Determining carbon isotope signatures from micrometeorological measurements: Implications for studying biosphere–atmosphere exchange processes

In recent years considerable effort has been focused on combining micrometeorological and stable isotope techniques to partition net fluxes and to study biosphere–atmosphere exchange processes. While much progress has been achieved over the last decade, some new issues are beginning to emerge as technological advances, such as laser spectroscopy, permit isotopic fluxes to be measured more easily and continuously in the field. Traditional investigations have quantified the isotopic composition of biosphere-atmosphere exchange by using the Keeling two-member mixing model (the classic Keeling plot). An alternative method, based on a new capacity to measure isotopic mixing ratios, is to determine the isotope composition of biosphere–atmosphere exchange from the ratio of flux measurements. The objective of this study was to critically evaluate these methods for quantifying the isotopic composition of ecosystem respiration (δ_R) over a period of three growing seasons (2003–2005) within a heterogeneous landscape consisting of C₃ and C₄ species. For C₄ canopies, the mixing model approach produced δ_R values that were 4–6‰ lower (isotopically lighter) than the flux-gradient method. The analyses presented here strongly suggest that differences between flux and concentration footprint functions are the main factor influencing the inequality between the mixing model and flux-gradient approaches. A mixing model approach, which is based on the concentration footprint, can have a source area influence more than 20-fold greater than the flux footprint. These results highlight the fact that isotopic flux partitioning is susceptible to problems arising from combining signals (concentration and fluxes) that represent very different spatial scales (footprint). This problem is likely to be most pronounced within heterogeneous terrain. However, even under ideal conditions, the mismatch between concentration and flux footprints could have a detrimental impact on isotopic flux partitioning where very small differences in isotopic signals must be resolved.     

Numerical analysis of flux footprints for different landscapes

Summary A model for the canopy – planetary boundary layer flow and scalar transport based on E- closure was applied to estimate footprint for CO₂ fluxes over different inhomogeneous landscapes. Hypothetical heterogeneous vegetation patterns – forest with clear-cuts as well as hypothetical heterogeneous relief – a bell-shaped valley and a ridge covered by forest were considered. The distortions of airflow caused by these heterogeneities are shown – the upwind deceleration of the flow at the ridge foot and above valley, acceleration at the crest and the flow separation with the reversed flow pattern at lee slopes of ridge and valley. The disturbances induce changes in scalar flux fields within the atmospheric surface layer comparing to fluxes for homogeneous conditions: at a fixed height the fluxes vary as a function of distance to disturbance. Correspondingly, the flux footprint estimated from model data depends on the location of the point of interest (flux measurement point) and may significantly deviate from that for a flat terrain. It is shown that proposed method could be used for the choice of optimal sensor position for flux measurements over complex terrain as well as for the interpretation of data for existing measurement sites. To illustrate the latter the method was applied for experimental site in Solling, Germany, taking into account the complex topography and vegetation heterogeneities. Results show that in certain situations (summer, neutral stratification, south or north wind) and for a certain sensor location the assumptions of idealized air flow structure could be used for measurement interpretation at this site, though in general, extreme caution should be applied when analytical footprint models are used in the interpretation of flux measurements over complex sites.     

Flux Footprint Simulation Downwind of a Forest Edge

Surface fluxes, originating from forest patches, are commonly calculated from atmospheric flux measurements at some height above that patch using a correction for flux arising from upwind surfaces. Footprint models have been developed to calculate such a correction. These models commonly assume homogeneous turbulence, resulting in a simulated atmospheric flux equal to the average surface flux in the footprint area. However, atmospheric scalar fluxes downwind of a forest edge have been observed to exceed surface fluxes in the footprint area. Variations in atmospheric turbulence downwind of the forest edge, as simulated with an E – model, can explain enhanced atmospheric scalar fluxes. This E – model is used to calculate the footprint of atmospheric measurements downwind of a forest edge. Atmospheric fluxes appear mainly enhanced as a result of a stronger sensitivity to fluxes from the upwind surface. A sensitivity analysis shows that the fetch over forest, necessary to reach equilibrium between atmospheric fluxes and surface fluxes, tends to be longer for scalar fluxes as compared to momentum fluxes. With increasing forest density, atmospheric fluxes deviate even more strongly from surface fluxes, but over shorter fetches. It is concluded that scalar fluxes over forests are commonly affected by inhomogeneous turbulence over large fetches downwind of an edge. It is recommended to take horizontal variations in turbulence into account when the footprint is calculated for atmospheric flux measurements downwind of a forest edge. The spatially integrated footprint is recommended to describe the ratio between the atmospheric flux and the average surface flux in the footprint.     

