outliers removed by the SS 2ITC(Fm) + IF approach and not the SS 2ITC(Lm) + IF one. It is also important to point out that the high quantity of data rejected by the SS 2ITC(Fm) + IF approach is due to the NA flags obtained at nighttime (Fig. 8). In fact, the lack of models re-analyzed by Mauder and Foken (2004) for a given value of the stability parameter under stable conditions explains the high number of NA flags at nighttime. This means that we could have some good quality H data but flagged NA that will potentially be rejected for a lack of similarity function with the SS 2ITC(Fm) + IF approach.

Furthermore, for the latent heat and carbon dioxide fluxes, the SS 2ITC(Fm) + IF approach does not take into account the ITC test on q and c due to the absence of models available for these variables in the literature. The improvement in the post-processing of LE and Fc data by the SS 2ITC(Fm) + IF approach compared with the SS ITC<sub>w</sub>(Fm) + IF approach (Figs. 6 and 7) is due to the fact that the interdependence of these fluxes with H is taken into account, since the latter benefited from both ITC tests (DT<sub>w</sub> and DT<sub>T</sub>). Nevertheless, LE and Fc data from the SS 2ITC(Fm) + IF approach contain more outliers compared with data from the SS 2ITC(Lm) + IF approach. The SS 2ITC(Lm) + IF approach could, therefore, be considered as the best procedure for effectively controlling flux data quality for our sites.
<figure><img src="image_12.png" /><figcaption>**Fig.8** Bellefoungou and Nalohou Bar plot of results for quality flags with the SS 2ITC(Fm) + IF (left) and SS 2ITC(Lm) + IF (right) approaches (for each site), separated between daytime and nighttime data.</figcaption></figure>

**3.6. Statistics on data availability after post-processing**

Figure 9 shows the percentages of available and missing data for fluxes post-treated with the SS 2ITC(Lm) + IF approach. The Bellefoungou and Nalohou sites have an average percentage of, respectively, 71% and 55% of high and medium quality flux data available. At each of these sites and, as expected, the LE and Fc data have the highest percentages of rejected data. As highlighted in the previous sections, Fig 9 confirms that measurements at the Bellefoungou site have a higher percentage of better quality data than at the Nalohou site. The heterogeneity of the Nalohou site, characterized by a mosaic of crops and herbaceous fallow, and large wind direction variability, as well as the unique characteristics of the forest site that create strong wind shear above the canopy, resulting in a mixed layer immediately above the canopy, could explain from our point of view the differences in results between these two sites.
<figure><img src="image_13.png" /><figcaption>**Fig. 9** Distribution of available and missing flux data after post-treatment with the SS 2ITC(Lm) + IF approach.</figcaption></figure>

**4. Conclusion**

Several quality control procedures were investigated in this study to enhance those proposed by Foken and Wichura (1996) to ensure adequate post-processing of flux data measured using the Eddy covariance method at two sites in northwest Benin (Bellefoungou, a woodland forest, and Nalohou, a mixed crop site). For each of these approaches, the turbulence development test was carried out with the empirical models re-analyzed by Mauder and Foken (2004) and the empirical models established locally by Hounsinou et al. (2022, 2023). Results from the two sites studied indicate that only ~10% of flux measurements have an unacceptable stationarity. The stationarity of fluxes is better verified at the Bellefoungou site than at the Nalohou site. The main result that came from this work is that turbulence development tests are highly dependent on ITC's empirical models. However, similar to the stationarity test, higher occurrences of well-developed turbulence conditions were observed at the Bellefoungou site when using local empirical ITC models. The latter indicate a higher percentage of data measured in the well-developed turbulence conditions than the models re-analyzed by Mauder and Foken (2004) at the Bellefoungou site during the daytime and nighttime, and at the Nalohou site during the daytime only.

Comparing the results obtained from different quality control approaches shows that performing the stationarity and turbulence development tests on the two variables which are
involved in flux computation using local models, while also considering the interdependence
of the fluxes, produced more satisfactory results at the two studied sites.

**Data Availability**

The analyses in this study are based on data from two AMMA – CATCH (African Monsoon Multidisciplinary Analysis – Coupling of the Tropical Atmosphere and Hydrological Cycle, doi:10.17178/AMMA-CATCH.all) observatory sites in Benin (Galle et al., 2018).

https://amma-catch.osug.fr/i-AMMA-CATCH-Donnees-in-situ

**Author contributions**

OM and MH conceptualized the manuscript and defined the methodology. MH prepared all
figures and table, processed outputs and wrote the first draft of the manuscript. All authors
wrote and reviewed the manuscript.

**Declarations of conflict interest**

The authors declare no competing interests.

**Acknowledgments**

M.H. was financially supported by the PhD grant provided by the ‘Ministère de l’Enseignement Supérieur et de la Recherche Scientifique’, Bénin, and the German Federal Ministry for Education through the German Academic Exchange Service (DAAD). OM is grateful to the Organization for Women in Science for the Developing World (OWSD); This work was carried out with the aid of a grant from UNESCO and the International Development Research Centre, Ottawa, Canada. The views expressed herein do not necessarily represent those of UNESCO, IRDC or its Board of Governors. The authors thank the three anonymous reviewers for their fruitful and helpful comments.
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Author contributions

Ossénatou Mamadou and Miriam Hounsinou conceptualized the manuscript and defined the methodology. Miriam Hounsinou prepared all figures and table, processed outputs and wrote the first draft of the manuscript. All authors wrote and reviewed the manuscript.
**Declarations of conflict interest**

The authors declare no competing interests.
Highlights

* Eddy covariance data Quality Control (QC) depends on the similarity functions used.

* Turbulence development test on the vertical wind speed only is not sufficient.

* Turbulence development test on T, q and c based on local similarity functions improved the QC.

* Considering the interdependence of H, LE and Fc improves the QC of these fluxes