The air density correction to eddy flux measurements

Under the usual assumptions for the atmospheric surface layer, we show that air density fluctuations, particularly those due to temperature fluctuations associated with a heat flux, result in a small mean vertical wind velocity. Because of this, there can be a significant correction to eddy flux measurements of passive scalars, for example CO₂, whose average concentration is very large compared to concentration fluctuations associated with the eddy flux.     

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).     

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.

     

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。     

Eddy-covariance CO2 flux measurements using open- and closed-path CO2 analysers: Corrections for analyser water vapour sensitivity and damping of fluctuations in air sampling tubes

Methods of calibrating infrared CO₂ analysers for sensitivity to CO₂ and water vapour are described. Equations to correct eddy covariance CO₂ flux measurements are presented for: (i) analyser cross-sensitivity to water vapour and the effects of density fluctuations arising from atmospheric fluxes of water vapour and sensible heat, (ii) flux losses caused by signal processing and limited instrument frequency response for open- and closed-path CO₂ analysers, and (iii) flux losses resulting from damping of concentration fluctuations in a tube used to sample air for closed-path CO₂ analysers. Examples of flux corrections required for typical instruments are presented.     

Vertical divergence of fogwater fluxes above a spruce forest

Two almost identical eddy covariance measurement setups were used to measure the fogwater fluxes to a forest ecosystem in the “Fichtelgebirge” mountains (Waldstein research site, 786 m a.s.l.) in Germany. During the first experiment, an intercomparison was carried out with both setups running simultaneously at the same measuring height on a meteorological tower, 12.5 m above the forest canopy. The results confirmed a close agreement of the turbulent fluxes between the two setups, and allowed to intercalibrate liquid water content (LWC) and gravitational fluxes. During the second experiment, the setups were mounted at a height of 12.5 and 3 m above the canopy, respectively. For the 22 fog events, a persistent negative flux divergence was observed with a greater downward flux at the upper level. To extrapolate the turbulent liquid water fluxes measured at height z to the canopy of height h_c, a conversion factor 1/[1+0.116(z−h_c)] was determined. For the fluxes of nonvolatile ions, no such correction is necessary since the net evaporation of the fog droplets appears to be the primary cause of the vertical flux divergence. Although the net evaporation reduces the liquid water flux reaching the canopy, it is not expected to change the absolute amount of ions dissolved in fogwater.     

Intra-field variability of scalar flux densities across a transition between a desert and an irrigated potato field

This paper reports on measurements of sensible and latent heat and CO₂ fluxes made over an irrigated potato field, growing next to a patch of desert. The study was conducted using two eddy correlation systems. One measurement system was located within the equilibrium boundary layer 800 m downwind from the edge of the potato field. The other measurement system was mobile and was placed at various downwind positions to probe the horizontal transition of vertical scalar fluxes. Latent (LE) and sensible (H) heat fluxes, measured at 4 m above the surface, exhibited marked variations with downwind distance over the field. Only after the fetch to height ratio exceeded 75 to 1 didLE andH become invariant with downwind distance. When latent and sensible heat fluxes were measured upwind of this threshold, significant advection of humidity-deficit occurred, causing a vertical flux divergence ofH andLE.The measured fluxes of momentum, heat, and moisture were compared with predictions from a second-order closure two-dimensional atmospheric boundary layer model. There is good agreement between measurements and model predictions. A soil-plant-atmosphere model was used to examine nonlinear feedbacks between humidity-deficits, stomatal conductance and evaporation. Data interpretation with this model revealed that the advection of hot dry air did not enhance surface evaporation rates near the upwind edge of the potato field, because of negative feedbacks among stomatal conductance, humidity-deficits, andLE. This finding is consistent with results from several recent studies.     

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.     

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).     

