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Fluxes of chemically reactive species inferred from mean concentration measurements
Pergamon
Atmospheric
En&wunenr
PII: S1352-2310(97)00026-5
Vol. 31, No. IS, pp. 2371~ 2374, 1997 Cl 1997 Elsevier Science Ltd All rights reserved. Printed in Great Bntain 1352-2310/97 17.00 -+ 0.00
SHORT COMMUNICATION FLUXES OF CHEMICALLY REACTIVE SPECIES INFERRED FROM MEAN CONCENTRATION MEASUREMENTS S. GALMARINI,*,T
J. VILk-GUERAU
DE ARELLANOS
and J. DUYZERg
*IMAU, Utrecht University, Utrecht, The Netherlands; $Departamento de Fisica aplicada, Univesidad Politecnica de Catalunya, Barcelona, Spain; and §TNO, Delft, The Netherlands (First received 17 June 1996 and
in jinal form 9 December 1996. Published May 1997)
Abstract-A method is presented for the calculation of the fluxes of chemically reactive species on the basis of routine measurements of meteorological variables and chemical species. The method takes explicity into account the influence of chemical reactions on the fluxes of the species. As a demonstration of the applicability of the method, micro-meteorological and atmospheric chemistry measurements (OS: NO and NOZ) collected at Zegveld (NL) in 1994 are used to calculate the fluxes of chemically reactive species. In the absence of direct flux measurements, the calculated fluxes are compared to the fluxes obtained without taking the chemical effect into account. At 2 m from the surface the effect of chemical transformation is less than lo%, whereas at 10 m it can be as much as 40%. An explanation of this effect is given in terms of the ratio of the gradients of the species and the ratio of the time scale of turbulence to that of chemistry. The
method presented is applicable to any surface-layer stability or chemical system. 0 1997 Elsevier Science Ltd. Keq’word index: Surface layer fluxes, chemically reactive species, modelling, measurements.
ments collected during the campaign at Zegveld (NL) in 1994.
I. INTRODUCTION
The determination of the flux of chemically reactive species has a very important role for a correct estimate of the rate of emission, deposition and chemical transformation of the species in the atmospheric boundary layer (Seinfeld, 1986). Experimental campaigns are currently taking place to quantify the emission and deposition of various chemical compounds under various atmospheric conditions (e.g. Duyzer and Fowler, 1994; Giisten and Heinrich, 1996). At present the measurements of turbulent fluxes of chemically reactive species are restricted to certain species only (e.g. O,, NO,), whereas others are difficult to measure due to the lack of fast instruments for determining the concentration of the species and the application of the eddy-correlation technique (Businger and Delany, 1990). The use of modelling techniques can be of help in this task when they are combined with actual measurements. In this note the flux-gradient method, which is currently being applied to scalars like heat and moisture, is modified to calculate the fiux of chemically reactive species and is applied to a set of measure_FPresent affiliation: IRC Ispra, TP321,21020 Ispra (VA), Italy.
2. MODIFIED-GRADIENT METHOD
As shown in previous works the flux of chemically reactive species can be calculated using second-order closure models (Fitzjarrald and Lenschow, 1983; VilaGuerau de Arellano et al., 1995; Galmarini et al., 1997). Briefly, the conservation equations of the flux of the species are solved accounting not only for the production and dissipation terms due to dynamical processes (i.e. mean gradient production, buoyancy and dissipation) but also for the production and the depletion of the flux due to chemical transformation. This modelling technique is modified here so that atmospheric chemistry measurements (namely mean concentration gradients) can be used to calculate the fluxes of chemically reactive species. Vila-Guerau de Arellano et al. (1995) have shown that the chemical term of the flux equation depends on the ratio of the time scale of turbulence to that of the chemical reaction (Damkijhler number) and on the ratio of the local fluxes of the species. The modi-
fied-gradient method consists of expressing the local fluxes of the chemically reactive species appearing in
2371
Short communication
2312 the flux equation
using the usual down-gradient
for-
mulation EiE
KZU*
---
aCi
@ci aZ
(1)
where Ci is the mean concentration of the species i at z, (rczu*/Qci) is the exchange coefficient (rc is the von Karman constant) and ~‘ci is the flux-gradient relationship of Ci. The flux-gradient relationship of the species is thus a function of the stability parameter z/L (as for an inert tracer), the Damkijhler number and the mean concentration gradient ratios. The modified-gradient method, which is based on a second-order closure model, allows one to obtain the following second moments of chemically reactive species: fluxes, flux-gradient relationships and concentration covariances. The flux of a chemical species is calculated taking into account the chemical transformation that the species undergoes during the turbulent transport process. The input parameters required are: the micro-meteorological variables (u* and z/L) and the concentration gradients of the chemically reactive species. The modified-gradient method can be used within any range of distances from the surface within the surface layer since it has been developed using parameterisations and scaling that are valid in the surface layer. Moreover, it can be used to calculate the flux of a chemical compound under any stability conditions provided the input parameters are the ones listed above (Vila-Guerau de Arellano et al., 1995; Galmarini et al., 1997).