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.     

Footprint estimation for scalar flux measurements in the atmospheric surface layer

The flux footprint is the contribution, per unit emission, of each element of a surface area source to the vertical scalar flux measured at height z _m ; it is equal to the vertical flux from a unit surface point source. The dependence of the flux footprint on crosswind location is shown to be identical to the crosswind concentration distribution for a unit surface point source; an analytic dispersion model is used to estimate the crosswind-integrated flux footprint. Based on the analytic dispersion model, a normalized crosswind-integrated footprint is proposed that principally depends on the single variable z/z _m , where z is a measure of vertical dispersion from a surface source. The explicit dependence of the crosswind-integrated flux footprint on downwind distance, thermal stability and surface roughness is contained in the dependence of z on these variables. By also calculating the flux footprint with a Lagrangian stochastic dispersion model, it is shown that the normalized flux footprint is insensitive to the analytic model assumption of a self-similar vertical concentration profile.The National Center for Atmospheric Research is funded by the National Science Foundation.     

Flux between soil and atmosphere, vertical concentration profiles in soil, and turnover of nitric oxide: 1. Measurements on a model soil core

A stainless steel soil corer which was filled with homogenized soil was used to measure the flux (J) of NO between soil and atmosphere and the vertical profile of the NO mixing ratios (m) in the soil atmosphere, both as function of the NO mixing ratio (mm _a ) in the atmosphere of the headspace. The NO emission flux decreased linearly with increasing NO mixing ratio and turned into a deposition flux after passage of the compensation point (m _c) at about 400 ppbv NO. Almost the same compensation point was obtained when the turnover of NO was measured in flask-incubated soil samples as function of the NO mixing ratio. The flux (J) of NO at the soil-atmosphere interface was calculated from the production rate (P) of NO and the NO uptake rate constant (k) that were measured in these flask-incubated soil samples using the diffusion model of Galbally and Johansson (1989). The calculated fluxes agreed within <15% with those actually measured. The vertical profiles of NO were fitted to an exponential function and analyzed by Fick's first law of diffusion. The shape of the profiles indicated a net production of NO in the upper 10 cm soil layer when the atmospheric NO mixing ratio was below the compensation point and in a net consumption of NO when the atmospheric NO mixing ratio was above the compensation point. In soil layers below 10 cm depth, the turnover of NO resulted in compensation of production and consumption rates. Measurement of the actual diffusion coefficient using SF₆ showed that gas transport in the soil core was not only due to molecular diffusion but in addition due to a bidirectional gas flow. The experimentally determined diffusion coefficient was smaller than that computed from soil porosities, but resulted together with the additional transport term in NO fluxes that were close (< ±15%) to those measured. This is the first comprehensive study of NO concentration profiles and turnover rates in soil providing a theoretical basis for modelling NO fluxes at the soil-atmosphere interface.     

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

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

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.     

Estimating Co2 Source/Sink Distributions Within A Rice Canopy Using Higher-Order Closure Model

Source/sink strengths and vertical fluxdistributions of carbon dioxide within and above arice canopy were modelled using measured meanconcentration profiles collected during aninternational rice experiment in Okayama, Japan (IREX96). The model utilizes an Eulerian higher-orderclosure approach that permits coupling of scalar andmomentum transport within vegetation to infer sourcesand sinks from mean scalar concentration profiles; theso-called `inverse problem'. To compute the requiredvelocity statistics, a Eulerian second-order closuremodel was considered. The model well reproducedmeasured first and second moment velocity statisticsinside the canopy. Using these modelled velocitystatistics, scalar fluxes within and above the canopywere computed and compared with CO<sub>2</sub>eddy-correlation measurements above the canopy. Goodagreement was obtained between model calculations offluxes at the top of the canopy and measurements. Close to the ground, the model predicted higherrespiratory fluxes when the paddy was drained comparedto when it was flooded. This is consistent with thefloodwater providing a barrier to diffusion ofCO<sub>2</sub> from the soil to the atmosphere. TheEulerian sources and flux calculations were alsocompared to source and flux distributions estimatedindependently using a Lagrangian Localized Near Fieldtheory, the first study to make such a comparison.Some differences in source distributions werepredicted by these analyses. Despite this, thecalculated fluxes by the two approaches compared wellprovided a closure constant, accounting for theinfluence of `near-field' sources in the Eulerian fluxtransport term, was given a value of 1.5 instead ofthe value of 8 found in laboratory studies.     

