Addressing Effects of Environment on Eddy-Covariance Flux Estimates at a Temperate Sedge-Grass Marsh

Abstract

We examined the net-ecosystem-exchange (NEE)-based annual carbon-balance estimates obtained from eddy-covariance (EC) measurements at an unmanaged sedge-grass marsh ecosystem (Třeboň, Czech Republic, 49°1′ N, 14°46′ E), seeking methods to improve the EC measurements in inhomogeneous environment. The data filtering procedure was developed using three thresholds: (a) a stationarity test; (b) a stability ${u}_{*}$-threshold; and (c) a high relative humidity RH-threshold. This procedure was tested in 2014, a year without significant floods and drought events led to a stable water table, reducing the effect of soil respiration on the EC measurements. Estimates of annual carbon-balance were reduced from 182 to 234 ± 12 gC m⁻² year⁻¹ for the initial data to 39–44 ± 8 gC m⁻² year⁻¹ after the $RH$ ≤ 95% filtering and to 24–26 ± 7 gC m⁻² year⁻¹ after the further ${u}_{*}$ ≥ 0.1 m s⁻¹ filtering. Applying the precipitation/fog threshold reduced this balance to 10–12 ± 7 gC m⁻² year⁻¹, closer to carbon neutrality. Up to 9.5% of this identified shift occurred during apparent nocturnal downslope katabatic drainage flows or plume descent coming from the nearby town of Třeboň. High-RH conditions account for up to 27% of this shift. Moreover, both conditions together account for an additional 67% of the identified carbon-balance change. Removing these non-ecosystem-related processes brings EC measurements closer to values of an unmanaged-ecosystem productivity, providing a better NEE-based estimate for the net ecosystem production. The presented procedure is applicable to EC measurements conducted at different wetlands or terrestrial ecosystems with similar conditions.

1 Introduction

We seek to identify improved ways how to process eddy-covariance (EC) data to account for environmental conditions in temperate wetlands that are incompatible with accurate EC-flux estimates. We examine data at the sedge-grass marsh part of the complex “Wet Meadows” ecosystem near the town of Třeboň, Czech Republic (49°1′ N, 14°46′ E) (CZ-wet—Integrated Carbon Observation System (ICOS) station ID, https://meta.icos-cp.eu/resources/stations/ES_CZ-Wet). Motivating this study is a number of consecutive years with apparent negative annual carbon balances obtained using conventional data processing of EC data—over the year, more carbon is released from the ecosystem than is assimilated.

Wetlands are unique ecosystems for which a critical factor is the water regime that creates a continuum gradient of depth, duration, and frequency of flooding (Brinson 1993). Based on that gradient and zonation of wetland plant communities (Casanova and Brock 2000), the distribution of the biogeochemical processes, including the carbon cycle, has been developed (Kayranli et al. 2010). Waterlogged (hydric) soils are formed under water saturation, flooding, or ponding long enough during the season to develop anaerobic conditions in the upper part of the soil profile (Richardson and Vepraskas 2001; Hurt 2013). These anaerobic conditions promote biogeochemical processes that accumulate soil organic matter. Wetland soils are rich in carbon contained primarily in organic matter. Stored carbon in the wetland soil and high primary productivity of wetland communities results in a complex carbon cycle (Reddy and DeLaune 2008).

In general, knowledge of carbon fluxes is important to understand functioning of wetland ecosystems, especially under climate change. The carbon cycle in the wetland ecosystems is usually dynamic, and wetlands can be a source or a sink of carbon in the form of CO₂ and CH₄ within a year (Knox et al. 2016). Though the carbon accumulation in wetlands occurs slowly over hundreds of years, carbon can be released rapidly over tens of years, depending on the soil disturbance and water-table changes (Dušek et al. 2009; Pavelka et al. 2016). Correctly tracking wetland fluxes is an important task given the significant amount of carbon stored in the soil potentially to be released as greenhouse gases that may accompany climate change and human activities, possibly exacerbating global climate change (Kayranli et al. 2010; Mitsch et al. 2013). Only with correct estimation of carbon fluxes obtained from wetland’ in situ measurements, the wetlands’ fundamental role in the carbon cycle can be clarified.

This surveillance is done by making continuous eddy-covariance (EC) measurements of CO₂ fluxes (Burba 2013), a method that allows for monitoring biogeochemical processes at different time scales at different levels. The eddy covariance uses the covariance between changes in vertical wind velocity and deviations in a scalar quantity (e.g. trace-gas mixing ratio, temperature). This method provides measurements of gas-emission and deposition (fluxes) as well as those of momentum, sensible-heat, and latent-heat fluxes (Aubinet et al. 2012; Burba 2013). Measured fluxes representative of specific areas (footprints) estimate the whole-ecosystem fluxes (Baldocchi 2014; Baldocchi et al. 2017).

In particular, the EC approach together with the CO₂ vertical-profile measurements allows for direct estimates of the net vertical CO₂ flux between the ecosystem and atmosphere defined as the net ecosystem exchange (NEE) subject to negligibility of advective processes (Wofsy et al. 1993; Chapin et al. 2006; Lovett et al. 2006; Rebmann et al. 2018; Reichle 2020). From the first principles by separating the fluctuating part of the continuity equation (Aubinet et al. 2012; Metzger 2018; Rebmann et al. 2018), the NEE can be written as following Eq. 1:

$$\mathrm{NEE}=\overline{{w }^{^{\prime}}{c}_{\mathrm{a}}^{^{\prime}}}+{\int }_{0}^{z}\frac{\partial {c}_{a}}{\partial t}\mathrm{d}z+{\mathrm{Adv}}_{\mathrm{hor}}+{\mathrm{Adv}}_{\mathrm{vert}}={F}_{\mathrm{co}2}+S+{\mathrm{Adv}}_{\mathrm{hor}}+{\mathrm{Adv}}_{\mathrm{vert}},$$

(1)

where ${F}_{\mathrm{co}2}=\overline{{w }^{^{\prime}}{c}_{\mathrm{a}}^{^{\prime}}}$ is the EC vertical CO₂-flux measured at the sensor height (z), $S={\int }_{0}^{z}\frac{\partial {c}_{a}}{\partial t}\mathrm{d}z$ is the storage term assessed from the CO₂-concentration (${c}_{\mathrm{a}}$) vertical-profile measurements, ${\mathrm{Adv}}_{\mathrm{hor}}$ and ${\mathrm{Adv}}_{\mathrm{vert}}$ are the terms describing the horizontal and vertical advective processes, ${w}^{^{\prime}}$ and ${c}_{\mathrm{a}}^{^{\prime}}$ are fluctuations of the vertical velocity and CO₂ concentration around their mean values, and the overbar is the time averaging for the EC-flux calculation.

The first two terms of NEE (Eq. 1) (${F}_{\mathrm{co}2}+S$) represent the net vertical CO₂ flux and at the same time is the difference between the ecosystem respiration (${R}_{\mathrm{e}}$) and the total organic carbon fixed by photosynthesis ($GPP$, gross primary production) (Wofsy et al. 1993; Chapin et al. 2006; Lovett et al. 2006 Prof. Dennis Baldocchi, personal communication 2022):

$$F_{{{\text{co2}}}} + S = R_{{\text{h}}} + \mathop \smallint \limits_{0}^{z} \left( {R_{{\text{a}}} - P} \right){\text{d}}z = R_{{\text{e}}} - GPP,$$

(1a)

in which the ecosystem respiration (${R}_{\mathrm{e}}$) includes two components: autotrophic respiration (${R}_{a}$, by plants) and heterotrophic respiration (${R}_{\mathrm{h}}$, from the soil) (Kirschbaum et al. 2001; Singh 2018).

Lovett et al. (2006) and Chapin et al. (2006) use the term net ecosystem production for this difference ($NEP = GPP - R_{{\text{e}}}$). From a biological point of view, creating new biomass (NEP > 0) is a positive process of CO₂ assimilation into organic plant tissues presented with a positive sign while NEE is presented with a negative sign owing the atmospheric surface-layer flux-measurement convention—the fluxes from the surface to atmosphere are positive. From Eq. 1 and above, the NEE–NEP relationship is:

$$NEE=-NEP+{\mathrm{Adv}}_{\mathrm{hor}}+{\mathrm{Adv}}_{\mathrm{vert}}.$$

(2)

Then, for the absolute values of NEE and NEP to equate (Eq. 2), the required condition is the inorganic-carbon sinks and sources such as inorganic-carbon advection (${\mathrm{Adv}}_{\mathrm{hor}}+{\mathrm{Adv}}_{\mathrm{vert}}$) be insignificant and can be disregarded (Chapin et al. 2006). With this underlying assumption, both NEE and NEP integrated over some time period can be directly used in ecosystem carbon-balance estimations (Verlinden et al. 2013; Baldocchi 2014).

