Particle fluxes above forests: Observations, methodological considerations and method comparisons

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Environmental Pollution 152 (2008) 667e678 www.elsevier.com/locate/envpol

Particle fluxes above forests: Observations, methodological considerations and method comparisons S.C. Pryor a,b,*, S.E. Larsen b, L.L. Sørensen b, R.J. Barthelmie a,b,c a

Atmospheric Science Program, Department of Geography, Indiana University, 701 E. Kirkwood Avenue, Bloomington, IN 47405, USA b Department of Wind Energy and Atmospheric Physics, Risø National Laboratory, Dk4000 Roskilde, Denmark c Institute for Energy Systems, School of Engineering and Electronics, University of Edinburgh, Edinburgh EH9 3JL, UK Received 2 March 2006; received in revised form 27 February 2007; accepted 29 June 2007

Number fluxes of ultra-fine particles over a forest computed using four micro-meteorological techniques are highly correlated but vary in magnitude. Abstract This paper reports a study designed to test, evaluate and compare micro-meteorological methods for determining the particle number flux above forest canopies. Half-hour average particle number fluxes above a representative broad-leaved forest in Denmark derived using eddy covariance range from 7  107 m2 s1 (1st percentile) to 5  107 m2 s1 (99th percentile), and have a median value of 1.6  106 m2 s1. The statistical uncertainties associated with the particle number flux estimates are larger than those for momentum fluxes and imply that in this data set approximately half of the particle number fluxes are not statistically different to zero. Particle number fluxes from relaxed eddy accumulation (REA) and eddy covariance are highly correlated and of almost identical magnitude. Flux estimates from the co-spectral and dissipation methods are also correlated with those from eddy covariance but exhibit higher absolute magnitude of fluxes. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Particle number fluxes; Eddy covariance; Spectral methods; Relaxed eddy accumulation; Forests

1. Introduction and objectives

computed as the mean cross-product of the perturbations of concentration (C0 ) and vertical velocity (w0 ):

Current understanding of particle dry deposition is incomplete due to the complexity of the functional dependences on physical and chemical properties of the particle ensemble, surface characteristics, and atmospheric conditions, and also the inherent difficulties in direct measurement of particle dry deposition fluxes. Micro-meteorological techniques applied to quantify atmosphereesurface exchange of trace materials include:

F ¼ w0 C0

(i) Eddy covariance (Sievering, 1987; Gallagher et al., 1997; Aubinet et al., 2000), where the flux (F ) is * Corresponding author. Tel.: þ1 812 855 5155; fax: þ1 812 855 1661. E-mail address: [email protected] (S.C. Pryor). 0269-7491/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.envpol.2007.06.068

ð1Þ

(ii) Eddy accumulation or relaxed eddy accumulation (Oncley et al., 1993; Gaman et al., 2004), where the flux is determined from the mean concentration of air differentially sampled based on the vertical velocity. Relaxed eddy accumulation (REA) is a variant of eddy accumulation in which air is differentially sampled at a constant flow rate based on the vertical velocity as the vertical velocity (w) exceeds a threshold (‘dead-band’) velocity (Businger and Oncley, 1990):   F ¼ bsw Cup  Cdown

ð2Þ

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where b is an experimental coefficient (the Businger coefficient) determined by the probability distribution of w, the dead-band width and sampling height, Cup and Cdown are average concentrations from samples collected when w is positive and negative, respectively, and sw is the standard deviation of w. (iii) Spectral approaches, where the flux is computed from the data after they have been transformed into the frequency domain. The inertial dissipation method (Fairall and Larsen, 1986; Edson et al., 1991) employs the universal laws for inertial range small scale turbulence combined with the MonineObukhov relations for surface layer turbulence, to derive the fluxes from the 5/3 slope of the high frequency of the power spectra, S( f ):  1=3 1=2  fSu ðf Þ 2p kz u ¼ f ð3Þ a u f3 "

a f3 fSg ðf Þ jw0 g0 j ¼ b fNg fSu ðf Þ

#1=2 u2

ð4Þ

where u is the mean wind speed (m s1), z is the effective measurement height (m), k is the von Karman constant, u* is the friction velocity, and g is any scalar quantity (temperature, water vapor, or number concentration of particles). The coefficients a and b are the Kolmogorov constants describing the intensity of the inertial range spectra, a for the velocity spectra and b for all scalar spectra. b is generally assumed to be the same for all scalars in accord with experimental data, and fundamental reasoning (Hill, 1989a,b). f3 and fNg are the normalized dissipation functions for velocity and g, respectively. Within the MonineObukhov formulation both are functions of the thermal stability (fNg is usually taken to be equal to the dissipation function for temperature). The co-spectral method employs the low frequency part of the co-spectra, Co( f ) to derive fluxes: w0 g0 z5nCowg ðnÞ; for 0:008  n  0:12