3. APPLICATION
TO A REAL CASE
In order to demonstrate the applicability of the method we consider a real set of measurements. The data relate to the measurements of NO, NOz and O3 in the surface layer during the campaign at Zegveld (NL). The measurement site was a peat grassland located in typical Dutch pasture landscape near Zegveld. A fetch of more than 50 km was available in the prevailing wind direction. A simple gradient system was used to detect the NO, NOz and O3 concentrations. Ambient air was drawn continuously from the measurement heights (0.5,1,2 and 4 m) above the surface to a central valve switching system. NO, NOz and O3 concentrations were detected on the basis of chemiluminescence. Possible effects of air density variations on the flux or the gradients (Venkatram, 1993; Webb et al., 1980) due to moisture are here in first approximation neglected due to the low humidity levels for the period considered and the stability of the layer. Every 20 min a gradient measurement was made and the measurements were stored. Further details about the measuring device for these species can be found in Duyzer and Fowler (1994). Turbulent parameters such as the friction velocity and sensible heat flux were measured using a three-dimensional sonic anemometer mounted at 5 m above the surface.
The modified-gradient method was applied to the data collected on 6 September 1994 (from 0:OO to 21:00 h local time). As mentioned earlier, in order to calculate the fluxes of the species, one also needs typical micrometeorological measurements, namely the sensible heat flux, H, the friction velocity, U* and the global radiation, G. The sensible heat flux and u* are needed to calculate the stability parameter z/L. The global radiation G is needed to calculate the photodissociation rate of NO2 (jNo2). The latter has been obtained by means of Bahe’s formula (Bahe et al., 1980) which relates jNOI to G linearly. The formula of Bahe is a reliable way of obtaining the value ofjNO, in absence of more detailed information on cloud conditions (van Wheele et al., 1995). For the time series considered, u* varied from approximately 0.1 m s- 1 during nighttime to an average value of 0.4 m s- ’ during the day. The stability of the surface layer was near-neutral. Figure 1 shows the daily variation of the mean concentration of 03, NO and NO2 at z = 2 m and the calculated photodissociation rate of NOz. As can be seen the concentration of NO rapidly increases between sunrise (OS:00 local time) and midday. The average concentration after 10:00 h is approximately 1 ppb and around 0.25 ppb during the night. The average concentration of O3 during day time hours is around 35 ppb but it decreases during the night to 20-25 ppb. A sudden increase in the O3 concentration was recorded between midnight and 03:OOprobably due to an outbreak of the species from higher altitudes or horizontal advection. The diurnal cycle of jNoz is clear from the figure as is its anti-correlation with the NOz concentration. In order to obtain an accurate estimate of the gradients of the mean concentration at a level z, we fitted the concentration profiles of the three species with linear or logarithmic profiles. A high degree of accuracy has to be achieved when fitting the profile because errors can influence the calculation of the flux. In the case analysed, the number of measuring
"0
5
10
15
20
”
LT (hours)
Fig. I. Time series of the 20 min average concentration of OS, NO2 and NO. The dashed line shows the time series of the photodissociation rate of NO2 (in s-r) obtained from the measured global radiation G.
Short communication .
2m
A
2373
10m
~“““““““““‘~
s
.
.
wN02
0.9 -
.
0.8 0.96
-
A I,
0
,
,
I
,
10
5
I
15
.
,
20
0
LT (hours) Fig. 2. Time series of the flux of 0s (in ppb m s-r) calculated at z = 2 and 10m with the modified-gradient method. The flux is normalised with that of the non-reactive tracer (A) assumed to have the same gradients at z of the three chemical species. .
