The fundamental equation of eddy covariance and its application in flux measurements

A fundamental equation of eddy covariance (FQEC) is derived that allows the net ecosystem exchange (NEE) N̅s of a specified atmospheric constituent s to be measured with the constraint of conservation of any other atmospheric constituent (e.g. N2, argon, or dry air). It is shown that if the condition │N̅s│ ˃˃ │X̅s│ │N̅co2│is true, the conservation of mass can be applied with the assumption of no net ecosystem source or sink of dry air and the FQEC is reduced to the following equation and its approximation for horizontally homogeneous mass fluxes: N̅s = c̅dw’X’s│h + ∫h0 c̅d(z) ∂Xs/∂t dz + ∫h0 [X̅s (z)- X̅s (h)] ∂̅c̅d̅/∂t dz = c̅d̅(h) {w̅’X̅’s│h + ∫h0 ∂Xs/∂t dz}. Here w is vertical velocity, c molar density, t time, h eddy flux measurement height, z vertical distance and Xs= cs/cd molar mixing ratio relative to dry air. Subscripts s, d and CO2 are for the specified constituent, dry air and carbon dioxide, respectively. Primes and overbars refer to turbulent fluctuations and time averages, respectively. This equation and its approximation are derived for non-steady state conditions that build on the steady-state theory of Webb, Pearman and Leuning (WPL; Webb et al., 1980. Quart. J. R. Meteorol. Soc. 106, 85–100), theory that is widely used to calculate the eddy fluxes of CO2 and other trace gases. The original WPL constraint of no vertical flux of dry air across the EC measurement plane, which is valid only for steady-state conditions, is replaced with the requirement of no net ecosystem source or sink of dry air for non-steady state conditions. This replacement does not affect the ‘eddy flux’ term c̅d̅w̅’X̅’s s but requires the change in storage to be calculated as the ‘effective change in storage’ as follows: ∫h0 ∂̅c̅s̅/ ∂̅t̅ dz – X̅s(h) ∫h0 ∂̅c̅d̅/∂t dz = ∫h0 c̅d̅ (z) - ∂Xs/∂t dz + ∫h0 [X̅s (z)- X̅s (h)] ∂̅c̅d̅/∂t dz= c̅d (h) ∫h0 ∂Xs/∂t dz. Without doing so, significant diurnal and seasonal biases may occur. We demonstrate that the effective change in storage can be estimated accurately with a properly designed profile of mixing ratio measurements made at multiple heights. However further simplification by using a single measurement at the EC instrumentation height is shown to produce substantial biases. It is emphasized that an adequately designed profile system for measuring the effective change in storage in proper units is as important as the eddy flux term for determining NEE

The fundamental equation of eddy covariance and its application in flux measurements

A fundamental equation of eddy covariance (FQEC) is derived that allows the net ecosystem exchange (NEE) N̅s of a specified atmospheric constituent s to be measured with the constraint of conservation of any other atmospheric constituent (e.g. N2, argon, or dry air). It is shown that if the condition │N̅s│ ˃˃ │X̅s│ │N̅co2│is true, the conservation of mass can be applied with the assumption of no net ecosystem source or sink of dry air and the FQEC is reduced to the following equation and its approximation for horizontally homogeneous mass fluxes: N̅s = c̅dw’X’s│h + ∫h0 c̅d(z) ∂Xs/∂t dz + ∫h0 [X̅s (z)- X̅s (h)] ∂̅c̅d̅/∂t dz = c̅d̅(h) {w̅’X̅’s│h + ∫h0 ∂Xs/∂t dz}. Here w is vertical velocity, c molar density, t time, h eddy flux measurement height, z vertical distance and Xs= cs/cd molar mixing ratio relative to dry air. Subscripts s, d and CO2 are for the specified constituent, dry air and carbon dioxide, respectively. Primes and overbars refer to turbulent fluctuations and time averages, respectively. This equation and its approximation are derived for non-steady state conditions that build on the steady-state theory of Webb, Pearman and Leuning (WPL; Webb et al., 1980. Quart. J. R. Meteorol. Soc. 106, 85–100), theory that is widely used to calculate the eddy fluxes of CO2 and other trace gases. The original WPL constraint of no vertical flux of dry air across the EC measurement plane, which is valid only for steady-state conditions, is replaced with the requirement of no net ecosystem source or sink of dry air for non-steady state conditions. This replacement does not affect the ‘eddy flux’ term c̅d̅w̅’X̅’s s but requires the change in storage to be calculated as the ‘effective change in storage’ as follows: ∫h0 ∂̅c̅s̅/ ∂̅t̅ dz – X̅s(h) ∫h0 ∂̅c̅d̅/∂t dz = ∫h0 c̅d̅ (z) - ∂Xs/∂t dz + ∫h0 [X̅s (z)- X̅s (h)] ∂̅c̅d̅/∂t dz= c̅d (h) ∫h0 ∂Xs/∂t dz. Without doing so, significant diurnal and seasonal biases may occur. We demonstrate that the effective change in storage can be estimated accurately with a properly designed profile of mixing ratio measurements made at multiple heights. However further simplification by using a single measurement at the EC instrumentation height is shown to produce substantial biases. It is emphasized that an adequately designed profile system for measuring the effective change in storage in proper units is as important as the eddy flux term for determining NEE