ð5Þ

where n is a normalized frequency given by n ¼ fz=u: The method was first proposed by Larsen (1986) is based on synthesis of literature on fluxes of momentum, heat and humidity that indicate relevant normalized co-spectra tend to have their peak for n between 0.008 and 0.12 with fairly broad maximums with a value around 0.2 of the total flux (Pond et al., 1971; Kaimal et al., 1972; McBean and Miyake, 1972; Schmitt et al., 1979; Smith and Anderson, 1984). As opposed to the inertial dissipation method there is no theoretical basis for this empirical result, and it is associated with a larger statistical uncertainty than the dissipation method (Edson et al., 1991). The inertial dissipation method and the cospectra method are differentially sensitive to the high and

the low frequency parts of the turbulence spectra and can therefore generally be considered statistically independent. The measurements reported herein were taken to test, evaluate and compare methods for determining the particle number flux to forest canopies. Specifically, we sought to quantify the corrections to, and errors associated with, application of eddy covariance to particle data and to compare particle number fluxes derived using the different micrometeorological methods described above. The fluxes we report are derived for particle ensembles with number geometric mean diameters of below 90 nm and hence may be characterized as fluxes of ultra-fine particles. For discussion of the size dependence of the flux of ultra-fine particles at the forest site considered herein (Sorø) and the Hyytia¨la¨ forest station in southern Finland, we direct the reader to Pryor (2006) and Gaman et al. (2004), respectively. 2. Site description and instrumentation The measurements described herein were conducted at the CarboEuroFlux experimental forest site at Sorø in Denmark (Pilegaard et al., 2003). The forest canopy reaches a height of approximately 24e25 m, and the peak canopy leaf area index is approximately 5 m2 m2 in this 80-year-old beech (Fagus silvatica L.) stand. The fetch is homogeneous for 0.5e 1 km depending on wind direction. The site is equipped with a 57-m meteorological mast (cross-section of 30  30 cm) and a 24-m scaffold tower (cross-section 3  3 m) which are separated by a horizontal distance of z5 m. The ongoing measurements at Sorø are described in brief in Pilegaard et al. (2003), and the measurements presented here were collected during a field experiment conducted in Maye June 2004 to study the particle characteristics and dynamics at this site. A TSI condensation particle counter (CPC) 3010 sampled air from 35 m via an 18 m copper tube (i.d. 4 mm). The TSI CPC 3010 was also used by Buzorius et al. (2000) and is reported to detect particles with a diameter of 10 nm with an efficiency of 50% (Mertes et al., 1995) and 80% of particles of 20 nm diameter in the laboratory study of Buzorius et al. (2000) even with a 4.5 m (3.6 mm i.d.) stainless steel tube with a flow rate of 5.6 l min1. The flow within the copper tubing deployed for this research was maintained at 14.2 l min1, giving a residence time of O(1 s) and Reynolds number O(5000) to maintain a turbulent regime. The resulting data which were logged at 10 Hz are used here in combination with the wind components from a Metek 3-D sonic to derive particle number fluxes. The physical size distribution above the canopy was also measured using a scanning mobility particle sampler (TSI SMPS3936L25) and an aerodynamic particle sizer (TSI APS 3321). The SMPS comprised an Electrostatic Classifier model #3080, long-DMA (model #3081) and a CPC 3025A and it was configured to scan from 10 nm to approximately 400 nm every 150 s. The APS 3321 was configured to measure the particle size spectrum from approximately 0.5 to 19 mm at the same scan frequency. Based on data collected with these instruments, the number geometric mean

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Fig. 1. (a) Time series of half-hour average particle number geometric mean diameter during the field experiment at Sorø derived using data from the SMPS. (b) The mean particle size distribution from the SMPS during 16 June 2004.

diameter during the field experiment ranged between 20 and 80 nm (Fig. 1a). The mean number particle size distribution observed during 16 June 2004 (the day presented in detail herein) indicate two modes between 10 and 400 nm centered at approximately 30 and 120 nm (Fig. 1b). Over 90% of half-hour average total particle concentrations observed using the CPC3010 were below 5  109 m3. At these concentrations the correction for particle coincidence is <3.5%, hence no correction for particle coincidence was applied to the data. Particle size-resolved composition integrated over 24 and 48 h periods was measured using an MSP MOUDI-110 with nano-MOUDI attachment. Aluminum foil substrates were coated using silicon spray to minimize particle bounce, extracted in oxalic acid (105 M) after exposure and analyzed on an ion chromatograph. The results indicate that during the field experiment sub-100 nm particles were dominated by ammonium sulfate (Pryor et al., 2005). 3. Calculation of particle fluxes from eddy covariance 3.1. Methodology Prior to applying the flux calculation methods, data from all half-hour periods when rain was observed or any instrument malfunction occurred were removed from the time series to leave a data set of 1377 half-hour periods. Direct flux estimation using eddy covariance relies on relatively few assumptions, but these are not typically met and so a number of corrections were applied to the data in addition to despiking of the 10 Hz time series: (i) Co-ordinate rotation. This procedure is designed to force the data to a co-ordinate system where the mean vertical velocity is zero. It has recently been demonstrated that the choice of whether to undertake co-ordinate rotation on individual time periods or via use of

