Effect of corrections for water vapor sensitivity of coumarin targets and for density fluctuations (WPL) on O3 fluxes measured with the eddy covariance technique

Ozone vertical fluxes above land surfaces are commonly measured with the eddy covariance (EC) technique which requires non-conventional ozone fast analyzer mostly based on a chemiluminescence reaction of ozone with a reagent, either gaseous or solid. Currently, the most adopted reagent for this kind of O3 analyzers is a coumarin-47 solid dye absorbed on silica gel targets. However, ozone-induced chemiluminescence of coumarin-47 is enhanced by the presence of water vapor in the air sample. The aim of this paper is to evaluate the magnitude of the corrections to the ozone flux measurements due to coumarin-47 sensitivity to water vapor fluctuations, performed above a forest ecosystem from 2013 to 2020, and the combined effect with the WPL correction (Webb–Pearman–Leuning correction), another well-established correction for density fluctuations related to water vapor and sensible heat fluxes. Results confirm that water vapor sensitivity correction for the chemiluminescence reaction between coumarin-47 and ozone is quite small and negligible in most of the environmental conditions. On the contrary, WPL correction is almost one order of magnitude greater than the former correction. The combination of the two corrections results, on average, in a 6.6% reduction of the absolute value of the uncorrected ozone fluxes. Since the combined effect of the two corrections can be remarkable depending on the seasonal period of measurements, both corrections to the measured ozone fluxes are recommended, as well as the indication of their application in the published works.


