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.     

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.     

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).     

Simplified expressions for adjusting higher-order turbulent statistics obtained from open path gas analyzers

When density fluctuations of scalars such as CO₂ are measured with open-path gas analyzers, the measured vertical turbulent flux must be adjusted to take into account fluctuations induced by ‘external effects’ such as temperature and water vapour. These adjustments are needed to separate the effects of surface fluxes responsible for ‘natural’ fluctuations in CO₂ concentration from these external effects. Analogous to vertical fluxes, simplified expressions for separating the ‘external effects’ from higher-order scalar density turbulence statistics are derived. The level of complexity in terms of input to these expressions are analogous to that of the Webb–Pearman–Leuning (WPL), and are shown to be consistent with the conservation of dry air. It is demonstrated that both higher-order turbulent moments such as the scalar variances, the mixed velocity-scalar covariances, and the two-scalar covariance require significant adjustments due to ‘external effects’. The impact of these adjustments on the turbulent CO₂ spectra, probability density function, and dimensionless similarity functions derived from flux-variance relationships are also discussed.     

Turbulent carbon exchange in very stable conditions

Turbulent fluxes obtained using the conventional eddy covariance approach result in erratic results with large time fluctuations in extremely stable conditions. This can limit efforts to estimate components of the nocturnal energy budget and respiratory CO₂ fluxes. Well-organized fluxes that show a clear dependence on turbulent intensity were obtained when multiresolution decomposition was used to estimate turbulent exchanges. CO₂, heat and water vapour fluxes were observed at a site in the eastern Amazon basin that had been cleared for agricultural purposes. Temporal scales of the carbon transfer were determined and shown to be similar to those of latent heat, but as much as three times larger than those of sensible heat. CO₂ eddy diffusivities at the temporal scales on which most of the vertical CO₂ exchange occurs are shown to be 50 times larger than the eddy diffusivity for heat. A process associated with the vertical scale of the scalar accumulation layer is suggested to explain these different scales and turbulent diffusivities of carbon and sensible heat transfer. For an appreciable range of turbulence intensities, the observed vertical turbulent carbon exchange is insufficient to account for the locally respired CO₂ estimated independently. Evidence that shallow drainage currents may account for this is given.     

Surface turbulent flux measurements over the Loess Plateau for a semi-arid climate change study

In order to provide high quality data for climate change studies, the data quality of turbulent flux measurements at the station of SACOL (Semi-Arid Climate & Environment Observatory of Lanzhou University), which is located on a semi-arid grassland over the Loess Plateau in China, has been analyzed in detail. The effects of different procedures of the flux corrections on CO₂, momentum, and latent and sensible heat fluxes were assessed. The result showed that coordinate rotation has a great influence on the momentum flux but little on scalar fluxes. For coordinate rotation using the planar fit method, different regression planes should be determined for different wind direction sectors due to the heterogeneous nature of the ground surface. Sonic temperature correction decreased the sensible heat flux by about 9%, while WPL correction (correction for density fluctuations) increased the latent heat flux by about 10%. WPL correction is also particularly important for CO₂ fluxes. Other procedures of flux corrections, such as the time delay correction and frequency response correction, do not significantly influence the turbulent fluxes. Furthermore, quality tests on stationarity and turbulence development conditions were discussed. Parameterizations of integral turbulent characteristics (ITC) were tested and a specific parameterization scheme was provided for SACOL. The ITC test on turbulence development conditions was suggested to be applied only for the vertical velocity. The combined results of the quality tests showed that about 62%–65% of the total data were of high quality for the latent heat flux and CO₂ flux, and as much as about 76% for the sensible heat flux. For the momentum flux, however, only about 35% of the data were of high quality.     

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。     

Dissimilarity of Scalar Transport in the Convective Boundary Layer in Inhomogeneous Landscapes

A land-surface model (LSM) is coupled with a large-eddy simulation (LES) model to investigate the vegetation-atmosphere exchange of heat, water vapour, and carbon dioxide (CO₂) in heterogeneous landscapes. The dissimilarity of scalar transport in the lower convective boundary layer is quantified in several ways: eddy diffusivity, spatial structure of the scalar fields, and spatial and temporal variations in the surface fluxes of these scalars. The results show that eddy diffusivities differ among the three scalars, by up to 10–12%, in the surface layer; the difference is partly attributed to the influence of top-down diffusion. The turbulence-organized structures of CO₂ bear more resemblance to those of water vapour than those of the potential temperature. The surface fluxes when coupled with the flow aloft show large spatial variations even with perfectly homogeneous surface conditions and constant solar radiation forcing across the horizontal simulation domain. In general, the surface sensible heat flux shows the greatest spatial and temporal variations, and the CO₂ flux the least. Furthermore, our results show that the one-dimensional land-surface model scheme underestimates the surface heat flux by 3–8% and overestimates the water vapour and CO₂ fluxes by 2–8% and 1–9%, respectively, as compared to the flux simulated with the coupled LES-LSM.     