With years of experience, mathematical approaches and processing workflows have been formalized with a clear procedure applicable to the turbulent, unstable conditions in the boundary layer (Foken and Wichura 1996; Foken et al. 2004; Papale et al 2006; Munger et al. 2012; Mauder et al. 2013). However, the following well-known limitations directly affect NEE estimates, such that the method should be carefully used in certain situations.

• Estimating nocturnal fluxes At night, the turbulence is generated wholly by surface-layer wind shear and is a subject to wind intermittency (Medeiros and Fitzjarrald 2014); and to ensure the thorough mixing in the layer below the EC system, selected events should be filtered by applying thresholds based on the friction velocity (${u}_{*}$, Hutyra et al. 2007) or the vertical velocity standard deviation (${\sigma }_{w}$Acevedo et al. 2008a; Medeiros and Fitzjarrald 2014; Jocher et al. 2020). During long calm periods, if a significant amount of data are removed by the thresholds, the direct estimation of carbon balances from EC fluxes is compromised. An alternate approach for these situations is to use the boundary-layer budget method (Moore et al. 1994; Fitzjarrald 2004; Acevedo et al. 2004, 2008b; Tóta et al. 2008) in which knowledge of the vertical profile of canopy biomass (Parker 1995; Parker et al. 2019) as well as concentration profiles are required to account for estimations of storage terms in carbon-balance equations.

• Flux estimation for the potentially inhomogeneous terrain Subcanopy drainage flows can occur in the sloped terrain due to negative buoyancy in stable conditions (Aubinet et al. 2003, 2010; Staebler and Fitzjarrald 2004; Tóta et al. 2008; Stull 2017). Under some conditions, gradients in CO₂ are such that horizontal advection occurs.

• Specific in situ conditions Carbon-dioxide flux measurements made in a wet and humid environment with high relative air humidity (RH) are prone to error and, in extremes, require air drying before conducting measurements and applying these corrections (Miller et al. 2010). It has been estimated that for RH > 92% foggy conditions occur at about 50% of cases; for air temperature below 10 °C, this fog occurrence reaches 100% (Wang and Chen 2014; Ma et al. 2014). Increasing RH from 90 to 100% and consequent fog formation causes EC-observed latent heat flux to become negative (LE < 0), while the RH decreases and fog evaporation is associated with the upward and positive EC-observed latent heat flux (Beiderwieden et al. 2008; Griffis et al. 2008; Baumberger et al. 2022; Wang et al. 2022).

• Urban surroundings The urban climate is usually more polluted (higher CO₂, NO_x, and volatile-organic-compound concentrations) than the nearby rural environment owing to flux divergence in surface layer, and a city also serves as the local heat source (especially in cold time of the year) generating a buoyant or non-buoyant plume of polluted air (Ziska et al. 2004; Oke et al. 2017). In the near-neutral and convective conditions, this plume can descent to the ground short distance from the city source downwind altering the concentration and flux measurements (Deardorff and Willis 1982, 1984; Geiger et al. 1995; Weil et al. 1997; Sorbjan and Uliasz 1999).

Moreover, for measurements to be representative, the EC system should be placed both within the height of the internal boundary layer formed by the edges of the homogeneous environment (Garratt 1990; Savelyev and Taylor 2005) and within the height from which the representative footprints should be estimated for different stability regimes (Hsieh et al. 2000; Munger et al. 2012).

The working hypotheses for our investigations are that the observed NEE > 0 (NEP < 0) anomaly at the sedge-grass marsh can occur due to two partially independent factors: (i) very high RH lead to incorrect NEE estimates and (ii) the presence of katabatic drainage flows or buoyant-plume descents from the town of Třeboň direction (representing ${\mathrm{Adv}}_{\mathrm{hor}}$ or ${\mathrm{Adv}}_{\mathrm{vert}}$ terms in Eqs. 1–2) advecting air with high CO₂ concentration and altering the representativeness of the samples.

In this study, we recalculate NEE at the sedge-grass marsh by applying (i) the selected on the base of nocturnal fluxes ${u}_{*}$ and ${\sigma }_{w}$ thresholds for separating the stable and neutral conditions and identification of potential katabatic drainage flows or buoyant-plume descents and (ii) separate high-RH periods that also affect measurements. This approach will also allow us to distinguish the importance of these conditions on NEE estimations and at the same time reduce the inaccuracy of measured NEE and related carbon balance.

2 Methods

2.1 Site Description

The sedge-grass marsh is a wetter part (1 ha) of the large wetland complex (450 ha) called “Wet Meadows” situated close to a man-made shallow lake called Rožmberk. The mean annual air temperature and mean annual precipitation for the period from 1977 to 2021 were 7.9 °C and 602 mm, respectively. The water table fluctuates in the range 0.5 m below and 1.0 m (up to 2.36 m in extremes) above the soil surface. Most frequently, the water table lies ≈ 0.03 m below the soil surface. In some years, spring or summer floods occur, usually a consequence of spring snowmelt or heavy summer rains.

For the present study, we examine data from 2014, a year with a relatively stable water-table level lacking large floods or drought events during the summer months (blue points, Fig. 1). For this year, the water level fluctuated significantly less than during the extreme years (e.g. 2002, 2006 and 2013). During the growing season (mid of April to the end of October), characterized by the presence of the carbon uptake (Fig. 12, Appendix 1) and mostly positive air temperatures (red points, Fig. 1), the water level mostly stays below the soil surface, reaching 0.35 m below the surface in June and July. During the dormant season (beginning of November to mid-April), characterized by the lack of carbon uptake (Fig. 13, Appendix 1) and negative air temperature onsets, the water level fluctuates in the range from 0.05 m above to 0.15 m below the soil surface.

Fig. 1

Air temperature (red) and water-table level (blue) for the year 2014: green area—growing season, white area—dormant season. The air temperature is fit by loess smoothing, creating a typical bell-shaped curve of the air temperature

Water is supplied and drained to the “Wet Meadows” wetland complex by the Middle channel, connected by small side canals collecting water linked to Rožmberk lake. Thus, the water level at the site is controlled by the lake water level. The presence of this channel and unique site topography makes the EC measurements susceptible to the very high air humidity (RH) events (Fig. 2) and significantly supports the accumulation of water vapour during stable or neutral conditions, especially at night all year around (Fig. 2, bottom). This favours fog formation, potentially compromising estimated NEE fluxes (Miller et al. 2010; Ma et al. 2014).

Fig. 2

Relative air humidity (RH) event distribution over the year 2014, growing and dormant seasons separately during the (light) day and (dark) night periods. The numbers above bars are portions of the RH counts in percentage

Vegetation of the sedge-grass marsh is dominated by tall sedges (Carex acuta, Carex vesicaria) and hydrophilic grasses (mostly Calamagrostis canescens, Phalaris arundinacea), creating a community classified as the association Caricetum gracilis (Almquist 1929; Květ et al. 2002; Prach 2008; Mejdová et al. 2021). The tall sedges develop a distinct stand pattern of sedge tussocks (Honissová et al. 2015; Vítková et al. 2017; Mejdová et al. 2021).

The site topography of the “Wet Meadows” wetland complex represents a flat shallow valley stretching in a south-east–north-west direction down towards the lake, surrounded by 20–50 m elevations on both the east and west (Fig. 3a). The central area around the EC tower (beige circle) and the 90%-footprint (dark blue circle surrounding the beige circle) is mostly flat with a very mild slope to the north-west. The town of Třeboň is located near the edge of a cliff about 1.5 km south-east of the site, elevated about 20 m. More details about the site are in Dušek et al. (2009, 2012, 2017).

Fig. 3

“Wet Meadows” complex wetland ecosystem: a topography, the beige black-filled circle at the bottom of the shallow valley (blue narrow indulation in between of the yellow and red elevations)—the sedge-grass marsh site with the EC tower, the dark-blue circle surrounding the beige circle—EC 90%-footprint extension; black polygon—the town of Třeboň extension; b wind rose 2014 year for the sedge-grass marsh with the directions towards the town of Třeboň and the lake Rožmberk

The distribution of the measured wind directions for the strongest wind velocities generally coincides with the direction of the shallow valley—the high elevation edges of the valley block the winds coming from north-east and south-south-west (Fig. 3a and b). At the same time, there is a strong lobe of the slow wind velocities (0–2 m s⁻¹) from direction about 200°, facilitating potential nocturnal drainage flows (Stull 2017) arising down from the town of Třeboň, possibly advecting air from the town to the site, potentially compromising the EC-flux measurements.

