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.     

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.     

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.     

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.     

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.     

Effects of heat and water vapor transport on eddy covariance measurement of CO2 fluxes

Flux densities of carbon dioxide were measured over an arid, vegetation-free surface by eddy covariance techniques and by a heat budget-profile method, in which CO₂ concentration gradients were specified in terms of mixing ratios. This method showed negligible fluxes of CO₂, consistent with the bareness of the experimental site, whereas the eddy covariance measurements indicated large downward fluxes of CO₂. These apparently conflicting observations are in quantitative agreement with the results of a recent theory which predicts that whenever there are vertical fluxes of sensible or latent heat, a mean vertical velocity is developed. This velocity causes a mean vertical convective mass flux (= _cw for CO₂, in standard notation). The eddy covariance technique neglects this mean convective flux and measures only the turbulent flux _c w. Thus, when the net flux of CO₂ is zero, the eddy covariance method indicates an apparent flux which is equal and opposite to the mean convective flux, i.e., _c w = – _c w. Corrections for the mean convective flux are particularly significant for CO₂ because _cw and _c w are often of similar magnitude. The correct measurement of the net CO₂ flux by eddy covariance techniques requires that the fluxes of sensible and latent heat be measured as well.     

Interpreting CO<Subscript>2</Subscript> Fluxes Over a Suburban Lawn: The Influence of Traffic Emissions

Turf-grass lawns are ubiquitous in the United States. However direct measurements of land–atmosphere fluxes using the eddy-covariance method above lawn ecosystems are challenging due to the typically small dimensions of lawns and the heterogeneity of land use in an urbanised landscape. Given their typically small patch sizes, there is the potential that CO₂ fluxes measured above turf-grass lawns may be influenced by nearby CO₂ sources such as passing traffic. In this study, we report on two years of eddy-covariance flux measurements above a 1.5 ha turf-grass lawn in which we assess the contribution of nearby traffic emissions to the measured CO₂ flux. We use winter data when the vegetation was dormant to develop an empirical estimate of the traffic effect on the measured CO₂ fluxes, based on a parametrised version of a three-dimensional Lagrangian footprint model and continuous traffic count data. The CO₂ budget of the ecosystem was adjusted by 135gCm⁻² in 2007 and by 134gCm⁻² in 2008 to determine the natural flux, even though the road crossed the footprint only at its far edge. We show that bottom-up flux estimates based on CO₂ emission factors of the passing vehicles, combined with the crosswind-integrated footprint at the distance of the road, agreed very well with the empirical estimate of the traffic contribution that we derived from the eddy-covariance measurements. The approach we developed may be useful for other sites where investigators plan to make eddy-covariance measurements on small patches within heterogeneous landscapes where there are significant contrasts in flux rates. However, we caution that the modelling approach is empirical and will need to be adapted individually to each site.     

An Alternative Approach for CO2 Flux Correction Caused by Heat and Water Vapour Transfer

Energy and CO₂ fluxes are commonly measured above plant canopies using an eddy covariance system that consists of a three-dimensional sonic anemometer and an H₂O/CO₂ infrared gas analyzer. By assuming that the dry air is conserved and inducing mean vertical velocity, Webb et al. (Quart. J. Roy. Meteorol. Soc. 106, 85-100, 1980) obtained two equations to account for density effects due to heat and water vapour transfer on H₂O/CO₂ fluxes. In this paper, directly starting with physical consideration of air-parcel expansion/compression, we derive two alternative equations to correct for these effects that do not require the assumption that dry air is conserved and the use of the mean vertical velocity. We then applied these equations to eddy flux observations from a black spruce forest in interior Alaska during the summer of 2002. In this ecosystem, the equations developed here led to increased estimates of CO₂ uptake by the vegetation during the day (up to about 20%), and decreased estimates of CO₂ respiration by the ecosystem during the night (approximately 4%) as compared with estimates obtained using the Webb et al. approach.     

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).     

Accounting for CO<Subscript>2</Subscript> variability over East Asia with a regional joint inversion system and its preliminary evaluation

A regional surface carbon dioxide (CO₂) flux inversion system, the Tan-Tracker-Region, was developed by incorporating an assimilation scheme into the Community Multiscale Air Quality (CMAQ) regional chemical transport model to resolve fine-scale CO₂ variability over East Asia. The proper orthogonal decomposition-based ensemble four-dimensional variational data assimilation approach (POD-4DVar) is the core algorithm for the joint assimilation framework, and simultaneous assimilations of CO₂ concentrations and surface CO₂ fluxes are applied to help reduce the uncertainty in initial CO₂ concentrations. A persistence dynamical model was developed to describe the evolution of the surface CO₂ fluxes and help avoid the “signal-to-noise” problem; thus, CO₂ fluxes could be estimated as a whole at the model grid scale, with better use of observation information. The performance of the regional inversion system was evaluated through a group of single-observation-based observing system simulation experiments (OSSEs). The results of the experiments suggest that a reliable performance of Tan-Tracker-Region is dependent on certain assimilation parameter choices, for example, an optimized window length of approximately 3 h, an ensemble size of approximately 100, and a covariance localization radius of approximately 320 km. This is probably due to the strong diurnal variation and spatial heterogeneity in the fine-scale CMAQ simulation, which could affect the performance of the regional inversion system. In addition, because all observations can be artificially obtained in OSSEs, the performance of Tan-Tracker-Region was further evaluated through different densities of the artificial observation network in different CO₂ flux situations. The results indicate that more observation sites would be useful to systematically improve the estimation of CO₂ concentration and flux in large areas over the model domain. The work presented here forms a foundation for future research in which a thorough estimation of CO₂ flux variability over East Asia could be performed with the regional inversion system.     