Towards Closing the Surface Energy Budget of a Mid-latitude Grassland

Observations for May and August, 2005, from a long-term grassland meteorological station situated in central Netherlands were used to evaluate the closure of the surface energy budget. We compute all possible enthalpy changes, such as the grass cover heat storage, dew water heat storage, air mass heat storage and the photosynthesis energy flux, over an averaging time interval. In addition, the soil heat flux was estimated using a harmonic analysis technique to obtain a more accurate assessment of the surface soil heat flux. By doing so, a closure of 96% was obtained. The harmonic analysis technique appears to improve closure by 9%, the photosynthesis for 3% and the rest of the storage terms for a 3% improvement of the energy budget closure. For calm nights (friction velocity u _* < 0.1 m s⁻¹) when the eddy covariance technique is unreliable for measurement of the vertical turbulent fluxes, the inclusion of a scheme that calculates dew fluxes improves the energy budget closure significantly.     

Energy Balance Closure Using Eddy Covariance Above Two Different Land Surfaces and Implications for CO<Subscript>2</Subscript> Flux Measurements

Components of the surface energy balance of a mature boreal jack pine forest and a jack pine clearcut were analysed to determine the causes of the imbalance that is commonly observed in micrometeorological measurements. At the clearcut site (HJP02), a significant portion of the imbalance was caused by: (i) the overestimation of net radiation (R _n ) due to the inclusion of the tower in the field of view of the downward facing radiometers, and (ii) the underestimation of the latent heat flux (λE) due to the damping of high frequency fluctuations in the water vapour mixing ratio by the sample tube of the closed-path infrared gas analyzer. Loss of low-frequency covariance induced by insufficient averaging time as well as systematic advection of fluxes away from the eddy-covariance (EC) tower were discounted as significant issues. Spatial and temporal distributions of the total surface-layer heat flux (T), i.e. the sum of sensible heat flux (H) and λE, were well behaved and differences between the relative magnitudes of the turbulent fluxes for several investigated energy balance closure (C) classes were observed. Therefore, it can be assumed that micrometeorological processes that affected all turbulent fluxes similarly did not cause the variation in C. Turbulent fluxes measured at the clearcut site should not be forced to close the energy balance. However, at the mature forest site (OJP), loss of low-frequency covariance contributed significantly to the systematic imbalance when a 30-min averaging time was used, but the application of averaging times that were long enough to capture all of the low-frequency covariance was inadequate to resolve all of the high-frequency covariance. Although we found qualitative similarity between T and the net ecosystem exchange (NEE) of carbon dioxide (CO₂), forcing T to closure while retaining the Bowen ratio and applying the same factor to CO₂ fluxes (F _C ) cannot be generally recommended since it remains uncertain to what extent long wavelength contributions affect the relationship between T, F _C and C.     

Scalar Similarity for Relaxed Eddy Accumulation Methods

The relaxed eddy accumulation (REA) method allows the measurement of trace gas fluxes when no fast sensors are available for eddy covariance measurements. The flux parameterisation used in REA is based on the assumption of scalar similarity, i.e., similarity of the turbulent exchange of two scalar quantities. In this study changes in scalar similarity between carbon dioxide, sonic temperature and water vapour were assessed using scalar correlation coefficients and spectral analysis. The influence on REA measurements was assessed by simulation. The evaluation is based on observations over grassland, irrigated cotton plantation and spruce forest.Scalar similarity between carbon dioxide, sonic temperature and water vapour showed a distinct diurnal pattern and change within the day. Poor scalar similarity was found to be linked to dissimilarities in the energy contained in the low frequency part of the turbulent spectra ( < 0.01 Hz).The simulations of REA showed significant change in b-factors throughout the diurnal course. The b-factor is part of the REA parameterisation scheme and describes a relation between the concentration difference and the vertical flux of a trace gas. The diurnal course of b-factors for carbon dioxide, sonic temperature and water vapour matched well. Relative flux errors induced in REA by varying scalar similarity were generally below ± 10%. Systematic underestimation of the flux of up to − 40% was found for the use of REA applying a hyperbolic deadband (HREA). This underestimation was related to poor scalar similarity between the scalar of interest and the scalar used as proxy for the deadband definition.     