2.2 Flux-Tower Measurement Systems

The sedge-grass marsh station belongs to the European network as an Associated ICOS (Integrated Carbon Observation System) station in different ecosystems equipped as a standard eddy-covariance (EC) site that also includes precise meteorological measurements. The flux-tower location and operation is conducted in accordance with the ICOS guidelines and protocols (http://www.icos-etc.eu/icos/documents/instructions). The CNR4 radiometer measures four components of net radiative flux: $L \uparrow$—longwave up, $L \downarrow$—longwave down, $S \uparrow$—shortwave up, $S \downarrow$—shortwave down. Licor 190R quantum sensors measure photosynthetically active radiation: PAR $\uparrow$—up, PAR $\downarrow$—down. The eddy-covariance system consists of: a Gill HS-50 sonic anemometer that measures 3D wind velocities (u, v, w) and temperature (T), and Licor-7200 enclosed-path gas analyser that measures CO₂ concentration (c_a) and specific humidity (q). The vertical profiles measure the air temperature (T) and relative humidity (RH) (Table 1). Other environmental measurements include soil-temperature profile and water-table and precipitation measurements. These environmental data were logged digitally on a datalogger (EMS, Brno, Czech Republic) each 30 s, and the averages over 30-min intervals (60 measurements) were stored (Dušek et al. 2009, 2012, 2017).

Table 1 Sedge-grass marsh (CZ-wet) measurement setup based on ICOS recommendations and guidelines (http://www.icos-etc.eu/icos/documents/instructions)

Given the ≈ 1-m vegetation height and measurement levels (Table 1), the footprint areas are: for the EC system ≈ 1000 m² (Kljun et al. 2015); for the $S\uparrow$ ≈ 3700 m²; for the $L\uparrow$ ≈ 400 m² (CNR 4 has 170° and 150° field of view for the shortwave and longwave upwelling-radiation sensors, respectively, https://www.kippzonen.com/Download/576/Kipp-Zonen-Product-Catalogue).

The sedge-grass marsh EC system is installed at 2.5 m above the ground level following guidance from the footprint estimates. It is elevated at least 1.5 m above the vegetation, placing it both above the roughness sublayer (1–5 roughness heights; Finnigan 1985; Katul et al. 1999) and above the internal boundary layer (≈ 1.4 m above the grass height) generated by surrounding non-homogeneous environment (Garratt 1990; Jegede and Foken 1999; Savelyev and Taylor 2005). Jegede and Foken (1999) internal-boundary-layer height estimates for this location potentially place the EC system into the unperturbed airflow above it. These all make the EC system susceptible to the possibly incorrect flux measurements in nocturnal stratified conditions, when the air advected from the outside environment may not be representative of the sedge-grass marsh itself.

2.3 Data Processing

For the initial data processing in EddyPro7™ (LI-COR Biosciences Trademarks) software, we apply the minimalistic processing scheme including the following steps:

• Spike removal with a Median-Absolute-Deviation (MAD) filter (Mauder et al. 2013);

• 2D coordinates rotation for wind velocity components to align the u-direction with the mean flow and make $\overline{v}=0$ and $\overline{w}=0$ (Kaimal and Finnigan 1994);

• WPL corrections of net-ecosystem-exchange CO₂ flux (NEE) for the sensible-heat (H) and evapotranspiration (E) fluxes (Webb et al. 1980) applicable for the Li-7200 enclosed-path gas analyser.

The time-lag correction (≈ 0.3 s) for the Li-7200 enclosed-path gas analyser was not applied due to the short tube length (the similar short-pipe gas-analyser design we encountered at the km-67 Large Scale Biosphere–Atmosphere Experiment (LBA) site located in the Tapajós National Forest, Brazil (2.86°S, 54.96°W), where not accounting for 1—2 s time lags reduced the fluxes < 2%; Kivalov and Fitzjarrald 2019).

We examined the spectral-correction schemes in EddyPro7™ to correct CO₂ fluxes for high-RH conditions (Ibrom et al. 2007a, b; Fratini et al. 2012) and found that they produce larger annual carbon-balance inaccuracy than if the corrections were not applied, probably due to the overcorrection of the nocturnal high-RH events. Therefore, we elected not to focus on these corrections in this study.

Due to the lack of the CO₂ vertical-profile measurements, we estimate $NEE={F}_{\mathrm{CO}2}$ (Eq. 1) without the storage term ($S$). However, due to the stable water table in the 2014 year of investigation (see Sect. 2.1) the possible CO₂ soil efflux affecting the storage term ($S$) should be largely reduced ensuring the feasibility of our $NEE={F}_{\mathrm{CO}2}$ estimation. The storage term in EddyPro7™ is being estimating through the single-point concentration-change measurements at the EC level allowing some S-correction to be applied as well (Aubinet et al. 2012; Montagnani et al. 2018; Xu et al. 2019).

2.4 Steps to Improve Flux-Estimation results

2.4.1 ${u}_{*}$and ${\sigma }_{w}$ Threshold Filtering

The rationale to use both friction-velocity (${u}_{*}$, Eq. 3a) and standard-deviation of vertical velocity (${\sigma }_{w}$, Eq. 3b) thresholds is that in turbulence-kinetic-energy (TKE) equation ${u}_{*}$ as a part of the shear-production term is the measure of wind-induced forced convection opposite to the buoyancy-production term measuring convection due to sensible heating (Stull 1988; Wyngaard 2010), while ${\sigma }_{w}^{2}$ through the integration of the power spectrum (${S}_{ww}$) over all frequencies (f) is proportional to the total energy available in turbulence due to both forced convection and buoyancy:

$${u}_{*}=\sqrt{\left|\overline{{u }^{^{\prime}}{w}^{^{\prime}}}\right|},$$

(3a)

$${\sigma }_{w}^{2}={\int }_{-\infty }^{\infty }\left|{S}_{ww}\left(f\right)\right|\text{d}f.$$

(3b)

.

The EddyPro7™ software applies two tests to filter out the eddy-covariance data: the stationarity test (STT, Eq. 4a) and the integral turbulence-characteristic test (ITCT, Eq. 4b) (Panofsky et al. 1977; Hicks 1981; Foken and Wichura 1996; Foken et al. 2004; Foken 2017). The STT checks the difference between the 30-min-based (${F}_{30\mathrm{min}}$) and the sum of 5-min-based (${F}_{5\mathrm{min}}$) EC fluxes for the same 30-min period. This flux difference arises due to the low-frequency losses occurred for the smaller time-averaging base (Sakai et al. 2001). The ITCT checks the difference in the similarity relationship estimating the dimensionless ratio (${\sigma }_{w}/{u}_{*}$) through the surface-layer stability parameterisation ($z/L$), where z is the height of the measurements and L is the Obukhov length (Monin and Obukhov 1954):

$${F}_{30\mathrm{min}}\approx \frac{1}{6}\sum {F}_{5\mathrm{min}},$$

(4a)

$$\frac{{\sigma }_{w}}{{u}_{*}}\approx f\left(\frac{z}{L}\right)\approx {a}_{1}{\varphi }_{m}{\left(\frac{z}{L}\right)}^{{b}_{1}}\approx 1.3{\left(1-2\frac{z}{L}\right)}^{1/3}.$$

(4b)

Tests assign 0 to the best-quality-data, 1 to the good-quality-data, and 2 to the bad-data flags; a finer data-quality division from 1 to 9 (smaller–better) has also been suggested (Foken and Wichura 1996; Foken et al. 2004). The best-quality-data flag is assigned if the terms in STT differ less than 30% and in ITCT differ less than 20%. The bad-data flag is assigned if larger than 70% difference occurs in both tests. However, the acceptable difference in STT (Eq. 4a) can be as large as 40% (Sakai et al. 2001; Doughty and Goulden 2008). This relaxes Foken and Wichura (1996) and Foken et al. (2004) constraints allowing some good-quality data (4–5) to be used equally with the best-quality data (1–3).

