The correct form of the Webb,Pearman and Leuning equation for eddy fluxes of trace gases in steady and non-steady state,horizontally homogeneous flows

The original density corrections proposed by Webb et al. [Webb EK, Pearman GI, Leuning R (1980) Quart J Roy Meteorol Soc 106:85–100] for calculating the eddy fluxes of trace gases are shown to be correct for both steady and non-steady state, horizontally homogeneous flows. The revised theory replaces the original assumption of zero vertical flux of dry air with the requirement of no sources or sinks of dry air in the layer below the height of measurement.     

Horizontal and Vertical Co2 Advection In A Sloping Forest

A system measuring the horizontal and vertical advection was devised and installed in a sloping forest at the Vielsalm site, Belgium. The measurements showed that under stable conditions a flow regime established below the canopy: air flowed horizontally along the slope and entrained the air above the canopy vertically. This movement occurs during stable nights characterised by strongly negative net radiation. It creates negative air concentration gradients in both the vertical and horizontal directions. The advection fluxes associated with these movements are opposite and of a similar order of magnitude. This implies that the horizontal advection cannot be ignored in the carbon budget equation at night. Unfortunately, the large variability of, and considerable uncertainty about, advection fluxes does not enable one to produce estimates of the source term from these equations. Advection measurement systems should be improved in order to enable such estimates to be made. Particular attention should be paid to the estimation of the vertical velocity above the canopy and to the vertical profiles of the horizontal velocity and horizontal CO₂ gradient below the canopy.     

Consequences of Incomplete Surface Energy Balance Closure for CO2 Fluxes from Open-Path CO2/H2O Infrared Gas Analysers

We present an approach for assessing the impact of systematic biases in measured energy fluxes on CO₂ flux estimates obtained from open-path eddy-covariance systems. In our analysis, we present equations to analyse the propagation of errors through the Webb, Pearman, and Leuning (WPL) algorithm [Quart. J. Roy. Meteorol. Soc. 106, 85–100, 1980] that is widely used to account for density fluctuations on CO₂ flux measurements. Our results suggest that incomplete energy balance closure does not necessarily lead to an underestimation of CO₂ fluxes despite the existence of surface energy imbalance; either an overestimation or underestimation of CO₂ fluxes is possible depending on local atmospheric conditions and measurement errors in the sensible heat, latent heat, and CO₂ fluxes. We use open-path eddy-covariance fluxes measured over a black spruce forest in interior Alaska to explore several energy imbalance scenarios and their consequences for CO₂ fluxes.     

On the Significance of the Webb Correction to Fluxes

For establishing correct mass or energy balances at the Earth's surface, detailed and correct measurements of air constituent fluxes are needed. Flux measurements obtained from the eddy covariance technique have to pass several corrections of different relevance in order to give correct flux data. One of these corrections, the Webb correction, is analysed herein from latent heat flux and CO₂ flux data recorded during two field experiments. The significance of this correction for the latent heat flux data varies with the air humidity and the Bowen ratio. The correction changes the latent heat flux values only a little, but significantly (by 2 to 3%). For other air constituents (like CO₂), the Webb correction is much more important (20 to 30% of the flux).     

Comparing CO2 Storage and Advection Conditions at Night at Different Carboeuroflux Sites

Anemometer and CO₂ concentration data from temporary campaigns performed at six CARBOEUROFLUX forest sites were used to estimate the importance of non-turbulent fluxes in nighttime conditions. While storage was observed to be significant only during periods of both low turbulence and low advection, the advective fluxes strongly influence the nocturnal CO₂ balance, with the exception of almost flat and highly homogeneous sites. On the basis of the main factors determining the onset of advective fluxes, the ‘advection velocity’, which takes net radiation and local topography into account, was introduced as a criterion to characterise the conditions of storage enrichment/depletion. Comparative analyses of the six sites showed several common features of the advective fluxes but also some substantial differences. In particular, all sites where advection occurs show the onset of a boundary layer characterised by a downslope flow, negative vertical velocities and negative vertical CO₂ concentration gradients during nighttime. As a consequence, vertical advection was observed to be positive at all sites, which corresponds to a removal of CO₂ from the ecosystem. The main differences between sites are the distance from the ridge, which influences the boundary-layer depth, and the sign of the mean horizontal CO₂ concentration gradients, which is probably determined by the source/sink distribution. As a consequence, both positive and negative horizontal advective fluxes (corresponding respectively to CO₂ removal from the ecosystem and to CO₂ supply to the ecosystem) were observed. Conclusive results on the importance of non-turbulent components in the mass balance require, however, further experimental investigations at sites with different topographies, slopes, different land covers, which would allow a more comprehensive analysis of the processes underlying the occurrence of advective fluxes. The quantification of these processes would help to better quantify nocturnal CO₂ exchange rates.     

