Flux-Variance Method for Latent Heat and Carbon Dioxide Fluxes in Unstable Conditions

Applied previously to momentum and heat fluxes, the present study extends the flux-variance method to latent heat and CO₂ fluxes in unstable conditions. Scalar similarity is also examined among temperature (θ), water vapour (q), and CO₂ (c). Temperature is adopted as the reference scalar, leading to two feasible strategies to estimate latent heat and CO₂ fluxes: the first one relies on flux-variance similarity relations for scalars, while the second is based on the parameterization of relative transport efficiency in terms of scalar correlation coefficient and a non-dimensional quantity. The relationship between the θ-to-q transport efficiency (λ _{θ q} ) and θ-q correlation coefficient (R _{θ q} ) is used to describe the intermediate hydrological conditions. We also parameterize the θ-to-c transport efficiency (λ _{θ c} ) as a function of the θ-c correlation coefficient (R _{θ c} ) by introducing a new non-dimensional ratio (α). The flux-variance method is a viable technique for flux gap-filling, when turbulence measurements of wind velocity are not available. It is worth noting that the extended method is not exempt from a correction for density effects when used for estimating water or carbon exchange.     

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.     

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.     

Influence of the boundary layer height on the global air–sea surface fluxes

Results from large-eddy simulations and field measurements have previously shown that the velocity field is influenced by the boundary layer height, z _i , during close to neutral, slightly unstable, atmospheric stratification. During such conditions the non-dimensional wind profile, φ _m , has been found to be a function of both z/L and z _i /L. At constant z/L, φ _m decreases with decreasing boundary layer height. Since φ _m is directly related to the parameterizations of the air–sea surface fluxes, these results will have an influence when calculating the surface fluxes in weather and climate models. The global impact of this was estimated using re-analysis data from 1979 to 2001 and bulk parameterizations. The results show that the sum of the global latent and sensible mean heat fluxes increase by 0.77 W m⁻² or about 1% and the mean surface stress increase by 1.4 mN m⁻² or 1.8% when including the effects of the boundary layer height in the parameterizations. However, some regions show a larger response. The greatest impact is found over the tropical oceans between 30°S and 30°N. In this region the boundary layer height influences the non-dimensional wind profile during extended periods of time. In the mid Indian Ocean this results in an increase of the mean annual heat fluxes by 2.0 W m⁻² and an increase of the mean annual surface stress by 2.6 mN m⁻².     

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.     

Influence of leaf water potential on diurnal changes in CO2 and water vapour fluxes

Mass and energy fluxes between the atmosphere and vegetation are driven by meteorological variables, and controlled by plant water status, which may change more markedly diurnally than soil water. We tested the hypothesis that integration of dynamic changes in leaf water potential may improve the simulation of CO₂ and water fluxes over a wheat canopy. Simulation of leaf water potential was integrated into a comprehensive model (the ChinaAgrosys) of heat, water and CO₂ fluxes and crop growth. Photosynthesis from individual leaves was integrated to the canopy by taking into consideration the attenuation of radiation when penetrating the canopy. Transpiration was calculated with the Shuttleworth-Wallace model in which canopy resistance was taken as a link between energy balance and physiological regulation. A revised version of the Ball-Woodrow-Berry stomatal model was applied to produce a new canopy resistance model, which was validated against measured CO₂ and water vapour fluxes over winter wheat fields in Yucheng (36°57′ N, 116°36′ E, 28 m above sea level) in the North China Plain during 1997, 2001 and 2004. Leaf water potential played an important role in causing stomatal conductance to fall at midday, which caused diurnal changes in photosynthesis and transpiration. Changes in soil water potential were less important. Inclusion of the dynamics of leaf water potential can improve the precision of the simulation of CO₂ and water vapour fluxes, especially in the afternoon under water stress conditions.     

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.     