2m
0
2
““I’ . ?? .
. 0 ??
0.4
’ 0
’
’
5
10
’ ’
1
’
5
10
15
20
LT (hours) Fig. 4. Time series of the flux of NOI (in ppb m s I) calculated at z = 2 and 10m with the modified-gradient method. The flux is normahsed with that of the non-reactive tracer (C) assumed to have the same gradients at z of the three chemical species.
IOm
“I”“I”/’
0.8
0.7
’ / 15
i 20
LT (hours) Fig. 3. Time series of the flux of NO (in ppb m s- ‘) calculated at z = 2 and 10 m with the modified-gradient method. The flux is normahsed with that of the non-reactive tracer (B) assumed to have the same gradients at z of the three chemical species. points (4) was sufficient to determine the fitting. Especially in the case of NO, however, a fitting was not possible for all the profiles of the time series because of the large scatter of the measurements. These cases were therefore discarded from the analysis. For this reason only 23 of the original 63 20-min-average concentration profiles of the time series, were used to calculate the fluxes of the three species. Figures 2,3 and 4 show the time series of the fluxes of OS, NO and NOz at 2 and at 10 m from the surface calculated using the modified-gradient method and the measurements described above. In the three figures the fluxes of the chemical species are presented as ratios to the fluxes of three inert tracers (namely of
concentrations A, B, C) which are assumed to be non-reactive and to have at the heights of 2 and 10 m the same gradients as the three chemical species (0,) NO and NOz, respectively). In the case of species A. B, and C the flux-gradient relationship is equal to that of heat. Figure 2 shows that at the two heights considered there is no substantial difference between the flux O3 and that of an inert species. The flux of NO (Fig. 3) shows the largest deviations from the flux of the inert species and it is in general smaller than that of B. The difference is more pronounced at 10 m during the nighttime hours. The large deviation of the flux of NO from the flux of the inert species is due to the fact that at a greater height above the surface the chemical term in the flux equation is large enough to cause a variation in the flux. The time-averaged Damkohler number of NO, which determines with the gradients ratio the chemical term of the flux equation, is 1.93 + 0.63 at 10 m. The NOz flux (Fig. 4) just like the NO flux, shows a greater sensitivity to the chemical transformation at 10 m than at 2 m. Whereas at 2 m the flux of NO2 is more or less equal to that of the inert species C, at 10 m it deviates by as much as lo-30% around midday. The time-averaged Damkiihler of NOz has a value of 1.73 f 0.67 for the considered time series. As indicated by the data, the ratio of the gradients of the species also increases at larger heights enhancing still further the role of the chemical term in the flux budget. This result shows that in general the largest deviations from the inert case occur far from the surface and for the lessabundant species. Nevertheless, as shown in the past studies (Galmarini et al., 1997) deviation can occur also in the vicinity of the surface in dependence of boundary conditions of the species considered and of the turbulent flow. Deviation occurs at small
Short communication
2314
tion gradients of the species of interest at a certain height. Moreover, it can be applied to any stability regime or chemical scheme. Concentration measurements of NO, O3 and NO1 -0.02
.
1
It . -4,
. -0.06
o
0
5
10
15
20
LT (hours.)
Fig. 5. Time series of the intensity of segragation calculated at z = 2 and 10 m with the modified-gradient method. distances from the surface also as a consequence of the reactivity of the species and its abundance (Vila-Guer-
au de Arellano et al., 1995). Using the proposed modified-gradient method and the measurements one can also calculate other second moments. In the case of the chemical system considered, a second moment of interest for atmospheric chemistry is the concentration covariances that arise from second-order chemical reactions between NO and O3 (NO’O’,). The concentration covariance normalised by the mean concentration of the two species gives the so-called intensity of segregation, I,, which is an estimate of the state of mixing of the species. Figure 5 shows the intensity of segregation calculated at 2 and at 10 m using the measurements. The figure shows that for the case considered the intensity of segregation is very small (less than 2%). I, is negative for the whole time series, confirming the anti-correlation of NO and 03. The concentration covariance is generally a difficult variable to derive from measurements because of its small order of magnitude.
