Accounting for CO_2 Variability over East Asia with a Regional Joint Inversion System and Its Preliminary Evaluation

A regional surface carbon dioxide(CO_2) 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 CO_2 variability over East Asia. The proper orthogonal decomposition-based ensemble four-dimensional variational data assimilation approach(POD-4 DVar) is the core algorithm for the joint assimilation framework, and simultaneous assimilations of CO_2 concentrations and surface CO_2 fluxes are applied to help reduce the uncertainty in initial CO_2 concentrations. A persistence dynamical model was developed to describe the evolution of the surface CO_2 fluxes and help avoid the "signal-to-noise" problem; thus, CO_2 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 CO_2 flux situations. The results indicate that more observation sites would be useful to systematically improve the estimation of CO_2 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 CO_2 flux variability over East Asia could be performed with the regional inversion system.     

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.     

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.     

The effect of optimization and the nesting domain on carbon flux analyses in Asia using a carbon tracking system based on the ensemble Kalman filter

To estimate the surface carbon flux in Asia and investigate the effect of the nesting domain on carbon flux analyses in Asia, two experiments with different nesting domains were conducted using the CarbonTracker developed by the National Oceanic and Atmospheric Administration. CarbonTracker is an inverse modeling system that uses an ensemble Kalman filter (EnKF) to estimate surface carbon fluxes from surface CO₂ observations. One experiment was conducted with a nesting domain centered in Asia and the other with a nesting domain centered in North America. Both experiments analyzed the surface carbon fluxes in Asia from 2001 to 2006. The results showed that prior surface carbon fluxes were underestimated in Asia compared with the optimized fluxes. The optimized biosphere fluxes of the two experiments exhibited roughly similar spatial patterns but different magnitudes. Weekly cumulative optimized fluxes showed more diverse patterns than the prior fluxes, indicating that more detailed flux analyses were conducted during the optimization. The nesting domain in Asia produced a detailed estimate of the surface carbon fluxes in Asia and exhibited better agreement with the CO₂ observations. Finally, the simulated background atmospheric CO₂ concentrations in the experiment with the nesting domain in Asia were more consistent with the observed CO₂ concentrations than those in the experiment with the nesting domain in North America. The results of this study suggest that surface carbon fluxes in Asia can be estimated more accurately using an EnKF when the nesting domain is centered in Asian regions.     

The First Global Carbon Dioxide Flux Map Derived from TanSat Measurements

Space-borne measurements of atmospheric greenhouse gas concentrations provide global observation constraints for top-down estimates of surface carbon flux.Here,the first estimates of the global distribution of carbon surface fluxes inferred from dry-air CO_2 column (XCO_2) measurements by the Chinese Global Carbon Dioxide Monitoring Scientific Experimental Satellite (Tan Sat) are presented.An ensemble transform Kalman filter (ETKF) data assimilation system coupled with the GEOS-Chem global chemistry transport model is used to optimally fit model simulations with the Tan Sat XCO_2 observations,which were retrieved using the Institute of Atmospheric Physics Carbon dioxide retrieval Algorithm for Satellite remote sensing (IAPCAS).High posterior error reduction (30%–50%) compared with a priori fluxes indicates that assimilating satellite XCO_2 measurements provides highly effective constraints on global carbon flux estimation.Their impacts are also highlighted by significant spatiotemporal shifts in flux patterns over regions critical to the global carbon budget,such as tropical South America and China.An integrated global land carbon net flux of 6.71±0.76 Gt C yr~(-1) over12 months (May 2017–April 2018) is estimated from the Tan Sat XCO_2 data,which is generally consistent with other inversions based on satellite data,such as the JAXA GOSAT and NASA OCO-2 XCO_2 retrievals.However,discrepancies were found in some regional flux estimates,particularly over the Southern Hemisphere,where there may still be uncorrected bias between satellite measurements due to the lack of independent reference observations.The results of this study provide the groundwork for further studies using current or future Tan Sat XCO_2 data together with other surfacebased and space-borne measurements to quantify biosphere–atmosphere carbon exchange.     