Comparative Measurements Of Co2flux Over A Forest Using Closed-Path And Open-Path Co2analysers

An eddy covariance system using a closed-path CO₂analyser was constructed for long-term CO₂flux measurements above a forest, and its total frequency response was valuated experimentally. The amplitude and phase responses of the system wereexamined through a preliminary test, in which a prescribed pattern of CO₂fluctuation was input to the system. The result showed that the amplitude of the output from the system was attenuated as frequency increased, with a half-power frequency of 0.3 Hz. The phase was delayed by the air sampling through a long tube, but the delay in phase decreased asfrequency increased. We then presented a new technique for the correction of flux loss due to the inadequate system response for the eddy covariance measurements of CO₂ flux. Using the present system and the correction technique, diurnal variations in CO₂ flux were measured over a temperate deciduous forest on three days in 1997. The results were compared with the CO₂fluxes measured with a fast response open-path gas analyser. The CO₂fluxes from the closed-path system agreed with those from the open-path system after the Webb, Pearman and Leuning correction was made for the latter. In the present test over a forest, the contribution of the frequency-response correction to the CO₂fluxes was small and its averaged percentage was only 3%in the daytime. However, the percentage would likely increase, if the system were applied to a shorter vegetation site where high frequency components are more important. The comparison confirmed that we can obtain correct measurements of CO₂flux using the present closed-path system and the correction technique.     

Consequences of Uncertainties in CO<Subscript>2</Subscript> Density for Estimating Net Ecosystem CO<Subscript>2</Subscript> Exchange by Open-path Eddy Covariance

Errors in the estimation of CO₂ surface exchange by open-path eddy covariance, introduced during the removal of density terms [Webb et al. Quart J Roy Meteorol Soc 106:85–100, (1980) - WPL], can happen both because of errors in energy fluxes [Liu et al. Boundary-Layer Meteorol 120:65–85, (2006)] but also because of inaccuracies in other terms included in the density corrections, most notably due to measurements of absolute CO₂ density (ρ _c ). Equations are derived to examine the propagation of all errors through the WPL algorithm. For an open-path eddy covariance system operating in the Sierra de Gádor in south-east Spain, examples are presented of the inability of an unattended, open-path infrared gas analyzer (IRGA) to reliably report ρ _c and the need for additional instrumentation to determine calibration corrections. A sensitivity analysis shows that relatively large and systematic errors in net ecosystem exchange (NEE) can result from uncertainties in ρ _c in a semi-arid climate with large sensible heat fluxes (H _s ) and (wet) mineral deposition. When ρ_c is underestimated by 5% due to lens contamination, this implies a 13% overestimation of monthly CO₂ uptake.     

On the relationship between the eddy covariance,the turbulent flux,and surface exchange for a trace gas such as CO<Subscript>2</Subscript>

In the context of CO₂ surface exchange estimation, an analysis combining the basic principles of diffusion and scalar conservation shows that the mixing ratio is the appropriate variable both for defining the (eddy covariance) turbulent flux and also for expressing the relationship between the turbulent flux and surface exchange in boundary-layer budget equations. Other scalar intensity variables sometimes chosen, both the CO₂ density and molar fraction, are susceptible to the influence of surface exchange of heat and water vapour. The application of a hypsometric analysis to the boundary-layer “control volume” below the tower measurement height reveals flaws in previously applied approaches: (a) incompressibility cannot be assumed to simplify mass conservation (the budget in terms of CO₂ density); (b) compressibility alone makes the analysis of mass conservation vulnerable to uncertainties associated with resultant non-zero vertical velocities too small to measure or model over real terrain; and (c) the WPL (Webb et al. (1980) Quart J Roy Meteorol Soc 106:85–100) “zero dry air flux” assumption is invalidated except at the surface boundary. Nevertheless, the definition and removal of the WPL terms do not hinge upon this last assumption, and so the turbulent CO₂ flux can be accurately determined by eddy covariance using gas analysers of either open- or closed-path design. An appendix discusses the necessary assumptions and appropriate interpretations for deriving the WPL terms.     