4. CONCLUSION
One can make up for the lack of sensitive and fast instruments for measuring the fluxes of chemically reactive species by using of the modelling techniques combined with accurate chemistry measurements. The modified-gradient method, which is based on a second-order closure model, solves the conservation flux equations of the chemical species and explicitly takes into account the chemical transformations. The main advantage of the method is that it requires only routine micro-meteorological and mean atmospheric chemistry measurements as input parameters for the calculation of the fluxes. The input parameters are the stability of the surface layer and the mean concentra-
have been used to determine the flux of the three chemical species. The fluxes calculated with the proposed method and the available data set have been compared with the fluxes of inert species to emphasise the effect of chemical transformation during the turbulent transport process. For the case considered, the esults show that close to the surface (2 m) there are small differences between the flux of the chemical species and the flux of the inert one (deviations of the order of 10%) whereas at a greater height above the surface the differences increase, amounting to approximately 40% in the case of NO. In both cases the differences are larger for the less-abundant species, i.e. NO and NO*, and they can be explained in terms of the parameters that govern the process: the Damkohler number and the concentration gradient ratios. The modified-gradient method and the available data also enabled us to determine the concentration covariance between NO and OX. For the case considered this was found to be of the order of a few percent of the mean concentration.
REFERENCES Bahe, F. C., Schurath, U. and Becker, K. H. (1980) The frequency of NO, photolysis at ground level, as recorded by a continuous actinometer. Atmospheric Environment 14, 711-718. Businger, J. A. and Delany, A. C. (1990) Chemical sensor resolution required for measuring surface fluxes by three common micrometeorological techniques. J. atmos. Chem. 10, 3999410. Duyzer, J. H. and Fowler, D. (1994) Modelling land surface exchanges of gaseous oxides of nitrogen in Europe. Tellus 46B, 3533372. Fitzjarrald, D. R. and Lenschow, D. (1983) Mean concentration and flux profile for chemically reactive species in the atmospheric surface layer. Atmospheric Environment 17, 2505-2512. Galmarini, S., Vi%-Guerau de Arellano, J. and Duynkerke, P. G. (1997) Scaling the turbulent transport of chemically reactive species in a neutral and stratified surface-layer. Q. Jl. R. Met. Sot. 123, 223-242. Gusten, H. and Heinrich, G. (1996) On-line measurements of ozone fluxes: Part I. Methodology and instrumentation. Atmospheric Environment 6, 897-909.
Seinfeld, J. H. (1986) Atmospheric Chemistry and Physics qf Air Pollution, p. 1098. Wiley, New York. van Weele, M., Vi&Guerau he Arellano, J. and Kuik, F. (1995) Combined measurements of UV-A actinic flux. UVA irradiance and global radiation in relation to photodissociation rates. Tellus 47B, 353-364. Venkatram, A. (1993) The parametrisation of the vertical dispersion of a scalar in the atmospheric boundary layer. Atmospheric Environment 27A, 1963-1996.
Vila-Guerau de Arellano, J., Duynkerke, P. G. and Zeller, K. (1995)Atmospheric surface-layer similarity theory applied to chemically reactive species. J. geophys. Res. 100, 1397-1408. Webb, E. K., Pearman, G. I. and Leuning, R. (1980) Correction of flux measurements for density effects due to heat and water vapour transfer Q. JL R. Met. Sot. 106,48875.
Atmospheric
En&wunenr
PII: S1352-2310(97)00026-5
Vol. 31, No. IS, pp. 2371~ 2374, 1997 Cl 1997 Elsevier Science Ltd All rights reserved. Printed in Great Bntain 1352-2310/97 17.00 -+ 0.00
SHORT COMMUNICATION FLUXES OF CHEMICALLY REACTIVE SPECIES INFERRED FROM MEAN CONCENTRATION MEASUREMENTS S. GALMARINI,*,T
J. VILk-GUERAU
DE ARELLANOS
and J. DUYZERg
*IMAU, Utrecht University, Utrecht, The Netherlands; $Departamento de Fisica aplicada, Univesidad Politecnica de Catalunya, Barcelona, Spain; and §TNO, Delft, The Netherlands (First received 17 June 1996 and
in jinal form 9 December 1996. Published May 1997)
Abstract-A method is presented for the calculation of the fluxes of chemically reactive species on the basis of routine measurements of meteorological variables and chemical species. The method takes explicity into account the influence of chemical reactions on the fluxes of the species. As a demonstration of the applicability of the method, micro-meteorological and atmospheric chemistry measurements (OS: NO and NOZ) collected at Zegveld (NL) in 1994 are used to calculate the fluxes of chemically reactive species. In the absence of direct flux measurements, the calculated fluxes are compared to the fluxes obtained without taking the chemical effect into account. At 2 m from the surface the effect of chemical transformation is less than lo%, whereas at 10 m it can be as much as 40%. An explanation of this effect is given in terms of the ratio of the gradients of the species and the ratio of the time scale of turbulence to that of chemistry. The
method presented is applicable to any surface-layer stability or chemical system. 0 1997 Elsevier Science Ltd. Keq’word index: Surface layer fluxes, chemically reactive species, modelling, measurements.