‘long term’ co-ordinate frame can have profound impacts on the resolved flux in regions with significant terrain variations (Finnigan et al., 2003). In this analysis we apply co-ordinate rotation on the individual halfhour periods. (ii) Detrending. Overlap of the diurnal cycle of concentrations and turbulence structure or instrument drift can lead to ‘trends’ in the data which are typically removed prior to calculation of the flux using linear detrending or application of a high-pass filter (Rannik and Vesala, 1999; Gash and Culf, 1996). In this analysis we detrend using ordinary linear regression. (iii) Webb correction (Webb et al., 1980). This correction is applied to take account of the variation in particle concentrations due to density variations caused by fluxes of heat/water vapor. The particle counts measured using the CPC are a description of the number of particles per volume of air and hence may be subject to errors due to fluctuations in air density. The correction to the flux due to density fluctuations is given by Webb et al. (1980): DF ¼ m

rc 0 0 w rv ra

ð6Þ

where m ¼ Ma/Mv (molecular mass of dry air and water vapor, respectively), and ra,c,v ¼ density of air, particles and water vapor, respectively. The Webb correction was calculated for the Sorø data using water vapor fluctuations measured using a Licor LI-6262. The correction is typically positive, reducing downward fluxes, and has an average value of <1% of the flux, with only 22 periods exhibiting a correction in excess of 20% of the flux. (iv) Correction for the attenuation of sensor response at frequencies above 1 Hz (Horst, 1997). The measured flux will underestimate the actual flux if some component of the eddy covariance system is not able to

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respond to variations across all the scales contributing to the flux. Many CPC have a first order time response which is considerably longer than 0.1 s, hence there is a need to correct the flux for the component associated with smaller wavelength eddies which are not accurately captured by the system. Buzorius (2001) derived a time response (tc) for the TSI CPC 3010 operating at 1 l min1 flow of 0.8 s based on Doebelin (1990) and the presumption that the CPC is a first order instrument. Normalized concentration time sequences presented in Buzorius (2001) suggest the instrument reaches an equilibrium level (i.e. within 5% of the equilibrium concentration) in 2.6 s after a step change in concentration, and the manufacturer reports a response time of <5 s for a 95% response to a concentration step change. The lag of maximum correlation of 10 Hz data with vertical velocity was found to be stable at 3.7 s for the configuration used in our set-up which taking account of the delay due to the sampling line leads to the inferred total response time of approximately 2.7 s, which is in good accord with the analysis of Buzorius (2001). Power spectra of particle concentrations indicate that the instrument set-up does truncate the spectrum at high frequency, so we applied the simple formulation of Horst (1997) to correct for the attenuation of the measured flux: Fm 1  a ¼ ð7Þ F 1 þ 2pnm tc uz nm ¼ 2:0 

1:915 1 þ 0:5z=L

ð8Þ

where u is the mean wind speed (m s1), z is the effective measurement height (m) computed from z ¼ z0 þ d, where d is the displacement height (d ¼ 3/4 canopy height (Jensen and Hummelshøj, 1995)) and z0 ¼ roughness length (1.6 m in the case of the Sorø beech forest (Pilegaard et al., 2003)). L is the MonineObukhov length (m), and a ¼ 1 for stable conditions, and 7/8 for unstable and near-neutral conditions. nm has a neutral limit of 0.085 which is also applied in unstable cases. The average flux underestimation in the data from Sorø due to the attenuation of the high frequencies was computed to be 13%. However, 150 half-hour periods exhibit a correction of 20e78%. (v) Correction for the influence of deliquescence (Fairall, 1984). Correlation of fluctuations in the saturation ratio (S ) with vertical wind speed can cause a bias in particle number fluxes. In the presence of humidity gradients, deliquescence of particles (uptake or release of water) will cause variations in the detection of particles by CPC as the particles grow or sink and hence move into or out of the size range to which the CPC is sensitive. We applied a correction based on the approach of Kowalski (2001). The correction is formulated in terms of the error in deposition velocity (vd) as a function of

the kinematic fluxes of temperature and water vapor, based on the assumption of a Junge particle size distribution and includes a single term to describe the hygroscopicity of the particles: Dvd ¼

Kf b

ð1  SÞ 2 3es ð1  SÞ þ3Kf es " # B 0 0 0 0  we e 2w T ðT þ CCÞ

ð9Þ

where b is a constant derived from the Junge power law size distribution (w3), S is the saturation ratio, es is the saturation vapor pressure, e is the vapor pressure, w0 e0 is the water vapor pressure flux (calculated here from 10 Hz measurements of specific humidity derived from the Licor LI-6262) and w0 T 0 is the temperature flux. Kf is a constant dependent on the ability of the particle ensemble to exhibit deliquescence, and is set here to 0.5 to represent a polluted continental air mass (Fitzgerald, 1975; Fairall, 1984), based on our composition measurements which indicate that the sub-200 mm particles are largely composed of ammonium and sulfate (Pryor et al., 2005). B and CC are coefficients from the relationship relating saturation vapor pressure to ambient temperature (T ):   BT es ¼ A exp ð10Þ T þ CC where A ¼ 6.111 mb, B ¼ 17.67 and CC ¼ 243.5  C. The average correction in the data collected at Sorø is 37%, although for approximately 100 half-hour periods the correction  the flux. This analysis thus indicates that of the corrections applied here the correction for deliquescence effects has the largest mean and absolute range, assuming, as we have here, that fluctuations in the ‘ambient’ saturation ratio (based on water vapor measurements in the LI-6262) are also manifest in the CPC. It should further be emphasized that this correction assumes the particle size distribution conforms to a Junge distribution (where N f particle diameter4). While the Junge distribution has been found to be a reasonable approximation over the diameter size range of 200 nm to 200 mm (Wen, 1996) it may not optimally represent observed size distributions for particles with diameters below 100 nm (see Fig. 1).

