Random uncertainties of flux measurements by the eddy covariance technique

Large variability is inherent to turbulent flux observations. We review different methods used to estimate the flux random errors. Flux errors are calculated using measured turbulent and simulated artificial records. We recommend two flux errors with clear physical meaning: the flux error of the covariance, defining the error of the measured flux as 1 standard deviation of the random uncertainty of turbulent flux observed over an averaging period of typically 30 min to 1 h duration; and the error of the flux due to the instrumental noise. We suggest that the numerical approximation by Finkelstein and Sims (2001) is a robust and accurate method for calculation of the first error estimate. The method appeared insensitive to the integration period and the value 200 s sufficient to obtain the estimate without significant bias for variety of sites and wide range of observation conditions. The filtering method proposed by Salesky et al. (2012) is an alternative to the method by Finkelstein and Sims (2001) producing consistent, but somewhat lower, estimates. The method proposed by Wienhold et al. (1995) provides a good approximation to the total flux random uncertainty provided that independent cross-covariance values far from the maximum are used in estimation as suggested in this study. For the error due to instrumental noise the method by Lenschow et al. (2000) is useful in evaluation of the respective uncertainty. The method was found to be reliable for signal-to-noise ratio, defined by the ratio of the standard deviation of the signal to that of the noise in this study, less than three. Finally, the random uncertainty of the error estimates was determined to be in the order of 10 to 30 % for the total flux error, depending on the conditions and method of estimation.Peer reviewe

Evaluation of mean concentration and fluxes in turbulent flows by Lagrangian stochastic models

Forward and backward stochastic Lagrangian trajectory simulation methods for calculation of the mean concentration of scalars and their fluxes for sources arbitrarily distributed in space and time are constructed and justified. Generally, absorption of scalars by medium is taken into account. A special case of the source structure, when the scalar is generated by a plane source, say, located close to the ground, is treated. This practically interesting particular case is known in the literature as the footprint problem

Direct and Adjoint Monte Carlo Algorithms for the Footprint Problem

Lagrangian stochastic models and algorithms are constructed and justified for solving the footprint problem, namely, the problem of calculation of the mean concentration and the flux of particles at a fixed point released from a source arbitrarily situated in the space. The direct and adjoint Monte Carlo algorithms are suggested, and rigorous justifications are given. Two different backward trajectory algorithms are considered: Thomson's method and a method based on probabilistic representations of the relevant initial value problem. The cost of the latter algorithm may increase with time, but it allows to treat the general situation when a set of reacting species is scattered by the flow. Thomson's approach is extended to general stochastic differental equations which is especially usefull when it is desired to find a solution at a fixed point, and for large time instances

Emission fluxes and atmospheric degradation of monoterpenes above a boreal forest: Field measurements and modelling

The contribution of monoterpenes to aerosol formation processes within and above forests is not well understood. This is also true for the particle formation events observed during the BIOFOR campaigns in Hyytiälä, Finland. Therefore, the diurnal variation of the concentrations of several biogenic volatile organic compounds (BVOCs) and selected oxidation products in the gas and particle phase were measured on selected days during the campaigns in Hyytiälä, Finland. α-pinene and Δ3-carene were found to represent the most important monoterpenes above the boreal forest. A clear vertical gradient of their concentrations was observed together with a change of the relative monoterpene composition with height. Based on concentration profile measurements of monoterpenes, their fluxes above the forest canopy were calculated using the gradient approach. Most of the time, the BVOC fluxes show a clear diurnal variation with a maximum around noon. The highest fluxes were observed for α-pinene with values up to 20 ng m−2 s−1 in summer time and almost 100 ng m−2 s−1 during the spring campaign. Furthermore, the main oxidation products from α-pinene, pinonaldehyde, and from β-pinene, nopinone, were detected in the atmosphere above the forest. In addition to these more volatile oxidation products, pinic and pinonic acid were identified in the particle phase in a concentration range between 1 and 4 ng m−3. Beside these direct measurement of known oxidation products, the chemical sink term in the flux calculations was used to estimate the amount of product formation of the major terpenes (α-pinene, β-pinene, Δ3-carene). A production rate of very low volatile oxidation products (e.g., multifunctional carboxylic) from ·OH- and O3-reaction of monoterpenes of about 1.3·104 molecules cm−3 s−1 was estimated for daylight conditions during summer time. Additionally, model calculations with the one-dimensional multilayer model CACHE were carried out to investigate the diurnal course of BVOC fluxes and chemical degradation of terpenes