The difficulty of defining the ${u}_{*}$ and ${\sigma }_{w}$ thresholds for nocturnal-flux estimates is to identify conditions when the surface layer is mixed throughout, which is unique for each site due to terrain topography, surface of canopy roughness, and place of measurement factors (Foken and Wichura 1996). Foken and Wichura (1996) noted that ITCT (Eq. 4b) could not be used for scalars. This mechanism can be well described through the changes in correlation coefficients (${r}_{Xw}={F}_{X}/{\sigma }_{{X}^{^{\prime}}}{\sigma }_{{w}^{^{\prime}}}$) in Kivalov and Fitzjarrald (2019, Fig. 15), in which the ${u}_{*}$ correlation coefficient (${r}_{uw}={u}_{*}^{2}/{\sigma }_{{X}^{^{\prime}}}{\sigma }_{{w}^{^{\prime}}}\approx {u}_{*}^{2}/{\sigma }_{{w}^{^{\prime}}}^{2}$) was shown to be inversely proportional to ITCT (squared) and is practically independent of buoyancy, while the scalar correlation coefficients strongly increase when buoyancy and organised convection increase. This indicates strong dependence of scalar fluxes on the change in organised transport by buoyancy. Moreover, since ${\sigma }_{w}$ often yields more consistent results over smaller time averages than does ${u}_{*}$ (Wyngaard 2010) it is often used to estimate ${u}_{*}$ in the Monin–Obukhov similarity relationships (Acevedo et al. 2008a). However, this similarity in surface roughness sublayer fails due to the surface roughness affecting its structure (Simpson et al. 1998; Zilitinkevitch et al. 2006). This makes ITCT unsuitable for studies in this sedge-grass marsh, where the measurement system is located close to the very rough tussock surface, limiting the ability to distinguish between the turbulence conditions as identified by the ${u}_{*}$ and ${\sigma }_{w}$ thresholds (Fig. 4).

Fig. 4

Comparison of a friction-velocity (${u}_{*}$, Eq. 3a) and b standard-deviation of vertical velocity (${\sigma }_{w}$, Eq. 3b) values with ITCT (flag_w from EddyPro7™) for the sedge-grass marsh shows that the later one cannot distinguish between the turbulence conditions identified by the ${u}_{*}$ and ${\sigma }_{w}$ (1–3 best-quality data; 4–6 good-quality data by Foken et al. 2004)

A closer look at the daily cumulative CO₂-flux behaviours with the change in the ${u}_{*}$ and ${\sigma }_{w}$ thresholds for the sedge-grass marsh for different RH (90–100%) shows that even though being different these thresholds are directly linked for ${u}_{*}$ < 0.15 m s⁻¹ (Fig. 5) by a simple approximation, ${1.2u}_{*}={\sigma }_{w}$ (red lines). It can be seen that above ${u}_{*}$≈ 0.15 m s⁻¹ the ${\sigma }_{w}$ threshold is no longer important. In the following, we use ${1.2u}_{*}={\sigma }_{w}$ to simplify our filtering to ${u}_{*}$ threshold only.

Fig. 5

${u}_{*} \mathrm{and} {\sigma }_{w}$ threshold relationships on the daily cumulative CO₂ fluxes for growing season; the red line ${1.2u}_{*}={\sigma }_{w}$ represents the equivalent behaviour for both thresholds; tiles—different RH [%] conditions specified

Because the stationarity test gives the important information about the 30-min flux-stability conditions, in the filtering approach we use together STT = 40% (both 0 and 1 data quality is partially allowed) and ${u}_{*}$ = 0.1 m s⁻¹ thresholds. The ${u}_{*}$ = 0.1 m s⁻¹ threshold is chosen to remove positive carbon uptake incorrectly “occurred” at nights, when there is no CO₂ uptake by the photosynthesis (blue dots, Fig. 6: left). This approach also takes care of the flux outliers that occurred in stable and neutral conditions and during calm periods when the EC system is not reliable (Fig. 6: left—before and right—after the ${u}_{*}$ filtering). At the same time, the technique provides us with ≈10% more data for the analysis than had we used only the level 0 (best-quality) data that still needed ${u}_{*}$ filtering. It should be noted that the automatic ${u}_{*}$-threshold identification approach based on the moving-point test (MPT, Gu et al. 2005; Papale et al. 2006) produces a lower ${u}_{*}$= 0.078 threshold, thus keeping some nocturnal carbon uptake intact (Fig. 6: centre, blue negative flux values).

Fig. 6

Application of the ${u}_{*}$-filtering approach to the growing (upper row) and dormant (lower row) season 30-min-based CO₂ fluxes (${F}_{\mathrm{CO}2}$) for good-quality data: (left) unfiltered; (centre) after MPT (Gu et al. 2005; Papale et al. 2006) ${u}_{*}$ filtering; (right) after the ${u}_{*}$ = 0.1 m s⁻¹ filtering applied; red—day-time and blue—nocturnal fluxes

Using ${1.2u}_{*}={\sigma }_{w}$, the identified ${u}_{*}$ = 0.1 m s⁻¹ threshold is equivalent to ${\sigma }_{w}$ = 0.12 m s⁻¹ threshold, 20% larger than the ${\sigma }_{w}$ = 0.1 m s⁻¹ threshold suggested by Medeiros and Fitzjarrald (2014) to deal with intermittency in the nocturnal surface layer above grassland and agricultural-field ecosystems, ensuring that our ${u}_{*}$ = 0.1 m s⁻¹ threshold correctly separates the unstable regime. The same ${u}_{*}$ = 0.1 m s⁻¹ low-turbulence separation threshold is used for a soybean study (Griffis et al. 2008), and the larger ${u}_{*}$ = 0.15 m s⁻¹ threshold is identified from the decreasing ${u}_{*}$–NEE-graph feature for the coastal-wetland study (Han et al. 2013; Fig. 3; Zhong et al. 2016). Note that this decreasing ${u}_{*}$–NEE-graph feature can be the indirect representation for accounting of the high-RH events (see Fig. 7).

Fig. 7

Daily cumulative CO₂-flux change due to RH change for June (top) and July (bottom); left—${u}_{*}=0$ m s⁻¹ no filtering; right—${u}_{*}=0.1$ m s⁻¹ filtering; red box—unreliable fluxes due to lack of continuous diurnal data; legend—QC data colour scheme

2.4.2 Relative Air Humidity Threshold Filtering

That the environmental RH significantly affects the EC-measured CO₂ and water-vapour fluxes has led to the development of spectral-correction schemes to readjust the fluxes for different RH conditions based on similarity principles (Ibrom et al. 2007a, b; Mammarella et al 2009; Fratini et al 2012; Runkle et al 2012; Nordbo and Katul 2013). However, when we tried the Ibrom- and Fratini-based corrections in EddyPro7™, the results were unsatisfactory, increasing the annual carbon-balance inaccuracy possibly due to the overcorrection of the nocturnal fluxes measured predominantly when RH > 95% (Fig. 2). Another possible issue is the applicability of similarity principles to the sedge-grass marsh site (see discussion above). The proper RH threshold has to be chosen for our analysis.

A closer examination of the flux change due to RH-level change reveals that there is a strong positive jump in CO₂ fluxes when RH approaches 100% (Fig. 7). When RH is reduced below 97–98%, there is a plateau at which CO₂ fluxes are stabilised, making them plausible candidates to be correct estimates.

However, when RH is reduced below 95%, the number of records is significantly reduced as well, especially at night time when up to 80% of the obtained data is associated with the RH > 95% (Fig. 2) and has to be filtered out, and the observed fluxes become inconsistent due to lack of the available continuous diurnal data for averaging (there are abrupt jumps in the fluxes when RH is further reduced). Even though the RH = 98% threshold is suitable for the drier soybean field (Griffis et al. 2008), for the sedge-grass marsh we must stay below 95–96% RH to obtain the representative (by reaching a RH-independent plateau) daily averaged results.

It should be noted that after the CO₂ fluxes associated with the high-RH values are removed, both the ${u}_{*}=0$ m s⁻¹ and ${u}_{*}=0.1$ m s⁻¹ filtered fluxes are close for the best-quality data. However, for the good-quality data the ${u}_{*}=0.1$ m s⁻¹ filtering is essential, bringing the CO₂-fluxes computed from both best- and good-quality data on the same level to proceed with the analysis.

The difference in June–July daily cumulative CO₂-flux change with RH is traced to the difference of the in situ water-table levels for different RH. In July, the water table was more stable and closer to the soil surface than in June (see Fig. 1), which led to more consistent RH < 95–97% results. The June fluxes could be possibly affected by the higher soil respiration due to lower water levels (Pavelka et al. 2016).