The Influence of Advection on the Short Term CO 2 -Budget in and Above a Forest Canopy

An experimental micrometeorological set-up was established at the CARBOEURO-FLUX site in Tharandt, Germany, to measure all relevant variables for the calculation of the vertical and horizontal advective fluxes of carbon dioxide. The set-up includes two auxiliary towers to measure horizontal and vertical CO₂ and H₂O gradients through the canopy, and to make ultrasonic wind measurements in the trunk space. In combination with the long-term flux tower an approximately even-sided prism with a typical side-length of 50 m was established. It is shown that under stable (nighttime) conditions the mean advective fluxes have magnitudes on the same order as the daily eddy covariance (EC) flux, which implies that they play a significant, but not yet fully understood, role in the carbon budget equation. The two advective fluxes are opposite and seem to cancel each other at night (at least for these measurements). During the day, vertical advection tends to zero, while horizontal advection is still present implying a flow of CO₂ out of the control volume. From our measurements, a mean daily gain of 2.2 gC m^–2 d^–1 for the horizontal advection and a mean daily loss of 2.5 gC m^–2d^–1 for the vertical advection is calculated for a period of 20 days. However the large scatter of the advective fluxes has to be further investigated. It is not clear yet whether the large variability is natural or due to measurement errors and conceptual deficiencies of the experiment. Similar results are found in the few comparable studies.     

Gap Filling and Quality Assessment of CO2 and Water Vapour Fluxes above an Urban Area with Radial Basis Function Neural Networks

Vertical turbulent fluxes of water vapour, carbon dioxide, and sensible heat were measured from 16 August to the 28 September 2006 near the city centre of Münster in north-west Germany. In comparison to results of measurements above homogeneous ecosystem sites, the CO₂ fluxes above the urban investigation area showed more peaks and higher variances during the course of a day, probably caused by traffic and other varying, anthropogenic sources. The main goal of this study is the introduction and establishment of a new gap filling procedure using radial basis function (RBF) neural networks, which is also applicable under complex environmental conditions. We applied adapted RBF neural networks within a combined modular expert system of neural networks as an innovative approach to fill data gaps in micrometeorological flux time series. We found that RBF networks are superior to multi-layer perceptron (MLP) neural networks in the reproduction of the highly variable turbulent fluxes. In addition, we enhanced the methodology in the field of quality assessment for eddy covariance data. An RBF neural network mapping system was used to identify conditions of a turbulence regime that allows reliable quantification of turbulent fluxes through finding an acceptable minimum of the friction velocity. For the data analysed in this study, the minimum acceptable friction velocity was found to be 0.15 m s⁻¹. The obtained CO₂ fluxes, measured on a tower at 65 m a.g.l., reached average values of 12 μmol m⁻² s⁻¹ and fell to nighttime minimum values of 3 μmol m ⁻² s⁻¹. Mean daily CO₂ emissions of 21 g CO₂ m⁻²d ⁻¹ were obtained during our 6-week experiment. Hence, the city centre of Münster appeared to be a significant source of CO₂. The half-hourly average values of water vapour fluxes ranged between 0.062 and 0.989 mmol m⁻² s⁻¹and showed lower variances than the simultaneously measured fluxes of CO₂.     

Limitations of an eddy-correlation technique for the determination of the carbon dioxide and sensible heat fluxes

A modified infrared CO₂ gas analyzer, a small thermocouple assembly, a heated-thermocouple anemometer for horizontal wind, and a propeller-type vertical wind sensor were used to measure the eddy fluxes of heat and CO₂ above a corn crop. Experimental results of these fluxes are discussed. The main sources of errors of the eddy fluxes using these instruments were estimated:

1. Sensors with a time constant of 0.5 s appear to be fast enough to detect most of the vertical CO₂ transfer as long as the sensors are located at least one meter above the crop surface.
2. The deviation from steady-state conditions for 10-min periods was found to have a significant effect on the eddy flux estimates.
3. Temperature fluctuations of the air sample passing through the CO₂ infrared gas analyzer were found to be non-negligible but could be easily corrected.
4. A 1° misalignment of the vertical anemometer affected these eddy fluxes by less than 10% under all circumstances studied.

     

Uptake and Storage of Anthropogenic CO2 in the Pacific Ocean Estimated Using Two Modeling Approaches

A basin-wide ocean general circulation model(OGCM) of the Pacific Ocean is employed to estimate the uptake and storage of anthropogenic CO 2 using two different simulation approaches.The simulation(named BIO) makes use of a carbon model with biological processes and full thermodynamic equations to calculate surface water partial pressure of CO 2,whereas the other simulation(named PTB) makes use of a perturbation approach to calculate surface water partial pressure of anthropogenic CO 2.The results from the two simulations agree well with the estimates based on observation data in most important aspects of the vertical distribution as well as the total inventory of anthropogenic carbon.The storage of anthropogenic carbon from BIO is closer to the observation-based estimate than that from PTB.The Revelle factor in 1994 obtained in BIO is generally larger than that obtained in PTB in the whole Pacific,except for the subtropical South Pacific.This,to large extent,leads to the difference in the surface anthropogenic CO 2 concentration between the two runs.The relative difference in the annual uptake between the two runs is almost constant during the integration processes after 1850.This is probably not caused by dissolved inorganic carbon(DIC),but rather by a factor independent of time.In both runs,the rate of change in anthropogenic CO 2 fluxes with time is consistent with the rate of change in the growth rate of atmospheric partial pressure of CO 2.     