ments collected during the campaign at Zegveld (NL) in 1994.
I. INTRODUCTION
The determination of the flux of chemically reactive species has a very important role for a correct estimate of the rate of emission, deposition and chemical transformation of the species in the atmospheric boundary layer (Seinfeld, 1986). Experimental campaigns are currently taking place to quantify the emission and deposition of various chemical compounds under various atmospheric conditions (e.g. Duyzer and Fowler, 1994; Giisten and Heinrich, 1996). At present the measurements of turbulent fluxes of chemically reactive species are restricted to certain species only (e.g. O,, NO,), whereas others are difficult to measure due to the lack of fast instruments for determining the concentration of the species and the application of the eddy-correlation technique (Businger and Delany, 1990). The use of modelling techniques can be of help in this task when they are combined with actual measurements. In this note the flux-gradient method, which is currently being applied to scalars like heat and moisture, is modified to calculate the fiux of chemically reactive species and is applied to a set of measure_FPresent affiliation: IRC Ispra, TP321,21020 Ispra (VA), Italy.
2. MODIFIED-GRADIENT METHOD
As shown in previous works the flux of chemically reactive species can be calculated using second-order closure models (Fitzjarrald and Lenschow, 1983; VilaGuerau de Arellano et al., 1995; Galmarini et al., 1997). Briefly, the conservation equations of the flux of the species are solved accounting not only for the production and dissipation terms due to dynamical processes (i.e. mean gradient production, buoyancy and dissipation) but also for the production and the depletion of the flux due to chemical transformation. This modelling technique is modified here so that atmospheric chemistry measurements (namely mean concentration gradients) can be used to calculate the fluxes of chemically reactive species. Vila-Guerau de Arellano et al. (1995) have shown that the chemical term of the flux equation depends on the ratio of the time scale of turbulence to that of the chemical reaction (Damkijhler number) and on the ratio of the local fluxes of the species. The modi-
fied-gradient method consists of expressing the local fluxes of the chemically reactive species appearing in
2371
Short communication
2312 the flux equation
using the usual down-gradient
for-
mulation EiE
KZU*
---
aCi
@ci aZ
(1)
where Ci is the mean concentration of the species i at z, (rczu*/Qci) is the exchange coefficient (rc is the von Karman constant) and ~‘ci is the flux-gradient relationship of Ci. The flux-gradient relationship of the species is thus a function of the stability parameter z/L (as for an inert tracer), the Damkijhler number and the mean concentration gradient ratios. The modified-gradient method, which is based on a second-order closure model, allows one to obtain the following second moments of chemically reactive species: fluxes, flux-gradient relationships and concentration covariances. The flux of a chemical species is calculated taking into account the chemical transformation that the species undergoes during the turbulent transport process. The input parameters required are: the micro-meteorological variables (u* and z/L) and the concentration gradients of the chemically reactive species. The modified-gradient method can be used within any range of distances from the surface within the surface layer since it has been developed using parameterisations and scaling that are valid in the surface layer. Moreover, it can be used to calculate the flux of a chemical compound under any stability conditions provided the input parameters are the ones listed above (Vila-Guerau de Arellano et al., 1995; Galmarini et al., 1997).