Stochastic Lagrangian footprint calculations over a surface with an abrupt change of roughness height

Forward and backward stochastic Lagrangian trajectory simulation methods are developed to calculate the footprint and cumulative footprint functions of concentration and fluxes in the case when the ground surface has an abrupt change of the roughness height. The statistical characteristics to the stochastic model are extracted numerically from a closure model we developed for the atmospheric boundary layer. The flux footprint function is perturbed in comparison with the footprint function for surface without change in properties. The perturbation depends on the observation level as well as roughness change and distance from the observation point. It is concluded that the footprint function for horizontally homogeneous surface, widely used in estimation of sufficient fetch for measurements, can be seriously biased in many cases of practical importance

Simulating ozone dry deposition at a boreal forest with a multi-layer canopy deposition model

A multi-layer ozone (O-3) dry deposition model has been implemented into SOSAA (a model to Simulate the concentrations of Organic vapours, Sulphuric Acid and Aerosols) to improve the representation of O-3 concentration and flux within and above the forest canopy in the planetary boundary layer. We aim to predict the O-3 uptake by a boreal forest canopy under varying environmental conditions and analyse the influence of different factors on total O-3 uptake by the canopy as well as the vertical distribution of deposition sinks inside the canopy. The newly implemented dry deposition model was validated by an extensive comparison of simulated and observed O-3 turbulent fluxes and concentration profiles within and above the boreal forest canopy at SMEAR II (Station to Measure Ecosystem-Atmosphere Relations II) in Hyytiala, Finland, in August 2010. In this model, the fraction of wet surface on vegetation leaves was parametrised according to the ambient relative humidity (RH). Model results showed that when RH was larger than 70% the O-3 uptake onto wet skin contributed similar to 51% to the total deposition during nighttime and similar to 19% during daytime. The overall contribution of soil uptake was estimated about 36 %. The contribution of sub-canopy deposition below 4.2m was modelled to be similar to 38% of the total O-3 deposition during daytime, which was similar to the contribution reported in previous studies. The chemical contribution to O-3 removal was evaluated directly in the model simulations. According to the simulated averaged diurnal cycle the net chemical production of O-3 compensated up to similar to 4% of dry deposition loss from about 06:00 to 15:00 LT. During nighttime, the net chemical loss of O-3 further enhanced removal by dry deposition by a maximum similar to 9 %. Thus the results indicated an overall relatively small contribution of airborne chemical processes to O-3 removal at this site.Peer reviewe

Quantifying the uncertainty of eddy covariance fluxes due to the use of different software packages and combinations of processing steps in two contrasting ecosystems

We have carried out an inter-comparison between EddyUH and EddyPro (R), two public software packages for post-field processing of eddy covariance data. Datasets including carbon dioxide, methane and water vapour fluxes measured over 2 months at a wetland in southern Finland and carbon dioxide and water vapour fluxes measured over 3 months at an urban site in Helsinki were processed and analysed. The purpose was to estimate the flux uncertainty due to the use of different software packages and to evaluate the most critical processing steps, determining the largest deviations in the calculated fluxes. Turbulent fluxes calculated with a reference combination of processing steps were in good agreement, the systematic difference between the two software packages being up to 2.0 and 6.7% for half-hour and cumulative sum values, respectively. The raw data preparation and processing steps were consistent between the software packages, and most of the deviations in the estimated fluxes were due to the flux corrections. Among the different calculation procedures analysed, the spectral correction had the biggest impact for closed-path latent heat fluxes, reaching a nocturnal median value of 15% at the wetland site. We found up to a 43% median value of deviation (with respect to the run with all corrections included) if the closed-path carbon dioxide flux is calculated without the dilution correction, while the methane fluxes were up to 10% lower without both dilution and spectroscopic corrections. The Webb-Pearman-Leuning (WPL) and spectroscopic corrections were the most critical steps for open-path systems. However, we found also large spectral correction factors for the open-path methane fluxes, due to the sensor separation effect.Peer reviewe

Urban nitrous-oxide fluxes measured using the eddy-covariance technique in Helsinki, Finland

Peer reviewe

Uncertainty of eddy covariance flux measurements over an urban area based on two towers