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.     

The Simulation of the Opposing Fluxes of Latent Heat and CO<Subscript>2</Subscript> over Various Land-Use Types: Coupling a Gas Exchange Model to a Mesoscale Atmospheric Model

A mesoscale meteorological model (FOOT3DK) is coupled with a gas exchange model to simulate surface fluxes of CO₂ and H₂O under field conditions. The gas exchange model consists of a C3 single leaf photosynthesis sub-model and an extended big leaf (sun/shade) sub-model that divides the canopy into sunlit and shaded fractions. Simulated CO₂ fluxes of the stand-alone version of the gas exchange model correspond well to eddy-covariance measurements at a test site in a rural area in the west of Germany. The coupled FOOT3DK/gas exchange model is validated for the diurnal cycle at singular grid points, and delivers realistic fluxes with respect to their order of magnitude and to the general daily course. Compared to the Jarvis-based big leaf scheme, simulations of latent heat fluxes with a photosynthesis-based scheme for stomatal conductance are more realistic. As expected, flux averages are strongly influenced by the underlying land cover. While the simulated net ecosystem exchange is highly correlated with leaf area index, this correlation is much weaker for the latent heat flux. Photosynthetic CO₂ uptake is associated with transpirational water loss via the stomata, and the resulting opposing surface fluxes of CO₂ and H₂O are reproduced with the model approach. Over vegetated surfaces it is shown that the coupling of a photosynthesis-based gas exchange model with the land-surface scheme of a mesoscale model results in more realistic simulated latent heat fluxes.     

Estimates of Large-Scale Fluxes in High Latitudes from Terrestrial Biosphere Models and an Inversion of Atmospheric CO2 Measurements

It is important to improve estimates of large-scale carbon fluxes over the boreal forest because the responses of this biome to global change may influence the dynamics of atmospheric carbon dioxide in ways that may influence the magnitude of climate change. Two methods currently being used to estimate these fluxes are process-based modeling by terrestrial biosphere models (TBMs), and atmospheric inversions in which fluxes are derived from a set of observations on atmospheric CO₂ concentrations via an atmospheric transport model. Inversions do not reveal information about processes and therefore do not allow for predictions of future fluxes, while the process-based flux estimates are not necessarily consistent with atmospheric observations of CO₂. In this study we combine the two methods by using the fluxes from four TBMs as a priori fluxes for an atmospheric Bayesian Synthesis Inversion. By doing so we learn about both approaches. The results from the inversion indicate where the results of the TBMs disagree with the atmospheric observations of CO₂, and where the results of the inversion are poorly constrained by atmospheric data, the process-based estimates determine the flux results. The analysis indicates that the TBMs are modeling the spring uptake of CO₂ too early, and that the inversion shows large uncertainty and more dependence on the initial conditions over Europe and Boreal Asia than Boreal North America. This uncertainty is related to the scarcity of data over the continents, and as this problem is not likely to be solved in the near future, TBMs will need to be developed and improved, as they are likely the best option for understanding the impact of climate variability in these regions.     

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

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

长江三角洲地区净生态系统二氧化碳通量及浓度的数值模拟

净生态系统碳通量(NEE)的计算对于准确模拟区域碳通量和大气CO₂浓度的时空变化至关重要。本文利用中尺度大气-温室气体耦合模式WRF-GHG(Weather Research and Forecasting Model with Greenhouse Gases Module),对2010年7月28日至2010年8月2日期间影响长江三角洲地区大气CO₂浓度及时空分布的各种过程进行了详尽模拟。结果表明,植被光合呼吸模型(VPRM)能模拟不同植被下垫面NEE的日变化;WRF-GHG模拟的大气CO₂浓度日变化与观测相吻合,但低估了大气CO₂浓度5~15 ppm(ppm表示10-6),这可能与人为排放源的低估、VPRM参数的不确定性以及气象场模拟的不准确性有关。太湖和植被覆盖较好的地区如浙江北部山区是该地区的主要碳汇,而城市为CO₂的主要排放源。太湖和陆地生态系统对区域内碳循环起到一定的调节作用,减缓区域大气CO₂浓度的升高。此外,局地气象条件如湖陆风对太湖周边地区大气CO₂浓度有显著影响。     

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.     