3 Results

3.1 CO₂ Directional Fluxes and Concentrations: High RH and Night-Time Advection from the Town of Třeboň Direction

The town of Třeboň is located south-west of the sedge-grass marsh—a predominant direction of the lobe of 0–2 m s⁻¹ speed winds (Fig. 3b). A closer examination of the wind and CO₂-flux roses both during the growing and dormant seasons (Fig. 3b; Online Resource, Figs. S1–S6) revealed more details about the occurrences of this lobe and the associated CO₂ flux and RH distributions.

From the site-terrain topography (Fig. 3a), we selected two directions with significantly different conditions affecting CO₂ fluxes and concentrations: the direction from the town of Třeboň (190 to 240 degrees, Fig. 3b) characterized by the 20-m change in elevation across the valley and urban surroundings; and the direction from Rožmberk lake (330 to 10 degrees, Fig. 3b) characterized by the flat surface along the valley and rural environment. We examined the change of CO₂ concentrations and CO₂ fluxes with the horizontal wind velocity $U=\sqrt{{u}^{2}+{v}^{2}}$ (Fig. 8a, b), the surface-layer stability $\left(z-d\right)/L=-\left(z-d\right)kg\overline{{w}^{^{\prime}}{\theta }^{^{\prime}}}/{u}_{*}^{3}{\theta }_{v}$ (Fig. 8c, d) calculated from the EC-measured ${u}_{*}$ and kinematic heat flux ($\overline{{w}^{^{\prime}}{\theta }^{^{\prime}}}$), and the gradient buoyancy $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$ (Fig. 8e, f) calculated from the vertical virtual potential-temperature (${\theta }_{v}$) profile taken at 1 and 4-m tower heights (z) and by this being independent from the EC measurements. $\overline{{w}^{^{\prime}}{\theta }^{^{\prime}}}\approx -{K}_{\theta }\Delta {\theta }_{v}/\Delta z$ through ${K}_{\theta }$—turbulent diffusion coefficient for the heat flux. Note that the square root from the minus of the gradient-buoyancy expression is the Brunt–Väisälä frequency ($N=\sqrt{\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z}$), often used as a measure of the stability within a statically stable environment (Stull 1995) and the upper bound frequency for the internal gravity waves (Gill 1982).

Fig. 8

Growing-season (left) and dormant-season (right) CO₂-concentration and CO₂-flux (F_CO2) comparison for Třeboň and Rožmberk directions for good-quality data: a, b by the horizontal wind velocity (U), c, d by the surface-layer stability ($(z-d)/L$), (E, F) by the gradient buoyancy ($-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$); red—daytime, blue—nighttime, black—stable-conditions filtering (${u}_{*}$ < 0.1 m s⁻¹); purple—RH > 97% filtering

Comparing winds from the Třeboň and Rožmberk directions during growing season, we found that from Třeboň there was a strong nocturnal inflow of CO₂-rich air (500—1200 ppm) accompanied by high positive and negative CO₂ fluxes (7–25 μmol m⁻² s⁻¹ in magnitude) during very low wind velocities U < 0.5 m s⁻¹ associated with RH > 97% (purple points) and ${u}_{*}$< 0.1 m s⁻¹ (black circles) and occurred mostly during neutral and stable conditions $\left(z-d\right)/L$ > 0 with negative buoyancy $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$ < − 0.005 s⁻².

Similarly comparing Třeboň and Rožmberk wind directions during the dormant season, we found that from Třeboň there was a smaller nocturnal inflow of CO₂-rich air (500–750 ppm), accompanied by high positive and negative CO₂ fluxes (7–20 μmol m⁻² s⁻¹ in magnitude) with very low wind velocities U < 0.7 m s⁻¹ associated with RH > 97% (purple points) and ${u}_{*}$ < 0.1 m s⁻¹ (black circles) and occurred mostly during neutral and stable conditions $\left(z-d\right)/L$ > 0 with negative buoyancy $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$ < − 0.005 s⁻².

There is little such CO₂ inflow observed from the rural Rožmberk-lake direction for RH < 97% and ${u}_{*}$< 0.1 m s⁻¹ (black and blue circles are on the same levels) in both seasons.

After RH > 97% (purple points) and ${u}_{*}$< 0.1 m s⁻¹ (black circles) conditions are filtered out, the remaining CO₂ concentrations (360–450 ppm) and CO₂ fluxes look similar for winds from both Třeboň-town and Rožmberk-lake directions:

• during the growing season: daytime: CO₂ fluxes 0 to − 20 μmol m⁻² s⁻¹; stability $\left(z-d\right)/L$ < 0; buoyancy $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$ > 0 s⁻² and night time: CO₂ fluxes 0–7 μmol m⁻² s⁻¹; stability 0 < $\left(z-d\right)/L$  < 0.2; buoyancy − 0.001 < $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$  < 0 s⁻²;

• during the dormant season: daytime: CO₂ fluxes 0–4 μmol m⁻² s⁻¹; stability $\left(z-d\right)/L$ < 0; buoyancy $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$ > 0.005 s⁻² and night time: CO₂ fluxes 0–4 μmol m⁻² s⁻¹; stability 0 < $\left(z-d\right)/L$  < 0.4; buoyancy -0.001 < $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$  < 0.005 s⁻².

These ensure that the resultant fluxes are uniform from both rural and urban directions, and, hence, they are representative of the sedge-grass marsh ecosystem.

This resultant-flux uniformity is also confirmed in terms of surface-layer similarity both for velocities in form of ${\sigma }_{w}/{u}_{*}$ (Fig. 9a) and CO₂ fluxes in form of correlation coefficients ${r}_{\text{co}_{2}w}$ (Fig. 9b) taken from both directions: Třeboň (brown lines) and Rožmberk (green lines).

Fig. 9

Surface-layer similarity for fluxes from Třeboň (brown) and Rožmberk (green) directions for good-quality data after the ${u}_{*}$ ≥ 0.1 m s⁻¹ and RH ≤ 95% filtering was applied: a ${\sigma }_{w}/{u}_{*}\sim \left(z-d\right)/L$, b ${r}_{c{o}_{2}w}\sim \left(z-d\right)/L$; vertical bars—standard deviations; dashed thick black line—similarity Eq. 4b; dashed thin black lines—20% thresholds for Eq. 4; black points—unfiltered data

Fig. 10

Terrain-elevation-profile example between the town of Třeboň and the sedge-grass marsh site (“Sedge-grass marsh”, 49°1′28.64″ N and 14°46′13.08″ E, Google Earth. October 2021. Sept. 23, 2022) with the illustration of the flows and CO₂-transport mechanisms for different Categories 1–4; NBL—nocturnal boundary layer, solid arrowed lines—flow directions, dashed lines—wind-velocity profiles; [CO₂]—CO₂-rich layers; F_CO2—CO₂-flux direction

Eq. 4b ITCT-similarity relationship (Panofsky et al. 1977), taken to be the standard one for the unstable and neutral conditions (Foken 2017), gives ≈ 10% higher values (dashed thick black line, Fig. 9a) in comparison with the obtained sedge-grass-marsh values (brown and green). This is in the agreement with our simple ${1.2u}_{*}={\sigma }_{w}$ relationship giving the ratio ${\sigma }_{w}/{u}_{*}$ ≈ 1.2, which is smaller than Lumley and Panofsky (1964) and Panofsky and Dutton (1984) specified value: ${\sigma }_{w}/{u}_{*}$ ≈ 1.25. Following Hicks (1981) and representing ${\sigma }_{w}/{u}_{*}={\left(({\sigma }_{w}/{\sigma }_{u})/(-{r}_{wu})\right)}^{0.5}$, the plausible explanation for the obtained reduced ${\sigma }_{w}/{u}_{*}$-ratios in unstable conditions is the presence of water at sedge-grass marsh that shifts site energy balance increasing the latent-heat and storage fluxes and by this decreasing the sensible heat flux and the buoyancy-generated turbulence included in ${\sigma }_{w}$ estimates (Eq. 3b)—this case is better represented for Třeboň (brown, Fig. 9a): the mean brown line is coming closer to the dashed thick black line (Eq. 4b) in neutral conditions. However, because for Rožmberk (green, Fig. 9a), the ${\sigma }_{w}/{u}_{*}$-ratio reduction occurs in all the conditions, the increased correlation-coefficient magnitude ${r}_{wu}$ due to along-the-valley flows with higher velocities (Fig. 8a, b) or possible downdrafts occurred at nighttime fostering organized convection should also be the cause of it.