Source areas for scalars and scalar fluxes

The spatial resolution of meteorological observations of scalars (such as concentrations or temperature) and scalar fluxes (e.g., water-vapour flux, sensible heat flux) above inhomogeneous surfaces is in general not known. It is determined by the surface area of influence orsource area of the sensor, which for sensors of quantities that are subject to turbulent diffusion, depends on the flow and turbulence conditions.Functions describing the relationship between the spatial distribution of surface sources (or sinks) and a measured signal at height in the surface layer have been termed thefootprint function or thesource weight function. In this paper, the source area of levelP is defined as the integral of the source weight function over the smallest possible domain comprising the fractionP of the total surface influence reflected in the measured signal. Source area models for scalar concentration and for passive scalar fluxes are presented. The results of the models are presented as characteristic dimensions of theP=50% source areas (i.e., the area responsible for 50% of the surface influence): the maximum source location (i.e., the upwind distance of the surface element with the maximum-weight influence), the near and the far end of the source area, and its maximal lateral extension. These numerical model results are related directly to non-dimensional surface-layer scaling variables by a non-linear least squares method in a parameterized model which provides a user-friendly estimate of the surface area responsible for measured concentrations or fluxes. The source area models presented here allow conclusions to be made about the spatial representativeness and the localness (these terms are defined in the text) of flux and concentration measurements.     

Buoyancy and The Sensible Heat Flux Budget Within Dense Canopies

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

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.     

A micrometeorological investigation of surface exchange of O3, SO2 and NO2: A case study

Data obtained in an intensive field study of the dry deposition of sulfur dioxide, ozone, and nitrogen dioxide, conducted in 1985 in central Pennsylvania, are used to illustrate the factors that must be considered to assure that high quality results are derived. In particular, the quality of the site must be such that flux measurements made above the surface are representative of surface values. For this purpose, tests involving momentum transfer and the surface energy budget are especially useful. In addition, conditions must not be changing rapidly, and the statistical uncertainty associated with flux measurement must be low. For the set of data presented here, conservative quality-assurance guidelines are used to reject potentially erroneous flux data. For ozone, most of the measured fluxes are of use in deriving surface resistances. For SO₂, far fewer data points are available. For NO₂, fluxes appear to lack the order of the O₃ and SO₂ fluxes, and do not enable surface resistances to be computed. The highest-quality SO₂ and O₃ data yield surface resistances in fair average agreement with model predictions for SO₂, but substantially higher than predictions for O₃.     

Utility of Assimilating Surface Radiometric Temperature Observations for Evaporative Fraction and Heat Transfer Coefficient Retrieval

Recent advances in land data assimilation have yielded variational smoother techniques designed to solve the surface energy balance based on remote observations of surface radiometric temperature. These approaches have a number of potential advantages over existing diagnostic models, including the ability to make energy flux predictions between observation times and reduced requirements for ancillary parameter estimation. Here, the performance of a recently developed variational smoother approach is examined in detail over a range of vegetative and hydrological conditions in the southern U.S.A. during the middle part of the growing season. Smoother results are compared with flux tower observations and energy balance predictions obtained from the two-source energy balance model (TSM). The variational approach demonstrates promise for flux retrievals at dry and lightly vegetated sites. However, results suggest that the simultaneous retrieval of both evaporative fraction and turbulent transfer coefficients by the variational approach will be difficult for wet and/or heavily vegetated land surfaces. Additional land surface information (e.g. leaf area index (L_AI) or the rough specification of evaporative fraction bounds) will be required to ensure robust predictions under such conditions. The single-source nature of the variational approach also hampers the physical interpretation of turbulent transfer coefficient retrievals. Intercomparisons between energy flux predictions from the variational approach and the purely diagnostic TSM demonstrate that the relative accuracy of each approach is contingent on surface conditions and the accuracy with which L_AI values required by the TSM can be estimated.     