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.     

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.     

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

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

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

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

土壤水分条件对内蒙古典型草原水汽和二氧化碳通量的影响研究

本文基于2007年和2008年生长季内蒙古羊草和大针茅草原湍流观测资料,分析了两种典型草原下垫面生长季的不同土壤水分条件下水汽和二氧化碳通量交换特征及其控制因子。主要结果如下:（1）在植被生长峰值期,日尺度上,干旱条件下土壤湿度是潜热通量的主要控制因子,而土壤水分条件较好时潜热通量主要受净辐射控制。（2）与大针茅草原相比,羊草草原叶面积指数较大,水分条件较好时,其潜热通量平均值更大,CO₂吸收能力更强,吸收CO₂更多;但在土壤水分胁迫出现时,羊草草原叶面的气孔闭合度急剧增加,大针茅草原的潜热通量、和CO₂吸收反而更大,表现出更为耐旱的植被特性。（3）地表导度可以用来解释土壤水分条件对羊草和大针茅草原碳水通量的影响。     

Carbon dioxide seasonality in dynamically ventilated caves: the role of advective fluxes

The seasonality in cave CO₂ levels was studied based on (1) a new data set from the dynamically ventilated Comblain-au-Pont Cave (Dinant Karst Basin, Belgium), (2) archive data from Moravian Karst caves, and (3) published data from caves worldwide. A simplified dynamic model was proposed for testing the effect of all conceivable CO₂ fluxes on cave CO₂ levels. Considering generally accepted fluxes, i.e., the direct diffusive flux from soils/epikarst, the indirect flux derived from dripwater degassing, and the input/output fluxes linked to cave ventilation, gives the cave CO₂ level maxima of 1.9 × 10⁻² mol m⁻³ (i.e., ∼ 440 ppmv), which only slightly exceed external values. This indicates that an additional input CO₂ flux is necessary for reaching usual cave CO₂ level maxima. The modeling indicates that the additional flux could be a convective advective CO₂ flux from soil/epikarst driven by airflow (cave ventilation) and enhanced soil/epikarstic CO₂ concentrations. Such flux reaching up to 170 mol s⁻¹ is capable of providing the cave CO₂ level maxima up to 3 × 10⁻² mol m⁻³ (70,000 ppmv). This value corresponds to the maxima known from caves worldwide. Based on cave geometry, three types of dynamic caves were distinguished: (1) the caves with the advective CO₂ flux from soil/epikarst at downward airflow ventilation mode, (2) the caves with the advective soil/epikarstic flux at upward airflow ventilation mode, and (3) the caves without any soil/epikarstic advective flux. In addition to CO₂ seasonality, the model explains both the short-term and seasonal variations in δ¹³C in cave air CO₂.

     

基于GRAPES四维变分的静止轨道微波观测系统模拟试验研究

地球静止轨道微波观测同时具有高频次、大视场和穿透云雨的全天候观测能力，因此中国在规划第二代静止轨道气象卫星“风云四号”系列时已经明确提出对静止轨道微波观测的需求。基于中国候选的50、118、183、380和425 GHz五频段静止轨道微波辐射计载荷方案，开展了地球静止轨道微波观测系统模拟试验，理解其观测时间分辨率、频段选取和观测误差对台风预报的影响。试验基于GRAPES全球四维变分同化系统，同化静止轨道微波模拟观测资料，以2018年台风“玛利亚”和“山竹”为例分析了静止轨道微波资料同化对台风预报的影响。试验结果表明，对于静止轨道微波资料同化应用，提高观测资料的时间分辨率、增加通道数量和降低噪声水平能够有效提升台风数值预报性能。      

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.