DOAS-measurement of the NO 2 formation rate from NO x emissions into the atmosphere

In the present work we deal with emissions originating from combustion processes containing SO 2, NO and NO2, emitted into the atmosphere by a localized source. We present a method for measuring the NO 2-formation rate (due to conversion of NO to NO2) from measurements of SO 2and NO2-slant column densities across different plume sections, under the (usually justified) assumption that the SO 2flux is constant. The advantages of the proposed method are that the measurements can be performed from an arbitrary location, without explicit reference to the wind speed and direction in the plume. We present results of ground based DOAS-measurements of SO 2 and NOx emissions from an oil refinery located in the northern part of Montevideo Bay and give recommendations for future applications of the method.


Introduction
Sulphur-and nitrogen-containing compounds are typical emission products from combustion processes.Their residence time in the atmosphere is affected by photochemical processes (i.e. by solar radiation), by wet and dry deposition, through interaction with aerosols as well as by chemical reactions with other species (e.g.ozone) already present in the airmass.Due to the role of nitrogen oxides in the chemistry of the atmosphere and the interplay with various cycles of other compounds, there is strong interest in having a tool for estimating their presence and time evolution together with other gases.
Remote sensing is an important tool for monitoring trace gases emitted in the atmosphere by stacks and other sources.
A widely used method to study chemical constituents of the atmosphere is the Differential Optical Absorption Spectroscopy (DOAS) (Platt and Stutz, 2008).A passive DOAS system with the sun as light source is the most simple and affordable way (McGonigle et al., 2004;Frins et al., 2006;Bobrowski and Platt, 2007;Louban et al., 2009) for monitoring the gases emitted by a localized source, e.g. a volcano or a stack.In particular SO 2 and NO 2 can be measured with passive DOAS, but not NO.The plume emitted by the source is cross-scanned through a vertical plane and the obtained absorption spectra are then analyzed using DOAS to retrieve the total slant column densities (SCDs).The data obtained at various distances from the emission source contribute to the knowledge of how the emitted gases are dispersed into the atmosphere, how they interact among themselves and with other gases, and also to achieve a better estimate of the formation rate of the gases involved in the measurement (Bobrowski et al., 2006;Hönninger, 2004;Rivera et al., 2010;Frins et al., 2011).
In order to calculate fluxes of the emitted gases, the knowledge of wind velocity in the plume is a necessary prerequisite.However, in general, the wind data (speed and direction) at the precise location of the plume is not accessible from the remote site of the measuring station.All this produces an inherent uncertainty in the determination of the trace gases fluxes and restricts the possibility of gaining information along the path of the plume.
In the present work we will deal with emissions from combustion processes containing SO 2 , NO, some NO 2 and other compounds, emitted by a stack or similar source originating from an oil refinery.Oxides of nitrogen are emitted mostly in the form of NO and some NO 2 .NO reacts rapidly (time scale of minutes) with ozone to yield NO 2 (Seinfeld and Pandis, 2006), i.e., During daytime there is a photochemical back-reaction to (R1): where hν denotes a photon with wavelength below 420 nm.Reaction (R1) is immediately (in the troposphere) followed by: where M denotes any air molecule.Initially and at night Reaction (R1) dominates, but in sunlight Reactions (R1)-(R3) eventually establish a photo-stationary-state ratio between NO 2 and NO (the well known "Leighton Ratio").Similarly, SO 2 is oxidized in the gas phase, since it possesses a relatively high solubility in water, e.g.contained in clouds, fog or aerosols, also liquid-phase oxidation plays a role.However, due to the relatively low rate of these reactions (time scale of days) SO 2 can be considered a stable compound in comparison to NO (Lee et al., 2011).The purpose of this paper is to present a method for measuring the formation rate of NO 2 (due to conversion of NO to NO 2 ) when SO 2 emissions are also present.Since we retrieve NO 2 -and SO 2 -SCD simultaneously from the same spectrum, i.e. both species are measured under the same conditions, it is possible to reference NO 2 against SO 2 .Thus, by scanning the plume across different plume sections, it is possible to determine the formation rate of NO 2 (assuming that the total SO 2 -flux is known and constant).The advantage of this approach relies on the fact that the measurements can be performed without explicit knowledge of the wind data at the different cross-sections of the plume.
In the next Section we describe the proposed method, and in Sects.3 and 4 illustrative experimental results are presented and discussed.