It can be seen that the 20% thresholds for the ITCT test (dashed thin black lines) keep some unfiltered data associated with the ${u}_{*}$ < 0.1 m s⁻¹, RH > 95%, and high-CO₂ fluxes and miss some proper-filtered fluxes (brown, green), showing that our scheme provides better results than if only the ITCT test would have been used and confirming our discussion for the limited usability of the ITCT test at sedge-grass marsh (see Fig. 4).

3.1.1 Accessing Presence of the Town of Třeboň Buoyant-Plume Descent

From Fig. 6a, d, we see that the high negative and positive CO₂ fluxes start occurring only ≈3 h after the sunset. This supports the hypotheses of gradual CO₂ accumulation in the air due to the flux divergence in stable layer at nights, plume descent, or katabatic flow development. The observed by the EC system (located 2.5 m above the ground) gradual CO₂-concentration increase with the rate above 100 ppm per hour in stable conditions, started after the horizontal wind calms below 0.5 m s⁻¹, cannot be sustained by only the local efflux from soil and plants (≈ 2 μmol m⁻² s⁻¹ in average; black lines, Fig. 6c, f), and the jumps in CO₂-concentration, having the change rates in 200–600 ppm per hour, make the local CO₂ sources even less sustainable. This puts the plume-descent and katabatic-flow hypotheses forward.

To address the possibility of the effect of the buoyant plume with the higher CO₂ concentration originated from the town of Třeboň as the result of the flux divergence in the surface layer (Ziska et al. 2004; Oke et al. 2017), note that most of the high CO₂-concentration and high CO₂-flux events are observed at night and towards early morning during stable or near-neutral atmospheric conditions (Fig. 8c, d). The stable conditions favour confining the buoyant plume in its zero-buoyancy layer above the source of the plume (Geiger et al. 1995; Beychok 2005) restricting its possible descent to the ground level.

The plume descent can occur at near-neutral and convective conditions (i) due to coning or fumigation from an entrainment and downdrafts when turbulence mixes the plume down to the ground in the convective boundary layer (Deardorff and Willis 1982; Geiger et al. 1995; Sorbjan and Uliasz 1999) or (ii) when the plume while looping reaches the ground (Deardorff and Willis 1984; Weil et al. 1997). Moreover, as it was discussed above, the plume descent should introduce the strong positive CO₂ gradients with height, which could artificially generate high negative (uptake) fluxes (${F}_{\mathrm{CO}2}=-{K}_{\mathrm{co}2}d\left[{\mathrm{CO}}_{2}\right]/\mathrm{d}z$). The plume descend should also significantly alter the storage term calculated from the difference in concentrations before and after the plume passes through the measurement level (${S}_{c}=\left(d\left[{\mathrm{CO}}_{2}\right]/\mathrm{d}t\right)z/{V}_{\mathrm{a}}$)), where V_a is the ambient molar volume of air and z is the height of the measurements.

Taking $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$ < − 0.01 s⁻² to favouring the downslope flow development and when the high CO₂ concentrations are started reporting (Fig. 8e, f), we identified four main flow categories affecting fluxes and concentrations (Tables 2, 3):

Table 2 Growing-season nocturnal conditions with negative buoyancy $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$ < − 0.01 s⁻² favouring katabatic flow development separated by categories of CO₂ concentrations (C_a ppm), CO₂ EC fluxes (${F}_{\mathrm{CO}2}$ μmol m⁻² s⁻¹), and CO₂ single-point storage fluxes (S_c μmol m⁻² s⁻¹); U m s⁻¹—horizontal wind velocity at EC level, $\overline{u^{\prime}w^{\prime}}$ m² s⁻²—vertical flux of horizontal momentum, Sk_w m s⁻¹—skewness of vertical velocity fluctuations

Table 3 Dormant-season nocturnal conditions with negative buoyancy $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$ < -0.01 s⁻² favouring katabatic flow development separated by categories of CO₂ concentrations (C_a ppm), CO₂ EC fluxes (${F}_{\mathrm{CO}2}$ μmol m⁻² s⁻¹), and CO₂ single-point storage fluxes (S_c μmol m⁻² s⁻¹); U m s⁻¹—horizontal wind velocity at EC level, $\overline{u^{\prime}w^{\prime}}$ m² s⁻²—vertical flux of horizontal momentum, Sk_w m s⁻¹—skewness of vertical velocity fluctuations

Category 1 (6% of the growing-season cases and 9% of the dormant-season cases) (bottom rows, Tables 2, 3; Fig. 10): The negative nocturnal CO₂ fluxes (${F}_{\mathrm{CO}2}$) are present only in neutral and unstable conditions (the vertical transport is possible) with $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$ < − 0.02 (− 0.15 for dormant season) indicating strong potential stability. Positive $\overline{u^{\prime}w^{\prime}}$ indicates that the velocity near the ground is higher than above the EC-measurement level, suggesting that there is a wind maximum below the measurement site. For these neutral and unstable conditions only, the single-point storage term (S_c) directly correlates with the skewness of vertical velocity fluctuations (Sk_w): S_c > 0—increase in CO₂ concentration in air, when Sk_w > 0—signalling downward CO₂ transport, and S_c < 0—decrease in CO₂ concentration in air, when Sk_w < 0—signalling upward cleaner-air transport (Sorbjan and Uliasz 1999). All of these are consistent with the presence of the CO₂-rich layer above the EC-measurement level, which is being mixed down to the ground in neutral and unstable conditions (Sorbjan and Uliasz 1999). This is also consistent with Stull (2017) suggestions that for the valley conditions the site is it is possible that the katabatic flow does not reach the bottom of the valley and stays on its neutral buoyancy level above the ground. The possible mixing in neutral and unstable conditions well describes not very high CO₂ concentrations observed at this case.

Category 2 (22% of the growing-season cases and 4% of the dormant-season cases) (lower middle rows, Tables 2, 3; Fig. 10): The highest CO₂ concentrations are associated with the highest positive ${F}_{CO2}$ and highest S_c, stable conditions with $-\left(g/{\theta }_{v}\right)\Delta {\theta }_{v}/\Delta z$ < − 0.01 (− 0.05 for dormant season) indicating reduces potential stability, and horizontal wind velocities (growing season: 0.32–0.34 m s⁻¹; dormant season: 0.36–0.41 m s⁻¹) with the positive ${\overline{u^{\prime}w^{\prime}}}$ for growing season suggesting presence of katabatic flow in early stage and with the near zero $\overline{u^{\prime}w^{\prime}}$ for dormant season suggesting presence of more developed katabatic flow (Stull 2017). The correlation between the S_c and Sk_w is absent, and the Sk_w > 0 together with $\overline{w}=0$ (2D rotation applied, Sect. 2.3) suggests downward air motion occurred due to the higher velocity of the lower layer of air. All of these are consistent with the presence of the CO₂-rich layer brought by the katabatic flow near the ground.

Category 3 (50% of the growing-season cases and 23% of the dormant-season cases) (upper middle rows, Tables 2, 3; Fig. 10): The more developed katabatic flow with the near zero $\overline{u^{\prime}w^{\prime}}$ (Stull 2017) in weakly stable and stable conditions features about the same horizontal wind velocities (growing season: 0.30–0.35 m s⁻¹; dormant season: 0.39–0.45 m s⁻¹) as in the Category 2 and reduced both ${F}_{\mathrm{CO}2}$ and S_c. The CO₂-concentration levels are lower for this case due to the deeper size of the flow and possible stronger mixing and consequently larger volume of air being involved into pollution carriage.

Category 4 (22% of the growing-season cases and 56% of the dormant-season cases) (upper rows, Tables 2, 3; Fig. 10): The highest horizontal wind velocities (growing season: 0.35–0.41 m s⁻¹; dormant season: 0.41–0.55 m s⁻¹) are associated with the significantly reduced ${F}_{\mathrm{CO}2}$ and S_c, lower level of CO₂ concentrations, and negative $\overline{u^{\prime}w^{\prime}}$ in weakly stable conditions. This indicates presence of the higher-level flow with higher velocities than at and below the EC-measurement level, mixing the pollution into a deep layer above the site. The reported for this case ${F}_{\mathrm{CO}2}$ are close to the filtered nighttime effluxes presented at Fig. 6c, f.