Comparison of eddy-covariance measurements of CO2 fluxes by open- and closed-path CO2 analysers

Eddy fluxes of CO₂ estimated using a sonic anemometer and a closed-path analyser were, on average, 16% lower than those obtained with the same anemometer and an adjacent open-path CO₂ analyser. Covariances between vertical windspeed and CO₂ density from the closed-path analyser were calculated using data points for CO₂ that were delayed relative to anemometer data by the time required for a parcel of air to travel from the tube inlet to the CO₂ sensor. Air flow in the intake tube was laminar. Densities of CO₂ that had been corrected for spurious fluctuations arising from fluctuations in temperature and humidity were used in the flux calculations. Corrections for the cross-sensitivity of CO₂ analysers to water vapour were also incorporated. Spectral analysis of the corrected CO₂ signal from the closed-path analyser showed that damping of fluctuations in the sampling tube at frequencies f > 0.1 Hz caused the apparent loss in flux. The measured losses can be predicted accurately using theory that describes the damping of oscillations in a sampling tube. High-frequency response of the closed-path system can be improved substantially by ensuring turbulent flow in the tube, using a combination of high volumetric flow rate and small tube diameter. The analysis of attenuation of turbulent fluctuations in flow through tubes is applicable to the measurement of fluxes of other minor atmospheric constituents using the eddy covariance method.     

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.     

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.     

Transfer coefficients of sensible heat on a snowmelt surface

Summary Field observations were carried out in order to determine the transfer coefficeient of sensible heat flux above a melting snow surface at the Moshiri experimental site. The coefficient is calculated as the ratio of the sensible heat flux determined by the eddy correlation method using a sonic anemometer to the product of the wind speed and the temperature difference between the air and snow surface. The sensible heat fluxes are also compared with the result of the precise heat balance observations. The nondimensional transfer coefficienth shows a good correlation with the atmospheric stability,Ri. The value ofh=2.3×10^–3 is obtained in the range of 0<Ri<0.1, however, it is smaller and scattered under stronger stable condition (Ri>0.1). The dimensional transfer coefficent for sensible heat flux is calculated, and a linear relationship is obtained as a function of the logarithm of atmospheric stability.With 11 Figures     

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.     

Eddy correlation measurements of methane flux in a northern peatland ecosystem

A pilot study to measure methane flux using eddy correlation sensors was conducted in a peatland ecosystem in north central Minnesota. A prototype tunable diode laser spectrometer system was employed to measure the fluctuations in methane concentration.The logarithmic cospectrum of methane concentration and vertical wind velocity fluctuations under moderately unstable conditions had a peak nearf = 0.10 (wheref is the nondimensional frequency) and was quite similar to the cospectra of water vapor and sensible heat. Daytime methane flux during the first two weeks of August ranged from 120 to 270 mg m^-2 day^-1. The temporal variation in methane fluxes was consistent with changes in peat temperature and water table elevation. Our results compared well with the range of values obtained in previous studies in Minnesota peatlands.These field observations demonstrate the utility of the micrometeorological eddy correlation technique for measuring surface fluxes of methane. The current state-of-the-art in tunable diode laser spectroscopy makes this approach practical for use in key ecosystems.Published as Paper No. 9556, Journal Series, Nebraska Agricultural Research Division.     

Effects Of Changing Surface Heat Flux On Atmospheric Boundary-Layer Flow Over Flat Terrain

We examine the unsteady response of a neutral atmospheric boundary layer (ABL) of depth h and friction velocity u _* when a uniform surface heat flux is applied abruptly or decreased rapidly over a time scale t<inf>θ</inf> less than about h /(10u _*). Standard Monin–Obukhov (MO) relationships are used for the perturbed eddy viscosity profile in terms of the changes to the heat flux and mean shear. Analytical solutions for changes in temperature, mean wind and shear stress profile are obtained for the surface layer, when there are small changes in h /|L_MO| over the time scale t_MO~|L _MO|/(10u_*) (where L _MO and t _MO are the length and time scales, respectively). They show that a maximum in the wind speed profile occurs at the top of the thermal boundary layer for weak surface cooling, i.e. a wind jet, whereas there is a flattening of the profile and no marked maximum for weak surface heating. The modelled profiles are approximately the same as those obtained from the U.K. Met Office Unified Model when operating as a mesoscale model at 12-km horizontal resolution. The theoretical model is modified when strong surface heating is suddenly applied, resulting in a large change in h /|L _MO| (>>1), over the time scale t _MO. The eddy structure is predicted to change significantly and the addition of convective turbulence increases the shear turbulence at the ground. A low-level wind jet can form, with convective turbulence adding to the mean momentum of the flow. This was verified by our laboratory experiment and direct numerical simulations. Additionally, it is shown that the effects of Coriolis acceleration diminish (rather than as suggested in the literature, amplify) the formation of the wind jets in the situations considered here. Hence, only when the surface heat flux changes over time scales greater than 1/f (where f is the Coriolis parameter) does the ABL adjust monotonically between its equilibrium states. These results are also applicable to the ABL passing over spatially varying surface heat fluxes.     