Experimental determination of turbulent fluxes over the heterogeneous LITFASS area: Selected results from the LITFASS-98 experiment

Summary ?During the LITFASS-98 experiment, local flux measurements were performed over five different types of underlying surface (grass, barley, triticale, pine forest, water) in a heterogeneous landscape using eddy covariance and profile techniques over a three week time period in June, 1998. Estimates of the area-integrated sensible heat flux during daytime were obtained from continuous measurements with a large aperture scintillometer (LAS) along a 4.7 km path. The calculation of a mean diurnal cycle of the fluxes during the experiment revealed significant differences between the main land use classes. A land-use weighted average of the sensible heat flux was found to be in good agreement with the LAS based estimate, which in turn was supported by other regionally integrated flux estimates from budget considerations and aircraft measurements for a few case studies. The profiles of turbulent quantities measured along a 99 m-tower significantly deviate from “idealised” profiles measured over homogeneous terrain. Peculiarities in the profile structure could be attributed to the heterogeneity of the terrain, namely to the differences in the surface characteristics of the footprint areas for the different tower levels. Received June 6, 2001; revised January 15, 2002; accepted April 4, 2002     

地气通量中存贮和平流项计算方案的探讨

从物质收支方程出发,推导了一个包含物质存贮、水平平流输送、垂直对流输送以及传统的涡度相关项的地气通量计算方程。平流项本质上是地表非均匀性的结果,不同下垫面的感热和潜热通量也不同,将会产生中尺度环流,使得辐合辐散过程得以维持,从而将体元内的物质输送到体元以外,因此可以通过计算水汽和感热的存贮,间接求出物质的水平平流输送。量纲分析和实际的资料应用都表明,存贮和平流的通量贡献是非常小的。尤其是在均匀下垫面下,方程中的存贮和平流项的通量贡献可以忽略,因此估算地气通量时仅需考虑涡度相关项和Webb修正项即可。而在非均匀下垫面下,在1 d以上的时间尺度上,为方便计算,可以忽略存贮和平流的通量贡献;而在小时这样的时间尺度上,从物质能量收支守恒的角度考虑,估算地气通量需要包括存贮和平流的通量贡献。     

Quality analysis applied on eddy covariance measurements at complex forest sites using footprint modelling

Summary Measuring turbulent fluxes with the eddy covariance method has become a widely accepted and powerful tool for the determination of long term data sets for the exchange of momentum, sensible and latent heat, and trace gases such as CO₂ between the atmosphere and the underlying surface. Several flux networks developed continuous measurements above complex terrain, e.g. AmeriFlux and EUROFLUX, with a strong focus on the net exchange of CO₂ between the atmosphere and the underlying surface. Under many conditions basic assumptions for the eddy covariance method in its simplified form, such as stationarity of the flow, homogeneity of the surface and fully developed turbulence of the flow field, are not fulfilled. To deal with non-ideal conditions which are common at many FLUXNET sites, quality tests have been developed to check if these basic theoretical assumptions are valid.In the framework of the CARBOEUROFLUX project, we combined quality tests described by Foken and Wichura (1996) with the analytical footprint model of Schmid (1997). The aim was to identify suitable wind sectors and meteorological conditions for flux measurements. These tools were used on data of 18 participating sites. Quality tests were applied on the fluxes of momentum, sensible and latent heat, and on the CO₂-flux, respectively. The influence of the topography on the vertical wind component was also checked. At many sites the land use around the flux towers is not homogeneous or the fetch may not be large enough. So the relative contribution of the land use type intended to be measured was also investigated. Thus the developed tool allows comparative investigations of the measured turbulent fluxes at different sites if using the same technique and algorithms for the determination of the fluxes as well as analyses of potential problems caused by influences of the surrounding land use patterns.     

青藏高原东部草甸下垫面涡旋相关观测数据的质量控制及评价研究

目前利用涡旋相关仪观测地表通量的方法已被广泛采用, 但由于涡旋相关法是建立在方程假设简化的基础上, 这对观测数据的质量提出了一定的要求, 所以对观测数据的处理及通量结果的质量状况分析就显得尤为重要。本文以理塘站2006年7月中到8月中的数据为例, 对其进行质量控制, 并将质量控制后的通量计算结果与原始值进行比较。质量控制后感热通量和潜热通量总和有所增长, 动量通量值则受质量控制影响较大。质量评价的结果为:动量通量、感热通量、潜热通量中高质量数据所占比例为68.2%、60.6%、63.3%。     

在华北玉米生育期观测的16 m高度CO2浓度及通量特征

利用中国气象局固城农业气象生态试验站2004年玉米生育期通量观测资料，分析了CO2浓度和通量随玉米生长的变化，并估算了玉米生育期陆地与大气CO2净交换量。结果表明:CO2浓度变化对农户活动和作物生长极其敏感；浓度在整个生育期始终有明显的日变化规律，峰值（谷值）出现在日出（日落）前后，通量仅在7月中旬至10月上旬之间出现明显的日变化特点，且位相超前于浓度，开花期通量最大；玉米播种期、苗期和成熟后地面向大气净排放碳， 拔节至成熟前地面从大气净吸收碳；开花期碳吸收最强，其后依次为吐丝－乳熟期和拔节期。比较分析了目前流行的通量计算方法对碳吸收估计的影响，结果显示不同计算方法能产生高达160%的碳吸收估计偏差，应当引起重视。生态系统碳平衡分析结果表明，玉米地在生长季表现为弱碳汇（大约660 kg/hm2），但这一结果可能低估了实际的碳汇强度，低估程度有待研究。     