3. APPLICATION
TO A REAL CASE
In order to demonstrate the applicability of the method we consider a real set of measurements. The data relate to the measurements of NO, NOz and O3 in the surface layer during the campaign at Zegveld (NL). The measurement site was a peat grassland located in typical Dutch pasture landscape near Zegveld. A fetch of more than 50 km was available in the prevailing wind direction. A simple gradient system was used to detect the NO, NOz and O3 concentrations. Ambient air was drawn continuously from the measurement heights (0.5,1,2 and 4 m) above the surface to a central valve switching system. NO, NOz and O3 concentrations were detected on the basis of chemiluminescence. Possible effects of air density variations on the flux or the gradients (Venkatram, 1993; Webb et al., 1980) due to moisture are here in first approximation neglected due to the low humidity levels for the period considered and the stability of the layer. Every 20 min a gradient measurement was made and the measurements were stored. Further details about the measuring device for these species can be found in Duyzer and Fowler (1994). Turbulent parameters such as the friction velocity and sensible heat flux were measured using a three-dimensional sonic anemometer mounted at 5 m above the surface.
The modified-gradient method was applied to the data collected on 6 September 1994 (from 0:OO to 21:00 h local time). As mentioned earlier, in order to calculate the fluxes of the species, one also needs typical micrometeorological measurements, namely the sensible heat flux, H, the friction velocity, U* and the global radiation, G. The sensible heat flux and u* are needed to calculate the stability parameter z/L. The global radiation G is needed to calculate the photodissociation rate of NO2 (jNo2). The latter has been obtained by means of Bahe’s formula (Bahe et al., 1980) which relates jNOI to G linearly. The formula of Bahe is a reliable way of obtaining the value ofjNO, in absence of more detailed information on cloud conditions (van Wheele et al., 1995). For the time series considered, u* varied from approximately 0.1 m s- 1 during nighttime to an average value of 0.4 m s- ’ during the day. The stability of the surface layer was near-neutral. Figure 1 shows the daily variation of the mean concentration of 03, NO and NO2 at z = 2 m and the calculated photodissociation rate of NOz. As can be seen the concentration of NO rapidly increases between sunrise (OS:00 local time) and midday. The average concentration after 10:00 h is approximately 1 ppb and around 0.25 ppb during the night. The average concentration of O3 during day time hours is around 35 ppb but it decreases during the night to 20-25 ppb. A sudden increase in the O3 concentration was recorded between midnight and 03:OOprobably due to an outbreak of the species from higher altitudes or horizontal advection. The diurnal cycle of jNoz is clear from the figure as is its anti-correlation with the NOz concentration. In order to obtain an accurate estimate of the gradients of the mean concentration at a level z, we fitted the concentration profiles of the three species with linear or logarithmic profiles. A high degree of accuracy has to be achieved when fitting the profile because errors can influence the calculation of the flux. In the case analysed, the number of measuring
"0
5
10
15
20
”
LT (hours)
Fig. I. Time series of the 20 min average concentration of OS, NO2 and NO. The dashed line shows the time series of the photodissociation rate of NO2 (in s-r) obtained from the measured global radiation G.
Short communication .
2m
A
2373
10m
~“““““““““‘~
s
.
.
wN02
0.9 -
.
0.8 0.96
-
A I,
0
,
,
I
,
10
5
I
15
.
,
20
0
LT (hours) Fig. 2. Time series of the flux of 0s (in ppb m s-r) calculated at z = 2 and 10m with the modified-gradient method. The flux is normalised with that of the non-reactive tracer (A) assumed to have the same gradients at z of the three chemical species. .
2m
0
2
““I’ . ?? .
. 0 ??
0.4
’ 0
’
’
5
10
’ ’
1
’
5
10
15
20
LT (hours) Fig. 4. Time series of the flux of NOI (in ppb m s I) calculated at z = 2 and 10m with the modified-gradient method. The flux is normahsed with that of the non-reactive tracer (C) assumed to have the same gradients at z of the three chemical species.