Flux between soil and atmosphere, vertical concentration profiles in soil, and turnover of nitric oxide: 2. Experiments with naturally layered soil cores

Intact soils cores were taken with a stainless steel corer from a sandy podzol and a loamy luvisol, and used to measure the flux (J) of NO between soil and atmosphere and the vertical profile of the NO mixing ratios (m) in the soil atmosphere, both as function of the NO mixing ratio (m _a) in the atmosphere of the headspace. These measurements were repeated after stepwise excavation of the soil column from the top, e.g. by removing the upper 2 cm soil layer. The gaseous diffusion coefficients of NO in the soil cores were either computed from soil porosity or were determined from experiments using SF6. The NO fluxes (J) that were actually measured at the soil surface were compared to the fluxes which were calculated either from the vertical NO profiles (J _c ) or from the NO production and uptake rates (J _m ) determined in the excavated soil samples. In the podzol, the actually measured (J) and the calculated (J _m , J_m) NO fluxes agreed within a factor of 2. In the luvisol, the measured NO fluxes (J) and those calculated from the vertical NO profiles (J _c ) also agreed well, but in the upper 6 cm soil layer the NO fluxes (J _m ) calculated from NO production and uptake rates were up to 7 times higher than the measured NO fluxes. This poor agreement was probably due to the inhomogeneous distribution of NO production and consumption processes and the change of diffusivities within the top layers of the luvisol. Indeed, the luvisol showed a pronounced maximum of the NO mixing ratios at about 6 cm depth, whereas the podzol column exhibited a steady and exponential decrease of the NO mixing ratios with depth. The inhomogeneities in the luvisol were confirmed by incubation of the soil cores under anoxic conditions. This treatment resulted in production of NO at several depths indicating a zonation of increased potential activities within the luvisol profile which may have biased the modelling of the NO surface flux from turnover measurements in soil samples. Inhomogeneities could be achieved even in homogenized soil by fertilization with nitrate solution.     

The Turbulent Lagrangian Time Scale in Forest Canopies Constrained by Fluxes,Concentrations and Source Distributions

One-dimensional Lagrangian dispersion models, frequently used to relate in-canopy source/sink distributions of energy, water and trace gases to vertical concentration profiles, require estimates of the standard deviation of the vertical wind speed, which can be measured, and the Lagrangian time scale, T _L , which cannot. In this work we use non-linear parameter estimation to determine the vertical profile of the Lagrangian time scale that simultaneously optimises agreement between modelled and measured vertical profiles of temperature, water vapour and carbon dioxide concentrations within a 40-m tall temperate Eucalyptus forest in south-eastern Australia. Modelled temperature and concentration profiles are generated using Lagrangian dispersion theory combined with source/sink distributions of sensible heat, water vapour and CO₂. These distributions are derived from a multilayer Soil-Vegetation-Atmospheric-Transfer model subject to multiple constraints: (1) daytime eddy flux measurements of sensible heat, latent heat, and CO₂ above the canopy, (2) in-canopy lidar measurements of leaf area density distribution, and (3) chamber measurements of CO₂ ground fluxes. The resulting estimate of Lagrangian time scale within the canopy under near-neutral conditions is about 1.7 times higher than previous estimates and decreases towards zero at the ground. It represents an advance over previous estimates of T _L , which are largely unconstrained by measurements.     

Effect of surface layer thickness on simultaneous transport of heat and water in a bare soil and its implications for land surface schemes

Abstract

A physically‐based multi‐layer numerical model is developed to determine the coupled transport of heat and water in the soil and in the soil‐atmosphere boundary layer. Using inputs of standard weather data and initial soil conditions the model is capable of predicting the surface energy balance components as well as water content and temperature profiles in the soil. It is used to predict these variables for a bare silt loam soil under two tillage treatments, viz. culti‐packed and left loose after disc‐harrowing, and the predicted results are compared with measurements. Very good agreement between the model predictions and measured evaporation and heat fluxes and soil water and temperatures for a ten‐day period shows that the model is capable of simulating the coupled transport of soil heat and soil water and their transfer across the soil surface‐atmosphere interface adequately.

Model predictions were compared with those of CLASS (Canadian Land Surface Scheme). It is shown that CLASS, version 2.6, provides good estimates of evaporation and hence the latent heat flux density, Q_E, under wetter soil conditions, but overestimates Q_E at moderately wet soil conditions and underestimates it under dry soil conditions. Under dry to moderately wet soil conditions the calculation of evaporation from bare soil is very sensitive to the thickness of the top layer particularly as the thickness approaches 10 cm.     

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.     

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.