3.2. Results and uncertainty analysis Half-hour average particle number fluxes (Fig. 2) are of comparable magnitude to those computed from the Hyytia¨la¨ research station in the Finnish Boreal forest (Buzorius et al., 2000, 2001), which has similar particle number concentrations but is a coniferous forest. The particle number fluxes are typically downwards during the daytime, but as in previous applications of the eddy covariance method to particle number

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data from a CPC 3010) at Hyytia¨la¨ have been ascribed to emissions from the research station (Buzorius et al., 2000), and/or formation of new particles near to or within the forest canopy (Buzorius et al., 1998), and/or random uncertainty of the fluxes (Gaman et al., 2004). The upward fluxes observed at Sorø may also be due to the physical causes postulated from the Hyytia¨la¨ data or others such as resuspension of particles from tree surfaces (Ould-Dada and Baghini, 2001) which might additionally explain why some of the largest upward fluxes are directly preceded by large deposition fluxes (see for example Fig. 3). In an effort to resolve the cause of the apparent emission fluxes, following Buzorius et al. (2000) the half-hour average particle number concentrations and fluxes were analyzed with respect to prevailing wind direction in 30 sectors. As shown in Fig. 4 downward fluxes are more frequently observed than upward fluxes in all wind direction sectors except in the case of the ESE sector in which there are slightly more upward flux cases (180 periods v. 158 periods of downward flux). Thus the upward fluxes do not appear to be related to a local emission source. High particle number concentrations (arbitrary defined as [N] > 5  109 m3, which equates to approximately the 90th percentile half-hour particle number concentration) were also observed from all wind direction sectors. The major difference between the frequency of low particle number concentrations and high particle number concentrations is the virtual absence of low particle number concentrations associated with westerly winds. Thus, in this data set, we do not see strong coincidence of upward fluxes and high number concentrations by wind direction. An analysis of data from the SMPS seems to imply a decrease in number GMD prior to daytime upward fluxes (Pryor, 2006) possibly implying a link to within/above canopy nucleation, but at least in this fairly small data set no definitive explanation of the upward fluxes can be advanced.

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fluxes over forests (Buzorius et al., 2000; Gallagher et al., 2002) a large number of positive (upward) fluxes are observed. Indeed over one-third of the half-hour average particle number fluxes from Sorø are positive, and while many of these periods are observed at night during stable conditions, as shown in Fig. 3, upward fluxes are also observed during the daytime. These periods are not associated with anomalous fluxes of heat or momentum (Fig. 3), or malfunction of the CPC 3010 and hence are assumed to have a physical cause. Upward particle number fluxes (derived using eddy covariance based on 4.0x107

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Fig. 4. Particle number concentrations (left) and particle flux direction (right) presented as a function of prevailing wind direction (where wind directions have been collapsed into 30 sectors). The frame on the left shows the total particle number concentrations in each half-hour period presented in two classes; low particle counts (below 2  109 m3) and high particle counts (above 5  109 m3). The frame on the right shows the frequency of occurrence of flux direction (up or down) also presented in terms of the prevailing wind direction during each half-hour period. Note that in both frames the radial axes are logarithmic.

Even in the absence of upward fluxes it is useful to provide a context for all flux estimates by considering the associated uncertainties. This is conducted here based on the work of Wyngaard (1973) and Lumley and Panofsky (1964) who sought to determine the averaging time necessary to generate useful approximations of turbulent properties. Following Wyngaard (1973) the error (given as the standard deviation on the ensemble statistics) on the half-hour averages derived from the 10 Hz measurements of horizontal wind speed (u), vertical wind speed (w) and particle number concentrations (C) may be derived from: s2 a2 ¼ 2 x J x T

ð11Þ

where a is the inherent uncertainty (or accuracy of the estimate), s2x is the variance of the parameter of interest (C, u or w), T is the time interval used to compute the mean, and Jx is the averaging time to determine the turbulence properties to a given accuracy. For simplicity we follow Wyngaard’s suggestion and assume Jx ¼ Ju ¼ Jw ¼ JC ¼ z/u, where z is the effective measurement height (as defined above). For u and C it is meaningful to consider the relative error: a2 =x2 ¼ 2s2x =ðx2 TÞJx ; while w ¼ 0; hence we compute only the absolute error on the mean vertical velocity (given by Eq. (11)). For the variance estimates, we have x02 ¼ u02 ; w02 ; C02 and the uncertainty is given by:

  2 2 2 2 ¼ 2Jx x04 þ x02  2x02 a2 ¼ 2Jx x02  x0  2 ¼ 2Jx x04  x02 04

ð12Þ

2 02

Kurtosis ðKÞ ¼ x =x , so: 2 2Jx ðK  1Þx02 ð13Þ T For the variance of C, u and w the relative uncertainty is the most relevant parameter and hence is presented here. For the flux terms, w0 x0 ¼ w0 u0 ; w0 C0 , the error estimates are given by:

a2 ¼

a2 ¼

2Jx  0 0 2 2 ðw x Þ  w0 x0 T

ð14Þ

and are presented here in absolute terms. The relative error on the half-hour C estimates is of lesser magnitude than those on u (Fig. 5a). The majority of the relative errors on the variance estimates for particle concentrations are slightly larger than those for the wind components (Fig. 5b). However, over half of the half-hour average particle number fluxes estimated using the eddy covariance are of lesser magnitude than the absolute error computed using Eq. (14) (Fig. 5c), while only 1/4 of momentum fluxes are not statistically different than zero (Fig. 5c). Wyngaard (1973) examined the variance, about the mean, of hourly momentum and heat fluxes using ððx0 w0 Þ2 =ðx0 w0 Þ2 Þ  1 computed from the Kansas data set (Haugen et al., 1971) and