The millennial atmospheric lifetime of anthropogenic CO<Subscript>2</Subscript>

The notion is pervasive in the climate science community and in the public at large that the climate impacts of fossil fuel CO₂ release will only persist for a few centuries. This conclusion has no basis in theory or models of the atmosphere/ocean carbon cycle, which we review here. The largest fraction of the CO₂ recovery will take place on time scales of centuries, as CO₂ invades the ocean, but a significant fraction of the fossil fuel CO₂, ranging in published models in the literature from 20–60%, remains airborne for a thousand years or longer. Ultimate recovery takes place on time scales of hundreds of thousands of years, a geologic longevity typically associated in public perceptions with nuclear waste. The glacial/interglacial climate cycles demonstrate that ice sheets and sea level respond dramatically to millennial-timescale changes in climate forcing. There are also potential positive feedbacks in the carbon cycle, including methane hydrates in the ocean, and peat frozen in permafrost, that are most sensitive to the long tail of the fossil fuel CO₂ in the atmosphere.     

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.     

CO<Subscript>2</Subscript> and non-CO<Subscript>2</Subscript> radiative forcings in climate projections for twenty-first century mitigation scenarios

Climate is simulated for reference and mitigation emissions scenarios from Integrated Assessment Models using the Bern2.5CC carbon cycle–climate model. Mitigation options encompass all major radiative forcing agents. Temperature change is attributed to forcings using an impulse–response substitute of Bern2.5CC. The contribution of CO₂ to global warming increases over the century in all scenarios. Non-CO₂ mitigation measures add to the abatement of global warming. The share of mitigation carried by CO₂, however, increases when radiative forcing targets are lowered, and increases after 2000 in all mitigation scenarios. Thus, non-CO₂ mitigation is limited and net CO₂ emissions must eventually subside. Mitigation rapidly reduces the sulfate aerosol loading and associated cooling, partly masking Greenhouse Gas mitigation over the coming decades. A profound effect of mitigation on CO₂ concentration, radiative forcing, temperatures and the rate of climate change emerges in the second half of the century.     

Spectra of CO<Subscript>2</Subscript> and Water Vapour in the Marine Atmospheric Surface Layer

Spectra of CO₂ and water vapour fluctuations from measurements made in the marine atmospheric surface layer have been analyzed. A normalization of spectra based on Monin–Obukhov similarity theory, originally developed for wind speed and temperature, has been successfully extended also to CO₂ and humidity spectra. The normalized CO₂ spectra were observed to have somewhat larger contributions from low frequencies compared to humidity spectra during unstable stratification. However, overall, the CO₂ and humidity spectra showed good agreement as did the cospectra of vertical velocity with water vapour and CO₂ respectively. During stable stratification the spectra and cospectra displayed a well-defined spectral gap separating the mesoscale and small-scale turbulent fluctuations. Two-dimensional turbulence was suggested as a possible source for the mesoscale fluctuations, which in combination with wave activity in the vertical wind is likely to explain the increase in the cospectral energy for the corresponding frequency range. Prior to the analysis the turbulence time series of the density measurements were converted to time series of mixing ratios relative to dry air. Some differences were observed when the spectra based on the original density measurements were compared to the spectra based on the mixing ratio time series. It is thus recommended to always convert the density time series to mixing ratio before performing spectral analysis.     

Effect of Data Assimilation Parameters on The Optimized Surface CO<Subscript>2</Subscript> Flux in Asia