Seasonal carbon dioxide balance and respiration of a high-arctic fen ecosystem in NE-Greenland

Summary  Turbulent fluxes of CO₂ were continuously measured by eddy correlation for three months in 1997 over a gramineous fen in a high-arctic environment at Zackenberg (74°28′12″N, 20°34′23″W) in NE-Greenland. The measurements started on 1 June, when there was still a 1–2 m cover of dry snow, and ended 26 August at a time that corresponds to late autumn at this high-arctic site. During the 20-day period with snow cover, fluxes of CO₂ to the atmosphere were small, typically 0.005 mg CO₂ m⁻² s⁻¹ (0.41 g CO₂ m⁻² d⁻¹), wheres during the thawed period, the fluxes displayed a clear diurnal variation. During the snow-free period, before the onset of vegetation growth, fluxes of CO₂ to the atmosphere were typically 0.1 mg CO₂ m⁻² s⁻¹ in the afternoon, and daily sums reached values up to almost 9 g CO₂ m⁻² d⁻¹. After 4 July, downward fluxes of CO₂ increased, and on sunny days in the middle of the growing season, the net ecosystem exchange rates attained typical values of about −0.23 mg m⁻² s⁻¹ at midday and max values of daily sums of −12 g CO₂ m⁻² d⁻¹. Throughout the measured period the fen ecosystem acted as a net-sink of 130 g CO₂ m⁻². Modelling the ecosystem respiration during the season corresponded well with eddy correlation and chamber measurements. On the basis of the eddy correlation data and the predicted respiration effluxes, an estimate of the annual CO₂ balance the calender year 1997 was calculated to be a net-sink of 20 g CO₂ m⁻² yr⁻¹. Received October 6, 1999 Revised May 2, 2000     

Relaxed Eddy Accumulation Simulations of Aerosol Number Fluxes and Potential Proxy Scalars

Direct eddy-covariance measurements of aerosol number fluxes obtained during the 2007 CHATS field experiment in Dixon, California, USA are compared with relaxed eddy accumulation simulations using temperature and water vapour concentration as proxy scalars. After a brief discussion of the limited time response of the aerosol measurement, the applicability of temperature and water vapour concentration as proxy scalars for aerosol number concentration is investigated by evaluating scalar and spectral correlation coefficients as simple measures of scalar similarity. In addition, the proportionality factor b, which compensates for the use of a constant sampling flow in relaxed eddy accumulation, is derived from the time series of aerosol number, temperature and water vapour, and its variability is analyzed. The reduction of the b factor due to application of a deadband, i.e. the rejection of data when the vertical wind speed is close to zero, is evaluated for all three studied scalars, and compared with published functional relationships. In this study, using temperature or water vapour as proxy scalars for aerosol number shows no advantage over the use of a constant b factor. Thus, it is suggested to apply a deadband H _REA  = w′/σ _w  = 0.6 to 0.8 (where w′ is the vertical velocity fluctuation and σ _w is its standard deviation), to use a theoretical b factor based on a parameterization that includes a stability dependence, and to calculate the deadband effect according to a derived relation for aerosol relaxed eddy accumulation.     

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.     

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.     

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.     

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.     

Uptake of the NO <Subscript>3</Subscript> Radical on Aqueous Surfaces

Using a single drop experiment, the uptake of NO₃ radicals on aqueous solutions of the dye Alizarin Red S and NaCl was measured at 293 K. Uptake coefficients in the range (1.7–3.1) ⋅ 10^{− 3} were measured on Alizarin Red S solutions. The uptake coefficients measured on NaCl solutions were in the range of (1.1–2.0) ⋅ 10⁻³ depending on the salt concentration. Both experiments lead to a consistent result for the mass accommodation coefficient of α_NO3 = (4.2_{− 1.7}^+2.2)⋅ 10⁻³. The product H(D_l k_Cl−^II)^0.5 for the NO₃ radical was determined to be (1.9 ± 0.2) M atm^{− 1} cm s^−0.5 M^−0.5 s^−0.5 by fitting the uptake data for the NaCl solutions to the so-called resistance model. The yield of the chemical NO₃ radical source was characterized using UV-VIS and FT-IR spectroscopy. The amount of gas-phase NO₃ radicals measured at elevated humidities was less than expected. Instead, a rise of the gas-phase HNO₃ concentration was found indicating a conversion of gas-phase NO₃ radicals to gas-phase HNO₃ on the moist reactor walls.     

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.     

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.     

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。     

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.