Buoyancy and The Sensible Heat Flux Budget Within Dense Canopies

In contrast to atmospheric surface-layer (ASL) turbulence, a linear relationship between turbulent heat fluxes (F_T) and vertical gradients of mean air temperature within canopies is frustrated by numerous factors, including local variation in heat sources and sinks and large-scale eddy motion whose signature is often linked with the ejection-sweep cycle. Furthermore, how atmospheric stability modifies such a relationship remains poorly understood, especially in stable canopy flows. To date, no explicit model exists for relating F_T to the mean air temperature gradient, buoyancy, and the statistical properties of the ejection-sweep cycle within the canopy volume. Using third-order cumulant expansion methods (CEM) and the heat flux budget equation, a “diagnostic” analytical relationship that links ejections and sweeps and the sensible heat flux for a wide range of atmospheric stability classes is derived. Closure model assumptions that relate scalar dissipation rates with sensible heat flux, and the validity of CEM in linking ejections and sweeps with the triple scalar-velocity correlations, were tested for a mixed hardwood forest in Lavarone, Italy. We showed that when the heat sources (S_T) and F_T have the same sign (i.e. the canopy is heating and sensible heat flux is positive), sweeps dominate the sensible heat flux. Conversely, if S_T and F_T are opposite in sign, standard gradient-diffusion closure model predict that ejections must dominate the sensible heat flux.     

Testing of the bandpass eddy covariance method for a long-term measurement of water vapour flux over a forest

The bandpass eddy covariance method has been used to measure the turbulent flux of scalar quantities using a slow-responsescalar sensor. The method issimilar in principle to the traditional eddy correlation method but includes the estimation of high-frequency components of the flux on the basis of cospectral similarity in the atmospheric surface layer. In order to investigate the performance of the method, measurements of the water vapour flux over a forest with the bandpass eddy covariance method and the direct eddy correlation method were compared. The flux obtained by the bandpass eddy covariance method agreed with that by the eddy correlation method within ±20% for most cases, in spite of a rather slow sensor-response of the adopted hygrometer. This result supports its relevance to a long-term continuous operation, since a stable, low-maintenance,general-purpose sensor canbe utilized for scalar quantities. Oneweak point of the method isits difficulty in principle to measure the correct flux when the magnitude of the sensible heat flux is very small, because the method uses the sensible heat flux as a standard reference for the prediction of undetectable high-frequency components of the scalar flux. An advanced method is then presented to increase its robustness. In the new method, output signals from a slow-response sensor are corrected using empirical frequency-responsefunctions for the sensor,thereby extending the width of the bandpass frequency region where components of the flux are directly measured (not predicted). The advanced method produced correct fluxes for all cases including the cases of small sensible heat flux. The advanced bandpass eddy covariance method is thus appropriate for along-term measurement of the scalar fluxes.     

A Simple Model for the Afternoon and Early Evening Decay of Convective Turbulence Over Different Land Surfaces

A simple model to study the decay of turbulent kinetic energy (TKE) in the convective surface layer is presented. In this model, the TKE is dependent upon two terms, the turbulent dissipation rate and the surface buoyancy fluctuations. The time evolution of the surface sensible heat flux is modelled based on fitting functions of actual measurements from the LITFASS-2003 field campaign. These fitting functions carry an amplitude and a time scale. With this approach, the sensible heat flux can be estimated without having to solve the entire surface energy balance. The period of interest covers two characteristic transition sub-periods involved in the decay of convective boundary-layer turbulence. The first sub-period is the afternoon transition, when the sensible heat flux starts to decrease in response to the reduction in solar radiation. It is typically associated with a decay rate of TKE of approximately t ⁻² (t is time following the start of the decay) after several convective eddy turnover times. The early evening transition is the second sub-period, typically just before sunset when the surface sensible heat flux becomes negative. This sub-period is characterized by an abrupt decay in TKE associated with the rapid collapse of turbulence. Overall, the results presented show a significant improvement of the modelled TKE decay when compared to the often applied assumption of a sensible heat flux decreasing instantaneously or with a very short forcing time scale. In addition, for atmospheric modelling studies, it is suggested that the afternoon and early evening decay of sensible heat flux be modelled as a complementary error function.