A Simple Model for the Vertical Transport of Reactive Species in the Convective Atmospheric Boundary Layer

We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO _x –O₃ triad problem. The chemical reactions involve one first-order reaction, the destruction of NO₂ with decay time τ, and one second-order reaction, the destruction of NO and O₃ with the reaction constant k. Since the fluxes of the sum concentrations of NO _x = NO + NO₂ and O₃ + NO₂ turn out to be constant throughout the boundary layer, the problem reduces to solving two differential equations for the concentration and the flux of NO₂. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between the free troposphere and the top of the boundary layer. The equations are solved in a dimensionless form by using 1/(kτ) as the concentration unit, the depth h of the boundary layer as the length unit, the convective velocity scale w _* as the velocity unit, and the surface temperature flux divided by w _* as the temperature unit. Special care has been devoted to the inclusion of the scalar–scalar covariance between the concentrations of O₃ and NO. Sample calculations show that the fluxes of the reactive species deviate significantly from those of non-reactive species. Further, the diffusivities, defined by minus the flux divided by the concentration gradient may become negative for reactive species in contrast to those of non-reactive species, which in the present model are never negative.     

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.     

Water vapour flux profiles in the convective boundary layer

Summary Water vapour flux profiles in the atmospheric boundary layer have been derived from measurements of water vapour density fluctuations by a ground-based Differential Absorption Lidar (DIAL) and of vertical wind fluctuations by a ground-based Doppler lidar. The data were collected during the field experiment LITFASS-2003 in May/June 2003 in the area of Lindenberg, Germany. The eddy-correlation method was applied, and error estimates of ±50 W/m² for latent heat flux were found. Since the sampling error dominates the overall measurement accuracy, time intervals between 60 and 120 min were required for a reliable flux calculation, depending on wind speed. Rather large errors may occur with low wind speed because the diurnal cycle restricts the useful interval length. In the lower height range, these measurements are compared with DIAL/radar-RASS fluxes. The agreement is good when comparing covariance and error values. The lidar flux profiles are well complemented by tower measurements at 50 and 90 m above ground and by area-averaged near surface fluxes from a network of micrometeorological stations. Water vapour flux profiles in the convective boundary layer exhibit different structures mainly depending on the magnitude of the entrainment flux. In situations with dry air above the boundary layer a positive entrainment flux is observed which can even exceed the surface flux. Flux profiles which linearly increase from the surface to the top of the boundary layer are observed as well as profiles which decrease in the lower part and increase in the upper part of the boundary layer. In situations with humid air above the boundary layer the entrainment flux is about zero in the upper part of the boundary layer and the profiles in most cases show a linear decrease.     

A cospectral correction model for measurement of turbulent NO2 flux

A correction model for eddy correlation flux measurements is developed and applied to nitrogen dioxide flux measurements obtained from a SOLENT sonic anemometer and a Scintrex Luminox LMA-3 analyser for NO₂. Four field campaigns were carried out near the village of Merenschwand in Central Switzerland from which two were selected for further analysis in this paper. The need for the correction of measured eddy covariance fluxes arises due to the damping loss of the NO₂ analyser at high frequencies. This damping loss is described by an analogy to inductance in an electronical alternating current circuit. The independent variables in the correction model are:z (measuring height above zero-plane displacement), (mean horizontal wind speed), (Monin-Obukhov stability parameter),f (natural frequency) and inductanceL. The value for inductanceL can be derived from spectral and cospectral analysis. The theoretical cospectrum of an ideal measurement is taken from Kaimalet al. (1972) and extended with a damping term in order to describe the real measurements of the cospectrum. The inductanceL of the LMA-3 with a 0.6 cm teflon aspiration tube of 5 m length lies in the order of 0.30 to 0.35 for the dataset from Merenschwand. With this inductance, a correction factor of 1.17 in August/September 1992 and of 1.18 in May 1993 was determined for the NO₂ flux maxima during daytime. The range of the correction factor is 1.05 to 1.31 for the mean daily cycles of both datasets.