IOm
“I”“I”/’
0.8
0.7
’ / 15
i 20
LT (hours) Fig. 3. Time series of the flux of NO (in ppb m s- ‘) calculated at z = 2 and 10 m with the modified-gradient method. The flux is normahsed with that of the non-reactive tracer (B) assumed to have the same gradients at z of the three chemical species. points (4) was sufficient to determine the fitting. Especially in the case of NO, however, a fitting was not possible for all the profiles of the time series because of the large scatter of the measurements. These cases were therefore discarded from the analysis. For this reason only 23 of the original 63 20-min-average concentration profiles of the time series, were used to calculate the fluxes of the three species. Figures 2,3 and 4 show the time series of the fluxes of OS, NO and NOz at 2 and at 10 m from the surface calculated using the modified-gradient method and the measurements described above. In the three figures the fluxes of the chemical species are presented as ratios to the fluxes of three inert tracers (namely of
concentrations A, B, C) which are assumed to be non-reactive and to have at the heights of 2 and 10 m the same gradients as the three chemical species (0,) NO and NOz, respectively). In the case of species A. B, and C the flux-gradient relationship is equal to that of heat. Figure 2 shows that at the two heights considered there is no substantial difference between the flux O3 and that of an inert species. The flux of NO (Fig. 3) shows the largest deviations from the flux of the inert species and it is in general smaller than that of B. The difference is more pronounced at 10 m during the nighttime hours. The large deviation of the flux of NO from the flux of the inert species is due to the fact that at a greater height above the surface the chemical term in the flux equation is large enough to cause a variation in the flux. The time-averaged Damkohler number of NO, which determines with the gradients ratio the chemical term of the flux equation, is 1.93 + 0.63 at 10 m. The NOz flux (Fig. 4) just like the NO flux, shows a greater sensitivity to the chemical transformation at 10 m than at 2 m. Whereas at 2 m the flux of NO2 is more or less equal to that of the inert species C, at 10 m it deviates by as much as lo-30% around midday. The time-averaged Damkiihler of NOz has a value of 1.73 f 0.67 for the considered time series. As indicated by the data, the ratio of the gradients of the species also increases at larger heights enhancing still further the role of the chemical term in the flux budget. This result shows that in general the largest deviations from the inert case occur far from the surface and for the lessabundant species. Nevertheless, as shown in the past studies (Galmarini et al., 1997) deviation can occur also in the vicinity of the surface in dependence of boundary conditions of the species considered and of the turbulent flow. Deviation occurs at small
Short communication
2314
tion gradients of the species of interest at a certain height. Moreover, it can be applied to any stability regime or chemical scheme. Concentration measurements of NO, O3 and NO1 -0.02
.
1
It . -4,
. -0.06
o
0
5
10
15
20
LT (hours.)
Fig. 5. Time series of the intensity of segragation calculated at z = 2 and 10 m with the modified-gradient method. distances from the surface also as a consequence of the reactivity of the species and its abundance (Vila-Guer-
au de Arellano et al., 1995). Using the proposed modified-gradient method and the measurements one can also calculate other second moments. In the case of the chemical system considered, a second moment of interest for atmospheric chemistry is the concentration covariances that arise from second-order chemical reactions between NO and O3 (NO’O’,). The concentration covariance normalised by the mean concentration of the two species gives the so-called intensity of segregation, I,, which is an estimate of the state of mixing of the species. Figure 5 shows the intensity of segregation calculated at 2 and at 10 m using the measurements. The figure shows that for the case considered the intensity of segregation is very small (less than 2%). I, is negative for the whole time series, confirming the anti-correlation of NO and 03. The concentration covariance is generally a difficult variable to derive from measurements because of its small order of magnitude.
4. CONCLUSION
One can make up for the lack of sensitive and fast instruments for measuring the fluxes of chemically reactive species by using of the modelling techniques combined with accurate chemistry measurements. The modified-gradient method, which is based on a second-order closure model, solves the conservation flux equations of the chemical species and explicitly takes into account the chemical transformations. The main advantage of the method is that it requires only routine micro-meteorological and mean atmospheric chemistry measurements as input parameters for the calculation of the fluxes. The input parameters are the stability of the surface layer and the mean concentra-
have been used to determine the flux of the three chemical species. The fluxes calculated with the proposed method and the available data set have been compared with the fluxes of inert species to emphasise the effect of chemical transformation during the turbulent transport process. For the case considered, the esults show that close to the surface (2 m) there are small differences between the flux of the chemical species and the flux of the inert one (deviations of the order of 10%) whereas at a greater height above the surface the differences increase, amounting to approximately 40% in the case of NO. In both cases the differences are larger for the less-abundant species, i.e. NO and NO*, and they can be explained in terms of the parameters that govern the process: the Damkohler number and the concentration gradient ratios. The modified-gradient method and the available data also enabled us to determine the concentration covariance between NO and OX. For the case considered this was found to be of the order of a few percent of the mean concentration.
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