Fig. 5. (a)Uncertainty analyses of the half-hour estimates of the mean horizontal wind speed (u), vertical wind speed (w) and particle concentrations (C). Histograms of the mean statistics are shown above and the relative errors (defined here as a2 from Eq. (11) divided by x2 ) on the mean horizontal wind speed and concentrations and absolute error on the vertical wind speed are shown below. (b) Uncertainty analyses of the half-hour estimates of the variance of horizontal wind speed, vertical wind speed and particle concentrations. Histograms of the half-hour statistics are shown above and the relative errors are shown below. (c) Uncertainty analyses of the half-hour estimates of the fluxes of momentum and particle number. Histograms of the half-hour statistics are shown above and the absolute errors are shown below.

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Fig. 5. (continued ).

found this ratio to vary between 1 and 100. The same index was calculated for the half-hour flux data from the Sorø experiment and it was found that over 98% of the momentum flux lay between the bounds of the Kansas data. Fifty percent of the particle number fluxes also fall in this range, but an almost equal fraction have indices of 102e104 (over 91% lie between 1 and 104). As in the temperature flux data presented by Wyngaard (1973), there is some evidence for an increase in variance of the particle number flux estimates with increasingly stable conditions, but the scatter in ððw0 C0 Þ2 =ðw0 C0 Þ2 Þ  1 is very large. These results imply that, as in the analysis of momentum and heat fluxes from the Kansas experiment presented by Wyngaard (1973), longer averaging times are required to measure the particle number flux than the variance. It may further be inferred that, for a fixed averaging interval, the errors associated with particle flux estimates typically exceed those for heat and momentum fluxes. 4. Comparison of particle fluxes from eddy covariance, relaxed eddy accumulation and spectral methods 4.1. Methodology As discussed in Section 1 there are multiple micro-meteorological methods that may be applied to estimate particle fluxes. Here we applied four to the data from a single day of

measurements e 16 June 2004. This day was selected because during the majority of the day the wind direction and speed were relatively constant and the stability was near-neutral (Fig. 6). Additionally, this day was characterized by a large number of periods which have fluxes determined by eddy covariance that are statistically different from zero in both the positive and negative directions (Fig. 3). To replicate the results of a REA based flux estimation we resampled the 10 Hz time series of particle concentrations and vertical velocity (after co-ordinate rotation and detrending) dividing the concentration data numerically into ‘Up’ and ‘Down’ bins based on the vertical velocity taking into account the lag between the w and C measurements. In this analysis we applied a dead-band of 0.5sw and computed the half-hour fluxes using b derived continuously based on the momentum and sensible heat fluxes (bw and bT). The flux corrections described above were applied. The co-spectra and dissipation methods were also applied to the data from Sorø (Fig. 7). The dissipation of the particle power spectra is estimated by extrapolation from the frequency area 0.1e1 Hz using a slope of 2/3. According to Sørensen and Larsen (2005) this frequency area can be used for extrapolation to inertial sub-range at the wind speed range (4e7 m/s) and at the height where the measurements were carried out. The dissipation method, which was applied using u* estimates for the 10 Hz signal, provides

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REA method gives comparable flux estimates to those from eddy correlation (Table 1). Indeed, application of the REA method results in fluxes that are statistically indistinguishable from those derived using eddy covariance, and only in a few half-hour periods did the fluxes differ by more than the uncertainty estimates for the eddy covariance approach. However, it should be noted that REA was applied here off-line, and hence this analysis is not a validation of REA as a direct measurement technique. Gaman et al. (2004) present results from an on-line size-resolved particle REA system and validation using carbon dioxide fluxes computed using the REA system and eddy covariance. The correlation between fluxes computed for the Sorø data set using the two spectral techniques is better than between fluxes from either of the spectral techniques and the eddy covariance approach (Fig. 8, Table 1). In contrast to the REA derived fluxes, those from the spectral methods tend to give higher magnitude fluxes than those estimated using eddy covariance (Table 1). The EC fluxes are an average of 77% of the fluxes from the dissipation method, and only one-third of those from the co-spectral method. The cause/s of the bias/es have yet to be fully resolved, but it is important to note that the differences frequently exceed the uncertainties in the eddy covariance approach. However, the scatter shown in Fig. 8 is in reasonable accord with results from Edson et al. (1991) who found latent heat fluxes from instrumentation deployed on a mast at sea computed using the inertial dissipation technique were within 45% of the eddy covariance derived fluxes. The biases in particle number fluxes computed herein via the spectral methods relative to eddy covariance estimates may be related to: B Errors in one or more of the flux estimates due to: B Noise in the particle spectrum and co-spectra. Noise at higher frequencies would contribute little to the flux but would increase the measured dissipation. B Use of too narrow a band-pass in determining the maximum amplitude of the co-spectrum which would lead to insufficient inclusion of Fourier nodes of the opposite sign leading to over-estimation of the flux. B Differences in the ‘flux footprints’ associated with fluxes derived using the various techniques. Schmid (1994) showed source area dimensions are perhaps an order of magnitude higher for scalar concentrations than scalar fluxes, and hence it may be inferred that fluxes over inhomogeneous surfaces computed using techniques that reflect different moments of the particle number probability distribution may differ as a result of differences in the associated source areas.