Remote measurement of the NO formation rate
An approach for monitoring the fluxes of trace gases emitted by a localized source and the formation rate of secondary compounds is schematically shown in Fig. 1.The technique uses a spectrometer attached to a telescope to scan the plume at different elevation angles (α i ) and cross-sections.In Fig. 1, the dashed lines represent the directions along which the telescope is pointing, n denotes the unit vector orthogonal to the corresponding cross-section, and v is the wind velocity.
The fluxes of NO 2 and SO 2 (to be denoted as NO 2 and SO 2 , respectively) are defined as where c NO 2 ,SO 2 (r, α) are the NO 2 -and SO 2 -concentrations as function of the elevation angle α(in radians), and r is the distance to the plume measured from the instrument location.
Assuming that the geometrical cross section of the plume is small in comparison with the distance R between observation site and plume center, and that the difference between two consecutive elevation angles is small (α i+1 −α i = α i 1), we can approximate Eq. (1) as where S iNO 2 ,SO 2 denotes the slant column densities of NO 2 and SO 2 measured at the elevation angle α i , i.e., As the slant column densities of NO 2 and SO 2 are obtained from the same spectrum, at a given elevation angle α i we will have the same values of n • v and R for both species.Thus, eliminating the factor n • v R from Eq. ( 2) one easily obtains For the sake of simplicity, in the following we will consider that the SO 2 -and the NO x -flux are constant during the time interval (minutes, see above) necessary for the measurements.
Then, comparing the measurements at two different cross sections of the plume, denoted as cross section 1 and cross section 2, from Eq. ( 4) it is possible to estimate the NO 2formation rate (molec s −1 or equivalent) in the volume between the cross sections: where n NO 2 is the number of NO 2 -molecules (or equivalent), and the subscripts 1 and 2 denote the cross section 1 and cross section 2, respectively.Equations ( 4) and ( 5) can be simplified by introducing mean slant column densities defined as where the index i runs through the slant column densities measured across the plume.Substituting Eq. ( 6) into (4), one obtains and then, from Eq. ( 5) it finally results This expression tells us that, under the assumption that SO 2 is known (and constant), one can obtain the NO 2 -formation rate (dn NO 2 /dt) alone from the measurement of slant column densities without explicit knowledge of the wind velocity and distance to the plume.In fact, the plume may be changing its shape, i.e. the wind may change its speed and direction between consecutive cross-scans.Even more, the distance between the measuring site and the plume (R) may be changing in time, e.g. the observation site may be in movement between consecutive cross-scans.Note, however, that the wind velocity inside the plume could actually be measured by correlation techniques (Galle et al., 2010), but this was not attempted in our study.
Actually, since we are assuming that the geometrical cross section of the plume is small in comparison with the distance to the observation site, we can consider that the range of elevation angles in which the slant column densities have significant values is relatively narrow.Thus, as a first approximation, in Eqs. ( 7) and ( 8) the mean values SNO 2 ,SO 2 could be calculated by considering only the slant column densities restricted to an interval of elevation angles, where the slant column densities are significantly higher than the background.
As discussed in detail below, for the separation of the plume from a possible background, it is important that the elevation scans cover the full plume.

Measurement procedure
In order to validate our proposal, we performed some test measurements of emissions from a petrochemical facility, located in the north of the Montevideo Bay (34.5 • S, 56.1 • W).The measurements were made in the period February-March 2011.
The refinery has many stacks and there is no public information about its emissions.For the flux estimation, we simplify the analysis by assuming a single emitter and use the slant column density data downwind after the last stack of the group.
The measurements were performed from the west side of the Bay, approximately 1.9 km away from the stacks of the refinery.From this place, we were able to perform vertical scans of the plume at different distances from the source.Also, from this place it was easy to find reference points in the city (e.g.telecommunication building, etc. evaluating the length of the distance traversed by the plume. A panoramic picture of the site is shown in Fig. 2 (the dotted rectangle indicates the location of the main stack group).
A miniaturized Multi Axis -Differential Optical Absorption Spectroscopic (MAX-DOAS) instrument with an instantaneous field of view of 0.4 • , spectral range of 311-460 nm and spectral resolution of ∼0.44-0.75nm was used.A detailed description of the instrument is in Bobrowski et al. (2006) (see also Hönninger, 2004;Frins et al., 2011).The vertical scans were performed in the range from 0 • -10 • in steps of 0.5 • -1 • .In addition, elevation angles of 45 • , 70 • and 90 • were also measured.
After a quick evaluation in place, it was found that the significantly enhanced trace gases concentrations were probably in the range of elevation angles 0 • -10 • .For viewing directions outside this range the SO 2 -SCD was typically of the order of 2 × 10 17 molec cm −2 (see Fig. 3), which is close to our detection limit (∼0.5-1 × 10 17 molec cm −2 ).
In our study, NO 2 -and SO 2 -slant column densities were evaluated in the spectral ranges 430-460 nm and 315-325 nm respectively.A zenith spectrum collected at midday of the same day was used as reference, and the slant column densities were computed using the WINDOAS software (Fayt and Van Roozendael, 2001), which implements the spectral analysis via a minimization algorithm.
For the NO 2 evaluation, the absorption cross sections of O 4 (Greenblatt et al., 1990) and NO 2 (Vandaele et al., 1998) at 294 K, O 3 (Burrows et al., 1999) at 294 K and water vapor at 290 K (Rothman et al., 2005) were utilized.Additionally a synthetic Ring spectrum was included in the evaluation (Wagner et al., 2009).
For the SO 2 analysis, absorption cross sections of SO 2 at 294 K (Vandaele et al., 1994), O 3 at 294 K (Burrows et al., 1999) and a synthetic Ring spectrum were included (Wagner et al., 2009).Since the literature cross sections are given in cm 2 molecule −1 we obtain column densities in molecules cm −2 and concentrations in molecules cm −3 .These concentrations were converted to kg m −3 using the known molar mass of the species.
We used wind data provided by a portable weather station located at our site and by Melilla Airport at 10 km north from our measuring site.Actually, we need the wind data only for the purpose of determining the SO 2 -flux, but this flux could eventually be known through other methods (e.g.in-stack monitors or fuel-consum mass-balance).