The eddy covariance (EC) technique is the most direct method for measuring the exchange between the surface and the atmosphere in different ecosystems. Thus, it is commonly used to get information on air pollutant and greenhouse gas emissions, and on turbulent heat transfer. Typically an ecosystem is monitored by only one single EC measurement station at a time, making the ecosystem-level flux values subject to random and systematic uncertainties. Furthermore, in urban ecosystems we often have no choice but to conduct the single-point measurements in non-ideal locations such as close to buildings and/or in the roughness sub-layer, bringing further complications to data analysis and flux estimations. In order to tackle the question of how representative a single EC measurement point in an urban area can be, two identical EC systems - measuring momentum, sensible and latent heat, and carbon dioxide fluxes - were installed on each side of the same building structure in central Helsinki, Finland, during July 2013-September 2015. The main interests were to understand the sensitivity of the vertical fluxes on the single measurement point and to estimate the systematic uncertainty in annual cumulative values due to missing data if certain, relatively wide, flow-distorted wind sectors are disregarded. The momentum and measured scalar fluxes respond very differently to the distortion caused by the building structure. The momentum flux is the most sensitive to the measurement location, whereas scalar fluxes are less impacted. The flow distortion areas of the two EC systems (40-150 and 230-340 degrees) are best detected from the mean-wind-normalised turbulent kinetic energy, and outside these areas the median relative random uncertainties of the studied fluxes measured by one system are between 12 % and 28 %. Different gap-filling methods with which to yield annual cumulative fluxes show how using data from a single EC measurement point can cause up to a 12 % (480 g C m(-2)) underestimation in the cumulative carbon fluxes as compared to combined data from the two systems. Combining the data from two EC systems also increases the fraction of usable half-hourly carbon fluxes from 45 % to 69 % at the annual level. For sensible and latent heat, the respective underestimations are up to 5 % and 8 % (0.094 and 0.069 TJ m(-2)). The obtained random and systematic uncertainties are in the same range as observed in vegetated ecosystems. We also show how the commonly used data flagging criteria in natural ecosystems, kurtosis and skewness, are not necessarily suitable for filtering out data in a densely built urban environment. The results show how the single measurement system can be used to derive representative flux values for central Helsinki, but the addition of second system to other side of the building structure decreases the systematic uncertainties. Comparable results can be expected in similarly dense city locations where no large directional deviations in the source area are seen. In general, the obtained results will aid the scientific community by providing information about the sensitivity of EC measurements and their quality flagging in urban areas.Peer reviewe

Impact of coordinate rotation on eddy covariance fluxes at complex sites

The choice of coordinate system to calculate eddy covariance fluxes becomes particularly relevant at complex measurement sites. The traditional way is to perform double rotation (DR) of the coordinate system i.e., to calculate turbulent fluxes in a coordinate system that is aligned with the flow streamlines within the flux averaging period (e.g., Kaimal and Finnigan, 1994). The second approach, the so-called planar-fitted (PF) coordinate system, averages the flow over a longer period of time, in practice a month or more. The PF method allows to derive an intercept coefficient of the vertical wind speed which can be attributed to the offset of the sonic anemometer or the average vertical flow related to meteorological conditions. We evaluated the variants of the PF methods using data from a variety of sites ranging from complex urban and forest sites to nearly ideal forest and peatland sites. At complex sites, we found that the intercept of the vertical wind speed derived from the PF method is a function of wind direction, time of day and/or stability. The sector-wise PF (SPF) method frequently led to insignificant statistical relationships. We tested a continuous PF (CPF) method where the relationship establishing the coordinate frame was represented as the continuous function in the form of Fourier series. The method enabled to obtain the PF with lower uncertainty as compared to the SPF method, by selecting necessary number of harmonics for each site based on confidence intervals of estimated parameters. Therefore, we recommend to use the CPF method in cases when the number of observations in some wind direction interval is low or the obtained SPF is insignificant due to large variance in measurements. We also showed that significant systematic difference can exist in cumulative turbulent fluxes between the DR and PF methods over a longer period of time. Derived vertical advection of carbon dioxide exhibited large variability with wind direction due to topography at complex sites and therefore, without considering horizontal advection, cannot be used to improve the net ecosystem exchange estimation during nocturnal, low turbulence conditions.Peer reviewe