only the absolute magnitude of the flux (see Eq. (4)) so the sign was assigned based on the eddy covariance estimate. The co-spectral method relies on assumptions regarding the shape of the co-spectra, which are not realized in all cases (see Fig. 7) and hence this approach could not be applied to all half-hour periods. It is worthy of note at this juncture that the observation that higher and low frequency components of the co-spectra have different signs was also made in the Kansas experiment (Larsen, 1986). Once the ‘raw’ fluxes were derived from the spectral approaches the Webb correction and the deliquescence correction were applied. The correction for the attenuation of the sensor response at high frequencies was not applied to the spectral methods since in principle both assume a universal form which we estimate at frequencies below the cut-off of the instrument response time. It is acknowledged that the forms of the corrections presented here, and derived on the basis of the eddy covariance approach, may not be optimal for application to ‘raw’ fluxes derived from other micro-meteorological approaches. They are used here as an approximation of the true corrections.

Future work will focus on providing robust corrections to, and uncertainties on, particle number fluxes derived from the other methods.

4.2. Results

5. Discussion

Comparison of half-hour average particle number fluxes computed from the four flux methods (Fig. 8) indicates the

The half-hour averaging period for flux calculation used here is common to many flux estimation studies (e.g. it is explicit in the

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AmeriFlux and EUROFLUX (CarboEuroFlux) methodologies for trace gas fluxes (Aubinet et al., 2000)) and is used as an implicit compromise between efforts to minimize the likely impact of non-stationarities and the reduction in accuracy in the flux statistics as the averaging time diminishes. The uncertainty in eddy covariance fluxes is also directly proportional to the effective measurement height and thus impacts the selection of a sampling height which is additionally something of a compromise between the desire to increase measurement heights to compensate for the relatively slow response of CPC (Buzorius et al., 2000) and to avoid the roughness sublayer (Raupach and Thom, 1981), versus the change in footprint caused by an increase in z (Markkanen et al., 2003). As shown herein, at a reasonably representative site in northern Europe with a somewhat standard deployment of instrumentation and integration times, approximately half of the particle flux estimates resolved using eddy covariance exhibit

statistical uncertainties of a sufficient magnitude that the fluxes are not statistically different from zero. It should be noted that the corrections to eddy covariance particle number fluxes and uncertainties calculated herein, are likely common to many particle flux studies that employ eddy covariance, and do not represent an exhaustive analysis of the totality of uncertainties associated with eddy covariance derived particle number fluxes. For additional considerations the reader is directed to the analysis of Buzorius et al. (2003) which is focused on the impact of limitations in particle instrumentation, and work by Sievering (1987) for a discussion of the influence of horizontal particle fluxes. 6. Conclusions Ten Hertz measurements of particle number concentrations over a Beech forest in Denmark are used in eddy covariance

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Fig. 8. Comparison of particle number fluxes on 16 June 2004 computed from the eddy covariance (EC) approach with those from the alternative micro-meteorological methods. The error bars on the eddy covariance estimates are those shown in Fig. 3. Frame (a) shows the comparison with flux estimates derived from the REA technique using both bw and bT. Frame (b) shows the comparison with flux estimates derived from the spectral approaches. The dashed lines on frame (b) indicate 45% around the 1:1 line which are shown to facilitate comparison with the analysis of Edson et al. (1991). Note the scales used in the two frames differ.

calculations to compute half-hour average particle number fluxes which range from 7  107 # m2 s1 (1st percentile) to 5  107 # m2 s1 (99th percentile), and have a median value of 1.6  106 # m2 s1. Of the corrections applied to compute the flux values the one that has the largest magnitude is that applied to correct for covariance of the saturation ratio with the vertical wind velocities. These deliquescence effects cause an underestimation of the flux to the surface by an average of 1/3, and indicate there is a need for additional research into the effects of deliquescence and into the feasibility of preheating the sample prior to entering the CPC or in better quantifying the degree to which saturation ratio fluctuations in the CPC reflect perturbations in the ambient environment. The statistical uncertainties associated with the particle number flux estimates are larger than those for momentum fluxes and imply that in this data set approximately half of the particle number fluxes are within one standard deviation of zero. We advocate that similar uncertainty analyses should be applied to all particle flux data sets and further suggest: Table 1 Linear fits of half-hourly average particle number fluxes for 16 June 2004 from the four micro-meteorological methods Method

Regression coefficient (m)

r2

EC v. REA (REA flux derived from b computed using the momentum flux analogy (bw)) EC v. REA (REA v. flux derived from b computed using the heat flux analogy (bT)) EC v. co-spectra EC v. dissipation REA (bw) v. REA (bT) Dissipation v. co-spectra

0.92

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0.52 0.73 1.00 0.88

These equations have the form: y ¼ mx, where y is the flux from the first method listed (in row 1 ¼ EC), x is the flux from the second method listed (in row 1 ¼ REA) and m is the regression coefficient. These equations were determined using the data presented in Fig. 8.