Experimental results
On 29 March 2011 we performed measurements across six vertical cross sections (numbered from 1 to 6, 3-4 min each single vertical scan) of the plume emitted by the oil refinery (see Fig. 2).We chose a sunny day with good meteorological conditions (a quite clear ambient atmosphere, free from clouds or aerosols).The plume was transparent and we did not observe any scattering inside the plume, thus we conclude that there was negligible aerosol scattering.We estimated the visibility range at about 30 km, corresponding to an aerosol scattering coefficient of about 0. It is assumed that the possible contribution from the background causes a smooth variaion of the SCDs (approximated) by the red line.The difference of the measured SCDs to the red line is attributed to the emission plume (Note that for scan 1 the contribution from the emission plume is probably even smaller, because the smooth variation of the SCDs can in principle be explained by the presence of a tropospheric background alone).
of 0.2 km this would correspond to a scattering probability of about 0.03 within the plume, and thus, clearly multiple scattering will be negligible under these conditions.The virtual absence of multiple scattering was also confirmed by the evaluation of O 4 .We used a cross scan near the stacks to quantify the flux SO 2 .During the measurements across section 1, the mean wind velocity was ∼6.4 km h −1 blowing from NNE.Using the measured SO 2 -SCDs as function of the elevation angle in Eq. ( 2), we obtained a SO 2 -flux of the order of 300 kg h −1 ± 120 kg h −1 .The uncertainty estimation of the SCD values measured in this work is based on the errors determined by the numerical fitting, depending on the size and structure of the residual.The estimated uncertainties (see Stutz and Platt, 1997) of the SCDs were of the order of 30 % and 10 % for SO 2 and NO 2 , respectively.The uncertainty of the wind speed was about 30 % (due to changes of the wind speed and direction).Thus, it results an uncertainty in the fluxes of the order of 40 %.As discussed below, for the estimation of the NO 2 flux, additional uncertainties arise from the contribution of a possible tropospheric background concentration.
In our case the distance to the plume was of the order of 2 km, and thus, no significant radiation dilution effects are to be expected (Kern et al., 2009).
During the measurements across sections 1-6 the wind was changing in speed (6.4-12.9km h −1 corresponding to 1.8-3.6 m s −1 ) and direction (NNE to NNW), but we will assume that the SO 2 -and NO x -flux emitted by the refinery remains constant in the short time interval (20 min) required for the measurements.
Figure 3 shows the obtained SO 2 -and NO 2 -slant column densities at the different cross sections at elevation angles between 1 • and 90 • .
For scans 1-4, the measured trace gas SCDs decrease when elevation angles increase from 1 • to 10 • .For elevation angles >10 • , the measured SCDs are typically even lower and close to the detection limit.In contrast, for scans 5 and 6, the SCDs at 10 • elevation show no clear decrease indicating that probably the emission plume is not fully covered  and 7 • ) and the whole range 1 • -10 • .The result for the lower limit (see Fig. 4) is also presented.
by elevation angles ≤10 • .Thus we skip these scans in the further analysis.Another limitation is found for the NO 2 SCDs: while for SO 2 , the highest SCDs (in scans 1-3) occur at different elevation angles (probably indicating that the plume is affected by turbulent transport), for NO 2 , the dependence of the SCDs on elevation angles shows a rather smooth behaviour.Thus for NO 2 we can not rule out that a substantial part of the measured SCDs might be caused by a tropospheric background (caused by the emissions from the city) and not by the emission plume.Moreover, since we have to assume that such a background contribution might vary with space and time, there is no simple way to quantify and subtract it from our MAX-DOAS measurements.
One conclusion from these findings is to improve the measurement strategies for future measurements.In particular, more observations should be performed to determine a possible background contribution and to separate it from the emission plume of interest.For that purpose we suggest the following strategies: a.The full plume should be covered with moderate distance between elevation angle.This will allow to identify the emission plume by its specific shape.
b. Emission plumes should be scanned from closer locations.This will cause higher elevation angles under which the plume will be seen.Under such angles, a possible background contribution will be smaller and can be better separated from the emission plume.
c.The sequence of scans at different azimuth angles should be repeated to quantify the temporal variabil-ity of both the emission plume and the background concentration.
d.The first elevation scan should be performed upwind of the emission source.
Unfortunately, for our measurements, we can not apply similar strategies to separate the contributions from plume and background due to the lack of observations.Instead we used the existing observations and determine an upper and lower limit for the contribution of the plume to the measured SCD: -To determine an upper limit, we simply assume that the measured NO 2 SCDs (below 10 • elevation) are entirely caused by the emission source.
-To determine the lower limit, we only assign the part of the measured NO 2 SCDs to the emission source, which can not be explained by a tropospheric background due to the specific dependence of the SCDs on elevation angle.This method is illustrated in Fig. 4.
Figure 5 shows these upper and lower limits of the normalized NO 2 -fluxes SNO 2 / SSO 2 (i.e., the NO 2 -fluxes normalized with SO 2 ) as function of the distance to the source.For illustrative purposes, the mean values SNO 2 ,SO 2 of the upper limits were calculated by considering the slant column densities restricted to different intervals of elevation angles (e.g. 3 • , 5 • , and 7 • ), and also for the whole range 1 • -10 • .Although there is an increased dispersion of the SNO 2 / SSO 2 values when the mean values SNO 2 ,SO 2 are calculated by considering small intervals of elevation angles, Fig. 5 shows clearly an increase of the NO 2 -flux with the distance to the source.
Also, the lower limits show an increase with distance from the source.However, as has to be expected, the absolute values are much lower.
A linear fit of the results obtained in the interval 1 • -10 • tells us that the NO 2 -formation rate per unit distance is of the order of 16 (±11) kg h −1 km −1 , assuming a SO 2 -flux of 300 kg h −1 .The NO 2 -formation rate per unit length considering 3 • interval of elevation angles is 18 (±12) kg h −1 km −1 , and 16 (±11) kg h −1 km −1 for 5 • and 7 • interval of elevation angles.
Following the procedure describe in Fig. 5 the obtained lower limit of the formation rate of NO 2 is of the order of 3 (± 2) kg h −1 km −1 .Upper and lower limits of the NO 2formation rate per unit distance was calculated as the product of SO 2 and the slope of the linear fit (slope ≈0.054 km −1 ; correlation coefficient ≈0.99 for the upper limit and slope ≈0.010 km −1 ; correlation coefficient ≈0.99 for the lower limit).