In this study, CarbonTracker, an inverse modeling system based on the ensemble Kalman filter, was used to evaluate the effects of data assimilation parameters (assimilation window length and ensemble size) on the estimation of surface CO₂ fluxes in Asia. Several experiments with different parameters were conducted, and the results were verified using CO₂ concentration observations. The assimilation window lengths tested were 3, 5, 7, and 10 weeks, and the ensemble sizes were 100, 150, and 300. Therefore, a total of 12 experiments using combinations of these parameters were conducted. The experimental period was from January 2006 to December 2009. Differences between the optimized surface CO₂ fluxes of the experiments were largest in the Eurasian Boreal (EB) area, followed by Eurasian Temperate (ET) and Tropical Asia (TA), and were larger in boreal summer than in boreal winter. The effect of ensemble size on the optimized biosphere flux is larger than the effect of the assimilation window length in Asia, but the importance of them varies in specific regions in Asia. The optimized biosphere flux was more sensitive to the assimilation window length in EB, whereas it was sensitive to the ensemble size as well as the assimilation window length in ET. The larger the ensemble size and the shorter the assimilation window length, the larger the uncertainty (i.e., spread of ensemble) of optimized surface CO₂ fluxes. The 10-week assimilation window and 300 ensemble size were the optimal configuration for CarbonTracker in the Asian region based on several verifications using CO₂ concentration measurements.     

Seasonal and diurnal dynamics of CO<Subscript>2</Subscript> emission from oligotrophic peat soil surface

The results of research of diurnal and seasonal dynamics of CO₂ emission from the oligotrophic swamp surface in the southern taiga subzone of Western Siberia in 2005–2007 are under consideration. During the summertime, the intensity of CO₂ emission increases from spring to the midsummer and then decreases by the fall. A mean CO₂ emission value was 118 mg CO₂/(m² hour). The analysis of diurnal dynamics of CO₂ emission showed that the maximum CO₂ flux is observed at 16:00, while the minimum, at 07:00. Mean amplitude of diurnal variations of the CO₂ emission is 74 mg CO₂/(m² hour). The relations established between air temperature and CO₂ flux allowed calculating carbon dioxide emission for the periods between measurements. It was found that in the summertime, the period between 10:00 and 13:00 was optimal for measuring CO₂ emission with a chamber method.     

CO<Subscript>2</Subscript> dynamics on the shelf of the East Siberian Sea

Expedition data obtained in the coastal-shelf zone of the East Siberian Sea in September 2003, 2004, and 2008 are generalized. Studies of carbonate system in water and CO₂ fluxes between ocean and atmosphere in this region confirmed that it was reasonable to divide the water area studied into two biogeochemical provinces and that the ecosystem of its coastal part is mainly of a heterotrophic nature. In different years, the extent of water supersaturation in carbon dioxide in the East Siberian Sea and the area of the CO₂ release significantly changed. Geographic localization of the atmosphere action centers over the Arctic and their intensity were main determining factors; that told both on the formation of a basic character of the atmospheric and hydrological processes and on the dynamics of the CO₂ exchange between water and air.     

Simulation of Non-Homogeneous CO<Subscript>2</Subscript> and Its Impact on Regional Temperature in East Asia

Carbon dioxide (CO₂) is an important greenhouse gas that influences regional climate through disturbing the earth’s energy balance. The CO₂ concentrations are usually prescribed homogenously in most climate models and the spatiotemporal variations of CO₂ are neglected. To address this issue, a regional climate model (RegCM4) is modified to investigate the non-homogeneous distribution of CO₂ and its effects on regional longwave radiation flux and temperature in East Asia. One-year simulation is performed with prescribed surface CO₂ fluxes that include fossil fuel emission, biomass burning, air–sea exchange, and terrestrial biosphere flux. Two numerical experiments (one using constant prescribed CO₂ concentrations in the radiation scheme and the other using the simulated CO₂ concentrations that are spatially non-homogeneous) are conducted to assess the impact of non-homogeneous CO₂ on the regional longwave radiation flux and temperature. Comparison of CO₂ concentrations from the model with the observations from the GLOBALVIEW-CO₂ network suggests that the model can well capture the spatiotemporal patterns of CO₂ concentrations. Generally, high CO₂ mixing ratios appear in the heavily industrialized eastern China in cold seasons, which probably relates to intensive human activities. The accommodation of non-homogeneous CO₂ concentrations in the radiative transfer scheme leads to an annual mean change of–0.12 W m^–2 in total sky surface upward longwave flux in East Asia. The experiment with non-homogeneous CO₂ tends to yield a warmer lower troposphere. Surface temperature exhibits a maximum difference in summertime, ranging from–4.18 K to 3.88 K, when compared to its homogeneous counterpart. Our results indicate that the spatial and temporal distributions of CO₂ have a considerable impact on regional longwave radiation flux and temperature, and should be taken into account in future climate modeling.     

Choosing a Stabilization Target for CO<Subscript>2</Subscript>

The choice of stabilization target for CO₂ concentration depends on the following: what is considered to be dangerous anthropogenic interference with the climate system; the forcings that might arise from non-CO₂ gases; and the climate sensitivity. These three factors are specified here probabilistically, as probability density functions (pdfs), and combined to produce a pdf for the CO₂ concentration target. There is a probability of 17% that the stabilization target should be less than the present level, and the median target is 536 ppm. The effects of reducing the emissions of non-CO₂ gases and/or implementing adaptation strategies are considered probabilistically and shown to alter these figures significantly.