(i) The results of the uncertainty analyses have real implications for intercomparisons of observational data and models. (ii) It may be advantageous to apply multiple parallel approaches to generate more robust estimates of particle number fluxes. Given that each micro-meteorological method relies on different statistical properties of the data and thus will have unique error structures (corrections and uncertainties), agreement between the differing approaches may lead to additional confidence in flux estimates. The intercomparison of flux estimates from different micrometeorological approaches indicates that the REA and eddy covariance particle number fluxes are highly correlated and have very similar magnitude. The two spectrally based approaches tend to give higher particle number flux estimations but are also correlated with fluxes derived using the eddy covariance approach. Future work will focus on developing robust corrections to and error estimates for particle number fluxes determined using REA and spectral techniques, and to advancing theoretical explanations for discrepancies between particle number flux estimates from the different micro-meteorological methods. Acknowledgements This research was funded by grants from NSF (ATM 0334321 and ATM 0544745), a fellowship from the Nordic Centre of Excellence on BiosphereeAerosoleCloudeClimate Interactions (BACCI) and support from the EU funded EUCAARI and ACCENT projects. Henrik Prip and Kasper Anderson are acknowledged for the loan of the CPC 3010 deployed in this research. Søren Lund and Lars Christensen are also acknowledged for assisting in deploying the instrumentation at the site. The comments of two reviewers were very helpful in clarifying this manuscript.

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References ¨ ., Moncrieff, J., Foken, T., Aubinet, M., Grelle, A., Ibrom, A., Rannik, U Kowalski, A., Martin, P., Berbigier, P., Bernhofer, C., Clement, R., Elbers, J., Granier, A., Grunwald, T., Morgenstern, K., Pilegaard, K., Rebmann, C., Snijders, W., Valentini, R., Vesala, T., 2000. Estimates of the annual net carbon and water exchange of forests: the EUROFLUX methodology. Advances in Ecological Research 30, 113e175. Businger, J.A., Oncley, S.P., 1990. Flux measurement with conditional sampling. Journal of Atmospheric and Oceanic Technology 7, 349e352. Buzorius, G., 2001. Cut-off sizes and time constants of the CPC TSI 3010 operating at 1e3 lpm flow rates. Aerosol Science and Technology 35, 577e585. ¨ ., Hakela, J.M., Vesala, T., Kulmala, M., 1998. Vertical Buzorius, G., Rannik, U aerosol particle fluxes measured by eddy covariance technique using condensational particle counter. Journal of Aerosol Science 29, 157e171. ¨ ., Makela, J.M., Keronen, P., Vesala, T., Kulmala, M., Buzorius, G., Rannik, U 2000. Vertical aerosol fluxes measured by the eddy covariance method and deposition of nucleation mode particles above a Scots pine forest in southern Finland. Journal of Geophysical Research 105 (D15), 19905e19916. ¨ ., Nilsson, D., Kulmala, M., 2001. Vertical fluxes and Buzorius, G., Rannik, U micrometeorology during aerosol particle formation events. Tellus 53B, 394e495. ¨ ., Nilsson, E.D., Vesala, T., Kumala, M., 2003. AnalBuzorius, G., Rannik, U ysis of measurement techniques to determine dry deposition velocities of aerosol particles with diameters less than 100 nm. Journal of Aerosol Science 34, 747e764. Doebelin, E.O., 1990. Measurement Systems: Application and Design. McGraw-Hill, New York, 772 pp. Edson, J.B., Fairall, C.W., Meystayer, P.G., Larsen, S.E., 1991. A study of the inertial dissipation method for computing airesea fluxes. Journal of Geophysical Research 96 (C7), 10689e10771. Fairall, C.W., 1984. Interpretation of eddy-correlation measurements of particulate deposition and aerosol flux. Atmospheric Environment 18, 1329e1337. Fairall, C.W., Larsen, S.E., 1986. Inertial dissipation methods and turbulent fluxes at the aireocean interface. Boundary-Layer Meteorology 34, 287e301. Finnigan, J., Clement, R., Malhi, Y., Leuning, R., Cleugh, H., 2003. A reevaluation of long-term flux measurement techniques. Part I: averaging and coordinate rotation. Boundary-Layer Meteorology 107, 1e48. Fitzgerald, J.W., 1975. Approximation formulas for the equilibrium size of an aerosol particle as a function of its dry size and composition and the ambient relative humidity. Journal of Applied Meteorology 14, 1044e1049. Gallagher, M., Beswick, K., Duyzer, J., Westrate, H., Choularton, T., Hummelshøj, P., 1997. Measurements of aerosol fluxes to Speulder forest using a micrometeorological technique. Atmospheric Environment 31, 359e373. Gallagher, M.W., Nemitz, E., Dorsey, J.R., Fowler, D., Sutton, M.A., Flynn, M., Duyzer, J., 2002. Measurements and parameterizations of small aerosol deposition velocities to grassland, arable crops, and forest: influence of surface roughness length on deposition. Journal of Geophysical Research 107 (D12). art # 4154. ¨ ., Aalto, P., Pohja, T., Siivola, E., Kumala, M., Gaman, A., Rannik, U Vesala, T., 2004. Relaxed eddy accumulation system for size resolved aerosol particle flux measurements. Journal of Atmospheric and Oceanic Technology 21, 933e943. Gash, J.H., Culf, A., 1996. Applying a linear detrend to eddy correlation data in real time. Boundary-Layer Meteorology 79, 301e306. Haugen, D.A., Kaimal, J.C., Bradley, E.F., 1971. An experimental study of Reynolds stress and heat flux in the atmospheric surface layer. Quarterly Journal of the Royal Meteorological Society 97, 168e180. Hill, R.J., 1989a. Implication of the MonineObukhov similarity theory for scalar quantities. Journal of Atmospheric Science 46, 2236e2244. Hill, R.J., 1989b. Structure functions and spectra of scalar quantities in the inertialeconvective and viscouseconvective ranges of turbulence. Journal of Atmospheric Science 46, 2245e2251. Horst, T., 1997. A simple formula for attenuation of eddy fluxes measured with first-order-response scalar sensors. Boundary-Layer Meteorology 82, 219e 233.