锡林浩特草原CO2通量特征及其影响因素分析

利用锡林浩特国家气候观象台开路涡度相关系统、辐射土壤观测系统,测得的长期连续通量观测数据,对锡林浩特草原2009—2011年期间的CO₂通量观测特征进行了分析。结果表明:CO₂通量存在明显的年际、季节和日变化特征。3 a中NEE年际变率达到200 g·m^-2,季节变率最大达到460 g·m^-2,日变化幅度生长季最大达到0.25 mg·m^-2·s^-1。通过不同时间尺度碳通量与温度、水分、辐射等环境因子的分析,认为CO₂通量日变化主要受温度和光合有效辐射影响,而季节变化和年变化主要受降水和土壤含水量的影响。降水强度及时间分布是制约牧草CO₂吸收的关键因素,大于15%的土壤含水量有利于促进牧草生长。     

Production of N2O,CH4, and CO2 from soils in the tropical savanna during the dry season

Emissions of N₂O, CH₄, and CO₂ from soils at two sites in the tropical savanna of central Venezuela were determined during the dry season in February 1987. Measured arithmetic mean fluxes of N₂O, CH₄, and CO₂ from undisturbed soil plots to the atmosphere were 2.5×10⁹, 4.3×10¹⁰, and 3.0×10¹³ molecules cm^-2 s^-1, respectively. These fluxes were not significantly affected by burning the grass layer. Emissions of N₂O increased fourfold after simulated rainfall, suggesting that production of N₂O in savanna soils during the rainy season may be an important source for atmospheric N₂O. The CH₄ flux measurements indicate that these savanna soils were not a sink, but a small source, for atmospheric methane. Fluxes of CO₂ from savanna soils increased ninefold two hours after simulated rainfall, and remained three times higher than normal after 16 hours. More research is needed to clarify the significance of savannas in the global cycles of N₂O, CH₄, CO₂, and other trace gases, especially during the rainy season.     

Estimates of anthropogenic CO<Subscript>2</Subscript> uptake in a global ocean model

A global ocean general circulation model (L30T63) is employed to study the uptake and distribution of anthropogenic CO₂ in the ocean. A subgrid-scale mixing scheme called GM90 is used in the model. There are two main GM90 parameters including isopycnal diffusivity and skew (thickness) diffusivity. Sensitivities of the ocean circulation and the redistribution of dissolved anthropogenic CO₂ to these two parameters are examined. Two runs estimate the global oceanic anthropogenic CO₂ uptake to be 1.64 and 1.73 Pg C yr^-1 for the 1990s, and that the global ocean contained 86.8 and 92.7 Pg C of anthropogenic CO₂ at the end of 1994, respectively. Both the total inventory and uptake from our model are smaller than the data-based estimates. In this presentation, the vertical distributions of anthropogenic CO₂ at three meridional sections are discussed and compared with the available data-based estimates. The inventory in the individual basins is also calculated. Use of large isopycnal diffusivity can generally improve the simulated results, including the exchange flux, the vertical distribution patterns, inventory, storage, etc. In terms of comparison of the vertical distributions and column inventory, we find that the total inventory in the Pacific Ocean obtained from our model is in good agreement with the data-based estimate, but a large difference exists in the Atlantic Ocean, particularly in the South Atlantic. The main reasons are weak vertical mixing and that our model generates small exchange fluxes of anthropogenic CO₂ in the Southern Ocean. Improvement in the simulation of the vertical transport and sea ice in the Southern Ocean is important in future work.     