Conclusions
In the present paper we deal with gaseous emissions originating from combustion processes containing SO 2 and NO x , emitted into the atmosphere by a localized source.We presented a method for measuring the NO 2 -formation rate (due to conversion of NO to NO 2 ) from measurements of mean SO 2 -and NO 2 -slant column densities across different plume sections.The proposed method is based on the assumption that the SO 2 -and NO x -flux emitted by the source remains constant during the measuring time.
The advantage of the proposed method is that explicit knowledge of the wind speed and direction across the different plume sections is not required.Actually, the wind may change its speed and direction between consecutive plume cross-section scans, and/or the distance to the plume (R) may be changing in time, e.g. the observation site may be in motion, as long as the line of sight traverses the entire plume section.
We present results of ground based measurements of SO 2 and NO 2 from the emissions of an oil refinery located in the northern part of Montevideo Bay.We derive a SO 2 flux of 300 kg h −1 and a NO 2 formation of 16 (±11) kg h −1 km −1 .The rather large uncertainties for the NO 2 fluxes are related to difficulties in separating the contribution from the emission plume from a possible tropospheric background.We give recommendations for future applications of our method to minimise such interference.

Fig. 2 .
Fig. 2. Panoramic view of the oil refinery and the Montevideo Bay from the measuring site.The dashed rectangle indicates the emitting stack group.The cross scanned sections are numbered from 1 to 6.