Even though there is a strong possibility of the town of Třeboň plume descent in neutral and unstable conditions associated with the negative nocturnal CO₂ fluxes in the small number of cases of the Category 1 (bottom rows, Tables 2, 3), the sedge-grass marsh site is located too far (1.5 km) from the town, while the distance where the town buoyant plume would have touched the ground (about the nocturnal mixed layer height) is typically less than 300 m (Deardorff and Willis 1982, 1984; Sorbjan and Uliasz 1999; Pournazeri et al. 2012). Then, the CO₂-rich air from the descended plume could be carried down by the katabatic flow along its zero-buoyancy level (high negative CO₂ fluxes in unstable and neutral conditions with the strong potential stability; Category 1) or along the ground surface (high positive CO₂ fluxes in stable conditions with the reduced potential stability; Category 2) describing the mechanism of the high negative and positive fluxes occurrence from the katabatic-flow perspective (Stull 2017). The Category 3 favours the developed-katabatic-flow based CO₂-rich-air transport mechanism (middle rows, Tables 2, 3), and the Category 4 (upper rows, Tables 2, 3) describes the forced convection case occurred with the wind from above and at weakly stable environment. Unfortunately, the CO₂ and wind-velocity vertical profiles above the site are not available for the year of 2014 to further distinguish between the plume descent or katabatic-flow occurrences.

From the results presented, it can be confirmed that the observed nocturnal stable conditions (EC measured) with the negative gradient buoyancy less than − 0.01 s⁻² (from the profiles) predominantly favour the development of the nocturnal katabatic drainage flows (low-velocity winds) downslope from the town of Třeboň bringing CO₂-rich air and high positive CO₂ fluxes to the sedge-grass marsh (Categories 2 and 3), while the nocturnal unstable and neutral conditions (EC measured) with the strong negative gradient buoyancy less than − 0.02 s⁻² (from the profiles) can be associated with either the descent of the town of Třeboň buoyant plume or the katabatic flow developed afloat on its buoyancy level bringing CO₂-rich air and high negative CO₂ fluxes to the sedge-grass marsh (Category 1). The higher wind velocities observed during the dormant season can be explained by the lack of vegetation, which increases the effective height of the EC sensor from 1.5 to 2.5 m above the surface. It should be noted that an introduction of the single-point storage correction did not change the filtering results in Figs. 8 and 9.

3.2 Recalculation of Ecosystem Carbon Balances After Applying the RH and ${{\varvec{u}}}_{\boldsymbol{*}}$ Filters

Comparing the monthly ecosystem carbon balances based on NEE (Fig. 11a) estimated from the initial best-quality data (solid blue), filtered with RH (solid green and red bars), and with ${u}_{*}$ (striped bars), we emphasise that both filters are essential to reducing the overall observed carbon-balance inaccuracy. This improvement is more pronounced in the late-spring–early autumn months (APR to SEPT) during the growing season (yellow horizontal bar) when high-RH conditions prevail, especially at night time in a stable environment favouring water-vapour flux convergence and humidity build-up (see Sect. 3.1). This statement is supported by the simultaneous negative shift of the same magnitude in monthly carbon-balance estimates once RH reduces below 100% (solid blue to green and red bars) or ${u}_{*}$ = 0.1 m s⁻¹ filtering is applied to RH = 100% (solid blue to striped bars).

Fig. 11

Monthly NEE-based carbon balances (a): solid blue bars—initial best-quality data before RH and ${u}_{*}$ filtering; solid green and red bars—after RH 97% and 95% filtering; striped bars—after ${u}_{*}$ = 0.1 m s⁻¹ filtering; yellow horizontal bar—growing-season extend (from mid-April to the end of October); negative is uptake; Annual NEE-based carbon balances (b): ${u}_{*}$ = 0 m s⁻¹—red lines, ${u}_{*}$ = 0.1 m s⁻¹—blue lines; solid lines—best-quality data and dashed lines—good-quality data by Foken (2004)

After the RH filtering is applied, the ${u}_{*}$ filtering further improves the balance by removing nocturnal high-CO₂ fluxes observable owing to the directional specific drainage flows from the town of Třeboň that occur in stable conditions with negative buoyancy (Sect. 3.1).

The annual NEE-based carbon balances (Fig. 11b) provide further evidence of the magnitudes of the balance-inaccuracy improvements due to the RH and ${u}_{*}$ filtering, respectively. The carbon-balance inaccuracy is being reduced from 182 to 234 ± 12 gC m⁻² year⁻¹ for the initial best- and good-quality data to 39–44 ± 8 gC m⁻² year⁻¹ for the RH = 95% filtered data and to 24–26 ± 7 gC m⁻² year⁻¹ for the further ${u}_{*}$ = 0.1 m s⁻¹ filtered data. Moreover, after the ${u}_{*}$ = 0.1 m s⁻¹ filtering is applied to data, both best- and good-quality data are being put practically on the same levels demonstrating the feasibility of using good-quality data with the filtering for an analysis.

The yearly carbon balance value we report before filtering: 182–234 ± 12 gC m⁻² year⁻¹ is about 5 times lower than it would be if the marsh was exposed to drying: ≈1000 gC m⁻² year⁻¹ (Morse et al. 2012; Miao et al. 2013; Batson et al. 2015). For our case, the Rožmberk lake with a dam regulates the water level at the sedge-grass marsh making it more stable and not exposing the CO₂-rich deposit layers deeper in the soil to the air so that the soil respiration should be greatly reduced (Sect. 2.1). On the other hand, this sedge-grass-marsh annual CO₂ emission is close to the value reported by Wang et al. (2018): 180 gC m⁻² year⁻¹. They attribute it to the lack of EC-sensitivity to the dissolved inorganic carbon could be advected to the marsh ecosystem while flooding. However, for our case we see that this can be mostly related to the combination of effects of both nearby urban surroundings and environmental conditions at the site, generating unrealistically high CO₂ fluxes being removed by our filtering procedure.

4 Discussion

4.1 Comparison with the Previously Developed Filtering Approaches

The ${u}_{*}$ and RH thresholds discussed have been used in a number of studies to filter the EC data obtained in grasslands, agricultural fields, and wetland sites (Table 4). In the highlighted wetland/swamp studies, about 50% of data was filtered out, and the gap-filling procedures (Falge et al. 2001; Reichstein et al. 2005) were employed to fill in the short gaps.

Table 4 Some previous EC studies of grassland, agricultural, and wetland ecosystems with the identified data-filtering thresholds

We do not conduct any gap-filling during this comparative study of the sedge-grass-marsh annual carbon-balance estimates with the parameters estimated in the research (Table 4, last column). Instead, we follow our monthly averaging procedure ensuring that there is data at each hourly timeslot to be averaged. For the larger threshold values such as ${u}_{*}$= 0.15 and ${u}_{*}$= 0.2, it occurs that there are missed hourly timeslots. Then, for this comparison we allow only interpolation of any single missed timeslot at night by its immediate-neighbour averages. The precipitation/fog threshold is estimated through $\lambda E<0$ (Beiderwieden et al. 2008; Griffis et al. 2008; Baumberger et al. 2022; Wang et al. 2022).

The best results of Griffis: 31–34 gC m⁻² year⁻¹ and Han and Zong: 35 gC m⁻² year⁻¹ methods (Table 4) are only about 6–11 gC m⁻² year⁻¹ larger than our results: 24–26 ± 7 gC m⁻² year⁻¹ (Fig. 11b) within our uncertainty. The $\lambda E<0$ precipitation/fog filtering used in both of these methods possibly keeps only the air-expansion (due to the water-droplet evaporation) part of the natural RH-change cycles and by this can artificially reduce the vertical gradients of scalars and the respective fluxes by ≈ 1–2% subject to air-temperature change.

However, if we also apply $\lambda E<0$ precipitation/fog filtering together with our filtering scheme, we get the annual-carbon-balance inaccuracy estimates down to 10–12 ± 7 gC m⁻² year⁻¹ for the best- and good-quality data, which shows about 9% improvement to our original results and, owing to the uncertainty, brings the sedge-grass marsh ecosystem close to carbon neutrality.

The results presented also highlight the importance of both ${u}_{*}$ and RH thresholds. The ${u}_{*}$ = 0.1 m s⁻¹ by filtering out stable conditions and the respective water-vapour build-ups also filters out practically all events with $\lambda E$ < − 5 W m⁻². Note that only 5% of these nocturnal events with $\lambda E$ ≈ 0 have 0 < H < 10 W m⁻². Periods with $\lambda E$ < 0 at night are associated with mostly negative sensible heat flux (H < 0) signalling a lack of any significant condensation of water vapour into the fog. The more conservative threshold ${u}_{*}$ = 0.1 m s⁻¹ with the presence of the RH thresholds (Griffis: 98%; ours: 95%) produces better results than the more aggressive ${u}_{*}$ = 0.15 m s⁻¹ and ${u}_{*}$ = 0.2 m s⁻¹ but without any RH constraints attempting to take care of everything at once. Moreover, the RH = 95% threshold we use for our wetland study is proven to be crucial.