Jensen, N.O., Hummelshøj, P., 1995. Derivation of canopy resistance for water vapour fluxes over a spruce forest using a new technique for the viscous sublayer resistance. Agricultural and Forest Meteorology 73, 339e352. Kaimal, J.C., Wyngaard, J.C., Izumi, Y., Cote´, O.R., 1972. Spectral characteristics of surface layer turbulence. Quarterly Journal of the Royal Meteorological Society 98, 563e589. Kowalski, A., 2001. Deliquescence induces eddy covariance and estimable dry deposition errors. Atmospheric Environment 35, 4843e4851. Larsen, S.E., 1986. Hot-wire measurements of atmospheric turbulence. Risø R - 232 . Risoe National Laboratory, Denmark, 342 pp., (In English). Lumley, J.L., Panofsky, H.A., 1964. The Structure of Atmospheric Turbulnce. Wiley Interscience, New York, 239 pp. ¨ ., Marcolla, B., Cescatti, A., Vesala, T., 2003. FootMarkkanen, T., Rannik, U prints and fetches for fluxes over forest canopies with varying structure and density. Boundary-Layer Meteorology 106, 437e459. McBean, G.A., Miyake, M., 1972. Turbulent transfer mechanisms in the atmospheric surface layer. Quarterly Journal of the Royal Meteorological Society 98, 383e398. Mertes, S., Schrooder, F., Wiedensohler, A., 1995. The particle detection efficiency curve of the TSI3010 CPC as a function of temperature difference between saturator and condenser. Aerosol Science and Technology 23, 257e270. Oncley, S.P., Delany, A.C., Horst, T.W., 1993. Verification of flux measurement using relaxed eddy accumulation. Atmospheric Environment 27 (15), 2417e2427. Ould-Dada, Z., Baghini, N., 2001. Resuspension of small particles from tree surfaces. Atmospheric Environment 35, 3799e3809. Pilegaard, K., Mikkelsen, T., Beier, C., Jensen, N.O., Ambus, P., Ro-Paulsen, H., 2003. Field measurements of atmosphereebiosphere interactions in a Danish beech forest. Boreal Environment Research 8, 315e333. Pond, S., Phelps, G.T., Paquin, J.E., MacBean, G., Stewart, R.W., 1971. Measurements of the turbulent fluxes of momentum, moisture and sensible heat over the ocean. Journal of Atmospheric Science 28, 901e917. Pryor, S.C., 2006. Size resolved particle deposition velocities of sub-100 nm diameter particles over a forest. Atmospheric Environment 40, 6192e6200. Pryor, S.C., Barthelmie, R.J., Prip, H., Sørensen, L.L., 2005. Observations of ultra-fine particles above a deciduous forest. Geophysical Research Letters 32, doi:10.1029/2004GL022261. L06804. ¨ ., Vesala, T., 1999. Autoregressive filtering versus linear detrending Rannik, U in estimation of fluxes by the eddy covariance method. Boundary-Layer Meteorology 91, 259e280. Raupach, M.R., Thom, A.S., 1981. Turbulence in and above plant canopies. Annual Review of Fluid Mechanics 13, 97e129. Schmid, H.P., 1994. Source areas for scalars and scalar fluxes. BoundaryLayer Meteorology 67, 293e318. Schmitt, G.E., Friehe, C.A., Gibson, C.H., 1979. Structure of the marine surface layer. Journal of Atmospheric Science 36, 602e628. Sievering, H., 1987. Small-particle dry deposition under high wind speed conditions: eddy flux measurements at the Boulder atmospheric observatory. Atmospheric Environment 21, 2179e2185. Smith, S.D., Anderson, R.J., 1984. Spectra of humidity, temperature and wind over the sea at Sable Island, Nova Scotia. Journal of Geophysical Research 91, 10529e10532. Sørensen, L.L., Larsen, S.E., 2005. Fluxes of water vapour and CO2 using the dissipation technique. In: 37th International Liege Colloquium on Ocean Dynamics. 2e6 May 2005, Liege, Belgium. Webb, E., Pearman, G., Leuning, R., 1980. Correction of flux measurements for density effects due to heat and water vapour transfer. Quarterly Journal of the Royal Meteorological Society 106, 85e100. Wen, C.S., 1996. The Fundamentals of Aerosol Dynamics. World Scientific Publishing, Singapore. Wyngaard, J.C., 1973. On surface-layer turbulence. In: Haugen, D.A. (Ed.), Workshop on Micrometeorology. American Meteorological Society, Boston, MA, pp. 101e149.