北京325米气象塔上CO2梯度观测数据质量控制与评价

近些年涡度相关系统在城市通量研究中得到了广泛应用,因城市下垫面的特殊性和复杂性,以及系统观测原理和仪器精度存在着局限性,使得结果存在10%以上偏差,故必须对原始观测数据进行质量控制和评价。本文对北京325 m气象塔七层高度上的CO₂(二氧化碳)、能量等通量进行了长期观测,研究了涡度相关技术在城市环境通量观测中的适用性,设计出了一套适合于复杂城市下垫面上的涡度相关系统资料前处理和质量控制方案,并对比了不同修正方案效果。分析结果表明,城市下垫面环境中计算CO₂通量的最优周期为30 min;二次坐标旋转法优于平面拟合法;频率响应修正后的感热通量提高5.21%,潜热通量和CO₂通量均提高9.42%。空气密度脉动修正Liu法(Liu,2005)优于WPL法(Webb et al.,1980);湍流谱在惯性副区满足-2/3次方定律,协方差谱满足-4/3次方定律。经过这套前处理和质量控制方案,原始数据中有79%能够用于基础研究,该质量控制与评价体系可为复杂城市下垫面通量研究提供参考。     

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).     

An Analysis and Implications of Alternative Methods of Deriving the Density (WPL) Terms for Eddy Covariance Flux Measurements

We explore some of the underlying assumptions used to derive the density or WPL terms (Webb et al. (1980) Quart J Roy Meteorol Soc 106:85–100) required for estimating the surface exchange fluxes by eddy covariance. As part of this effort we recast the origin of the density terms as an assumption regarding the density fluctuations rather than as a (dry air) flux assumption. This new approach, which is similar to the expansion/compression approach of Liu (Boundary-Layer Meteorol 115:151–168, 2005), eliminates the dry-air mean advective vertical velocity from the development of the WPL terms and allows us to directly compare Liu’s assumptions for deriving the WPL terms with the analogous assumptions appropriate to the original expression of the WPL terms. We suggest, (i) that the main difference between these two approaches lies in the interpretation of the turbulent exchange flux, and (ii) that the original WPL formulation is the more appropriate approach. Given the importance of the WPL terms to accurate and reliable measurements of surface exchange fluxes, a careful analysis of their origins and their proper mathematical expression and interpretation is warranted.     

Horizontal and Vertical Turbulent Fluxes Forced by a Gravity Wave Event in the Nocturnal Atmospheric Surface Layer Over the Amazon Forest

A nocturnal gravity wave was detected over a south-western Amazon forest during the Large-Scale Biosphere–Atmosphere experiment in Amazonia (LBA) in the course of the dry-to-wet season campaign on October 2002. The atmospheric surface layer was stably stratified and had low turbulence activity, based on friction velocity values. However, the passage of the wave, an event with a period of about 180–300 s, caused negative turbulent fluxes of carbon dioxide (CO₂) and positive sensible heat fluxes, as measured by the eddy-covariance system at 60 m (≈30 m above the tree tops). The evolution of vertical profiles of air temperature, specific humidity and wind speed during the wave movement revealed that cold and drier air occupied the sub-canopy space while high wind speeds were measured above the vegetation. The analysis of wind speed and scalars high frequency data was performed using the wavelet technique, which enables the decomposition of signals in several frequencies allowed by the data sampling conditions. The results showed that the time series of vertical velocity and air temperature were −90° out of phase during the passage of the wave, implying no direct vertical transport of heat. Similarly, the time series of vertical velocity and CO₂ concentration were 90° out of phase. The wave was not directly associated with vertical fluxes of this variable but the mixing induced by its passage resulted in significant exchanges in smaller scales as measured by the eddy-covariance system. The phase differences between horizontal velocity and both air temperature and CO₂ concentration were, respectively, zero and 180°, implying phase and anti-phase relationships. As a result, the wave contributed to positive horizontal fluxes of heat and negative horizontal fluxes of carbon dioxide. Such results have to be considered in nocturnal boundary-layer surface-atmosphere exchange schemes for modelling purposes.     

Carbonyl sulfide emissions from biomass burning in the tropics

Carbonyl sulfide emissions from biomass burning have been studied during field experiments conducted both in an African savanna area (Ivory Coast) and rice fields, central highland pine forest and savanna areas in Viet-Nam. During these experiments CO₂, CO and C₂H₂ or CH₄ have also been also monitored. COS values range from 0.6 ppbv outside the fires to 73 ppbv in the plumes. Significant correlations have been observed between concentrations of COS and CO (R ²=0.92,n=25) and COS and C₂H₂ (R ²=0.79,n=26) indicating a COS production during the smoldering combustion. COS/CO₂ emission factors (COS/CO₂) during field experiments ranged from 1.2 to 61×10^–6 (11.4×10^–6 mean value). COS emission by biomass burning was estimated to be up to 0.05 Tg S/yr in tropics and up to 0.07 Tg S/yr on a global basis, contributing thus about 10% to the global COS flux. Based on the S/C ratio measured in the dry plant biomass and the COS/CO₂ emission factor, COS can account for only about 7% of the sulfur emitted in the atmosphere by biomass burning.