4.2 Effects of Filtering High RH and Drainage Flows or Plume Descent on Carbon-Balance Estimations

From Fig. 11 and Online Resource, Figs. S1–S6, we see that the high RH > 95% and ${u}_{*}$ < 0.1 m s⁻¹ stable conditions are partially overlapped, especially during stable nocturnal regimes. However, this overlapping is incomplete, and there are distinct high-RH events in unstable conditions and low-RH events in stable conditions. Trying to partition the effect of the RH > 95% and ${u}_{*}$ < 0.1 m s⁻¹ filtering applied to the EC data, we employ the statistical probabilistic approach for overlapping sets (Eq. 5a–c):

$$P\left({u}_{*}\right)+P\left(RH\right)=P\left({u}_{*}\cup RH\right)+P\left({u}_{*}\cap RH\right),$$

(5a)

,

$$P\left({u}_{*}/RH\right)=P\left({u}_{*}\right)-P\left({u}_{*}\cap RH\right),$$

(5b)

,

$$P\left(RH/{u}_{*}\right)=P\left(RH\right)-P\left({u}_{*}\cap RH\right),$$

(5c)

, where $P\left(*\right)$ is the probability measure applied to the sets described in Table 5, Eq. 5b describes the extend on the distinct ${u}_{*}$ katabatic-flow or plume-descent related impact, and Eq. 5c describes the extend of distinct high-RH-related impact on the carbon balances.

Table 5 Statistical partitioning of the RH > 95% and ${u}_{*}$ < 0.1 m s⁻¹ filtered events: common part (undistinguishable)—$P\left({u}_{*}\cap RH\right)$; distinguishable high-RH conditions—$P\left(RH/{u}_{*}\right)$; distinguishable katabatic-flow or plume-descent conditions—$P\left({u}_{*}/RH\right)$, and their impacts on the carbon balances for the best- and good-quality data by Foken et al. (2004)

Applying Eqs. 5a–c to the best- and good-quality data results (Fig. 11b), we obtain (Table 5) that the undistinguishable set of events $P\left({u}_{*}\cap RH\right)$ accounts for 64–67%, the distinguishable katabatic flows or plume descent $P\left({u}_{*}/RH\right)$ from town of Třeboň direction are 8.8–9.5%, and the distinguishable high-RH $P\left(RH/{u}_{*}\right)$ are 24–27% of the total impact on the annual carbon-balance inaccuracy.

The distinguishable katabatic-flow or plume-descent related events (about 3% of all events) bringing high CO₂ fluxes from the town of Třeboň direction are unrepresentative of the ecosystem carbon balance and can be disregarded. The distinguishable high-RH conditions (15–20% of all events) are mostly related to low CO₂-flux events that occur due to humid foggy conditions often observed at the site. Dr. George Burba (personal communication, 2021) noted that if RH > 97%, the fog is formed (see also Ma et al. 2014) and water droplets from the air intake can enter into the gas analyser, and these measurements should be disregarded at all. Moreover, the Li-7200 gas analyser is designed to work only at RH < 95%. This all means that these high-RH events also have to be disregarded from the flux carbon-balance summary.

5 Conclusions

Wetlands have specific microclimatic conditions with higher air humidity (RH) and lower air temperature (reduced surface-layer instability) in comparison with the “drier” terrestrial ecosystems, and this provides challenges when making high-quality EC-flux measurements.

Our research identifies two main causes (Table 6) of the NEE-based annual carbon-balance inaccuracy issue at the sedge-grass marsh: (i) high-RH > 95% conditions mostly associated with the humid and foggy environment and very low CO₂ fluxes, and (ii) nocturnal katabatic drainage flows or plume descent from the town of Třeboň direction associated with the high positive and negative nocturnal CO₂ fluxes, respectively, accompanied by the high CO₂-storage fluxes (Sect. 3.1.1). In all these cases, the obtained CO₂ fluxes are not representative of the ecosystem, and these events should be discarded.

Table 6 Main in situ causes affecting the sedge-grass marsh NEE-based annual carbon-balance inaccuracy

To reduce this inaccuracy, we developed the data-filtering procedure based on applying three thresholds:

• Stationarity test: STT = 40% (5 from 9 by Foken et al. 2004) (both best-quality data—0 and good-quality data—1 is partially allowed);

• Stability threshold (filtering out non-turbulent conditions causing questionable EC measurements): ${{\varvec{u}}}_{\boldsymbol{*}}$ = 0.1 m s⁻¹;

• High-RH threshold (filtering out EC measurements during foggy environment and out of the Li-7200 measurement range): RH = 95%.

These chosen thresholds applied to both best- and good-quality data allow us to save about 10% more data for analysis than if the only best-quality data (still requiring ${u}_{*}$ filtering) would have been chosen for analysis.

The resulting fluxes are uniform regardless of the direction from Rožmberk lake: rural environment, flat terrain or from the town of Třeboň: urban surroundings, sloped terrain towards the sedge-grass marsh site (Sect. 3.1) and consistent with the surface-layer stability (Fig. 9), footprint size, air temperature, and vapour-pressure deficit, depending on the PAR levels (Fig. 12, Appendix 1). Note that our candidate year 2014 is used as a reference because here were no significant floods or drought events, reducing the effect of anomalous soil respiration on the EC measurements.

Results (Sect. 3.2) show that sedge-grass marsh annual-balance inaccuracy reduces from 182 to 234 ± 12 gC m⁻² year⁻¹ for the initial (both best- and good-quality) data to 24–26 ± 7 gC m⁻² year⁻¹ after the developed filtering was applied. Additionally applying the latent-heat-flux-based precipitation/fog threshold $\lambda E$ < 0 (Beiderwieden et al. 2008; Griffis et al. 2008; Baumberger et al. 2022; Wang et al. 2022) helped to reduce the inaccuracy to 10–12 ± 7 gC m⁻² year⁻¹ bringing ecosystem NEE-measurement results closer to carbon neutrality.

The observed remained inaccuracy can be attributed to the possible carbon- and carbon-matter advection, accumulation, and release of soil carbon in sedge-grass marsh wetland ecosystem (Lovett et al. 2006; Verlinden et al. 2013; Baldocchi 2014).

The remained inaccuracy in carbon balance could be addressed in the further study by installing additional measurement equipment. The foggy conditions can be distinguished with the leaf-wetness sensor, and the additional Li-7200 gas-analyser for high-RH measurements issue (RH > 95%) can be equipped with air-dryer functionality. This way, not only better flux measurements in lower RH can be done by reducing WPL correction (Ibrom et al. 2007a, b), but also some high-RH data (without water droplets in the air) can be recovered for the analysis.

Appendix 1: \({{\varvec{u}}}_{*}\) Filtered Flux Behaviour with the Surface-Layer Stability, Footprint Size, Air Temperature, and Vapour-Pressure Deficit Depending on the PAR Levels

After the ${u}_{*}$ = 0.1 filtering was applied to the good-quality data (see Fig. 6c, f) removing all the positive nocturnal carbon uptake, the remained data show consistent behaviour:

• For both growing season (Fig. 12) and dormant seasons (Fig. 13), fluxes do not practically depend on atmospheric-stability ($\left(z-d\right)/L$) and 70%-footprint change providing the consistent flux results with the stability change and signalling that most of the remained data was collected within the sedge-grass marsh ecosystem footprint.

• For the growing season (presence of photosynthesis), fluxes maximize (by absolute value) with the intermediate air temperatures (${T}_{\mathrm{air}}$) and vapour-pressure deficit (VPD) signalling that the high ${T}_{\mathrm{air}}$ and VPD constitute for stress-related conditions.

• For the dormant season (lack of photosynthesis), fluxes maximize together with ${T}_{\mathrm{air}}$ and VPD signalling higher soil carbon efflux with higher temperatures.

Fig. 12

Growing-season PAR—F_CO2 relationships for good-quality data: flux change with stability a, air temperature b, 70%-footprint size c, vapour-pressure deficit d

Fig. 13

Dormant-season PAR—F_CO2 relationships for good-quality data: flux change with stability a, air temperature b, 70%-footprint size c, vapour-pressure deficit d