Aircraft Regional-Scale Flux Measurements over Complex Landscapes of Mangroves, Desert, and Marine Ecosystems of Magdalena Bay, Mexico

Natural ecosystems are rarely structurally simple or functionally homogeneous. This is true for the complex coastal region of Magdalena Bay, Baja California Sur, Mexico, where the spatial variability in ecosystem fluxes from the Pacific coastal ocean, eutrophic lagoon, mangroves, and desert were studied. The Sky Arrow 650TCN environmental research aircraft proved to be an effective tool in characterizing land–atmosphere fluxes of energy, CO2, and water vapor across a heterogeneous landscape at the scale of 1 km. The aircraft was capable of discriminating fluxes from all ecosystem types, as well as between nearshore and coastal areas a few kilometers distant. Aircraft-derived average midday CO2 fluxes from the desert showed a slight uptake of −1.32 μmol CO2 m−2 s−1, the coastal ocean also showed an uptake of −3.48 μmol CO2 m−2 s−1, and the lagoon mangroves showed the highest uptake of −8.11 μmol CO2 m−2 s−1. Additional simultaneous measurements of the normalized difference vegetation index (NDVI) allowed simple linear modeling of CO2 flux as a function of NDVI for the mangroves of the Magdalena Bay region. Aircraft approaches can, therefore, be instrumental in determining regional CO2 fluxes and can be pivotal in calculating and verifying ecosystem carbon sequestration regionally when coupled with satellite-derived products and ecosystem models

The FLUXNET2015 dataset and the ONEFlux processing pipeline for eddy covariance data

The FLUXNET2015 dataset provides ecosystem-scale data on CO2, water, and energy exchange between the biosphere and the atmosphere, and other meteorological and biological measurements, from 212 sites around the globe (over 1500 site-years, up to and including year 2014). These sites, independently managed and operated, voluntarily contributed their data to create global datasets. Data were quality controlled and processed using uniform methods, to improve consistency and intercomparability across sites. The dataset is already being used in a number of applications, including ecophysiology studies, remote sensing studies, and development of ecosystem and Earth system models. FLUXNET2015 includes derived-data products, such as gap-filled time series, ecosystem respiration and photosynthetic uptake estimates, estimation of uncertainties, and metadata about the measurements, presented for the first time in this paper. In addition, 206 of these sites are for the first time distributed under a Creative Commons (CC-BY 4.0) license. This paper details this enhanced dataset and the processing methods, now made available as open-source codes, making the dataset more accessible, transparent, and reproducible.Peer reviewe

Climate control of terrestrial carbon exchange across biomes and continents

Peer reviewe

A Perspective on Thirty Years of the Webb, Pearman and Leuning Density Corrections

The density correction theory of Webb et al. (1980, Q J Roy Meteorol Soc 106: 85–100, hereafter WPL) is a principle underpinning the experimental investigation of surface fluxes of energy and masses in the atmospheric boundary layer. It has a long-lasting influence in boundary-layer meteorology and micrometeorology, and the year 2010 marks the 30th anniversary of the publication of the WPL theory. We provide here a critique of the theory and review the research it has spurred over the last 30 years. In the authors’ opinion, the assumption of zero air source at the surface is a fundamental novelty that gives the WPL theory its enduring vitality. Considerations of mass conservation show that, in a non-steady state, the WPL mean vertical velocity and the thermal expansion velocity are two distinctly different quantities of the flow. Furthermore, the integrated flux will suffer a systematic bias if the expansion velocity is omitted or if the storage term is computed from time changes in the CO2 density. A discussion is provided on recent efforts to address several important practical issues omitted by the original theory, including pressure correction, unintentional alternation of the sampled air, and error propagation. These refinement efforts are motivated by the need for an unbiased assessment of the annual carbon budget in terrestrial ecosystems in the global eddy flux network (FluxNet)

A column canopy-air turbulent diffusion method for different canopy structures

An accurate simulation of the sensible heat flux (H) over vegetation from thermal remote sensing requires an a priori estimate of roughness length and the excess resistance parameter kB −1 . Despite being the subject of considerable interest in hydrometeorology, there still does not exist a uniform method for estimating roughness length from remote sensing techniques. This study demonstrates a turbulent diffusion method to simulate canopy-air sensible heat. The performance of the roughness length scheme as described in Chen et al. (2013, https://doi.org/10.1175/JAMC-D-12-056.1 ) was examined by comparing simulated H to measured values at 28 flux tower stations, which include seven different land covers (needle forest, broadleaf forest, shrub, savanna, grassland, cropland, and sparsely vegetated land). The model predictions of H for grass, crop, and sparsely vegetated land compare favorably with observed values, when actual canopy height is given. H is significantly underestimated at forest sites due to a high value of kB −1 . Among the different physical representations for the canopy, canopy-soil mixture, and soil component, it is found that such a high kB −1 value is caused by the high kB −1 value for the canopy part. The reasons for this high kB −1 were investigated from canopy-air physical process of turbulent diffusion. This study introduces the vertical foliage density information into a column canopy-air turbulent diffusion model to include the different momentum and heat transfer efficiencies in the vertical canopy layers to enhance the thermal turbulent transfer intensity above the tall canopy. The new model has been verified to provide accurate simulation over different canopy structures