Introduction
Fast ozone analyzers are required to measure vertical ozone fluxes above land surfaces with the eddy covariance techniques. The most common of them are based on solid dry targets made of a porous silica matrix impregnated with coumarin-47 (7-diethylamino-4-methylcoumarin), a dye which reacts with ozone emitting photons following the two-step mechanism described by Ermel et al. (2013). The chemiluminescence reaction of coumarin with ozone is very selective, and no other oxidizing gases react with the target to generate photons. However, ozone-induced chemiluminescence of coumarin-47 absorbed on silica gel is enhanced by the presence of water (Jiménez et al. 1997). This sensitivity enhancement seems not being related to the adopted specific dye, but rather with the porous structure of the substrate. Schurath et al. (1991) experimentally characterized the response of coumarin-47 dye to water vapor and found an analytical expression for the correction factor f.
where p H2O is the partial pressure of H 2 O (hPa) and f is the sensitivity ratio between the target response in humid and in dry air ( p H2O = 0hPa ), respectively. Güsten et al. (1992) observed that "the sensitivity increases rapidly at very low humidity, but levels off at humidity which is normally encountered in ambient air" (i.e., RH > 35% at 20 °C). Thus, they concluded that the "deviations from the mean sensitivity in the humid boundary layer should be relatively small, and often negligible" (Schurath et al. 1991).
Moreover, they found that the coumarin response to abrupt water vapor change was considerably longer (relaxation time t 90 = 22 ± 5s ) than the response time to changing ozone concentrations, i.e., nearly two orders of magnitude longer that the response time to changes in ozone. Then, they concluded that the high frequency O 3 measurements performed with chemiluminescence fast analyzers based on coumarin-47 dye are not affected by water vapor.
Following these conclusions, Güsten and Günther (1996), who developed their novel fast ozone analyzer (GFAS) together with Schurath (Güsten et al. 1992), excluded the application of the Schurath et al. (1991) factor f to correct their ozone flux measurements for fluctuations of sensitivity due to water vapor in the air.
The vast scientific literature on ozone flux measurements performed with coumarin based fast O 3 analyzers never mentions the application of the correction for water vapor sensitivity of coumarin targets, giving evidence that likely the ozone flux data were never corrected for this type of bias.
The question on the correction for sensitivity fluctuations due to water vapor in ozone flux measurements was raised again by Boylan et al. (2014). They employed a Fast Response Ozone Instrument (FROI) based on a gas-phase technique where chemiluminescence is caused by the reaction of ozone with nitric oxide (Williams et al. 2006). Gas phase NO-O 3 chemiluminescence allows powerful and accurate measurements, but it is very sensitive to a quenching effect due to the presence of water vapor (Matthews et al. 1977). Lenschow et al. (1981) and Ridley et al. (1992) proposed to correct the ozone signal O 3 (nmol mol −1 ) of the fast ozone analyzer with a correction factor (mol mmol −1 ) dependent on the water vapor mixing ratio r (mmol mol −1 ): and found that was around 5 • 10 −3 mol mmol −1 . Based on Eq. 2 and the use of Reynolds averaging (Stull 1988), Boylan et al. (2014) developed a formula to correct the kinematic ozone fluxes measured with their Fast Response Ozone Instrument ( F O3 ) for the influence of slow and rapid water vapor fluctuations (Boylan's correction): where F O3,corr is the corrected ozone flux (nmol mol −1 m s −1 ), r (mmol mol −1 ) and O 3 (nmol mol −1 ) are the mean mole fractions of water vapor and ozone, respectively, and w'r' (mmol mol −1 m s −1 ) is the water vapor vertical flux, with w the vertical wind speed and the prime symbols indicating fluctuations from their respective temporal means.
They concluded that the quenching effect of water vapor resulted in a loss of up to 11% in the ozone mole fraction measured by their instrument. However, they did not evaluate the effect of this correction on ozone fluxes measured in field conditions. They simply made a theorical estimation of the correction magnitude for a range of water vapor and ozone fluxes at conditions of air humidity and ozone concentration typical for the air over the oceans, and they found that the correction roughly ranged between − 20% and + 20%. Nevertheless, their results are in line with the findings of Bariteau et al. (2010) who reported corrections of up to 25% to the ozone fluxes due to the water vapor flux in several open-ocean campaigns.
Corrections of this magnitude for ozone fluxes are not negligible, and we questioned if, despite the use of the solid dye instead of gas-phase technique, the assumption of negligibility of the correction to account for the sensitivity of coumarin targets to water vapor made by Güsten et al. (1992) is still valid in case of real ozone flux measurements. For this sake, we tested the magnitude of this correction on multiannual eddy covariance measurements available for a terrestrial ecosystem, just to expand the range of variability of air humidity and water fluxes with respect to those of the marine environment assessed by Bariteau et al. (2010).
Water vapor fluctuations, together with fluctuations of air temperature, are also responsible for changes of air density which, in turn, cause fluctuations of trace gases concentrations. A correction of the measured O 3 fluxes for air density fluctuations is thus needed to avoid that the related fluctuations of O 3 concentrations produce an apparent upward or downward O 3 flux, thus modifying the size of the real deposition fluxes. Webb et al. (1980) have developed a well-known correction for density fluctuations in carbon dioxide flux measurements (WPL correction), but its assumptions can also be applied to any trace gas, such as ozone: where F WPL c is the WPL corrected vertical flux of the trace gas c, w ′ ′ c is the uncorrected vertical flux of c, c , a , and v are the actual density of the air constituent c, of the air, and of the water vapor, respectively, w'T' is the vertical flux of sensible heat (with T the air temperature), w ′ ′ v is the vertical flux of water vapor, is the ratio between the molecular masses of air and water vapor ( M a ∕M v ), and is the water vapor mixing ratio ( v ∕ a ), with overbars indicating average values.
As highlighted by Ibrom et al. (2007), this correction involves two terms: a dilution term (the second one in the right-hand side of Eq. 4) which is related to the water vapor flux, and an expansion one (the third one in the right-hand side of Eq. 4) which is linked to the sensible heat flux. The WPL correction is well established in the micrometeorological practice, but some care should be paid to its application in case of closed-path (Ibrom et al. 2007) and on the order of the application with respect to the correction for high-frequency losses (Massman 2004;Liu et al. 2006). The object of this paper is thus to evaluate the effect of the Boylan's correction for water vapor variation on the measurements of ozone fluxes by chemiluminescence with coumarin-47 above a forest ecosystem and its combined effect with the application of the WPL correction for density fluctuations due to water vapor and sensible heat fluxes.

Instrumentation and methodology
Ozone flux measurements were performed continuously from 2013 to 2020 in a broadleaf deciduous forest in northern Italy (Gerosa et al. 2022). The forest is located in a vast flood plain (Po plain), and it is composed mainly by European hornbeam (Carpinus betulus) and English oak (Quercus robur) trees. A 40-m-tall scaffold tower with instrumentation for eddy covariance flux measurements on the top level was installed inside the forest (45°11′52.27″ N, 10°44′32.27″ E). The instrumentation for flux measurements consisted of an ultrasonic anemometer (mod. USA-1, Metek, D), a fast IRGA analyzer (mod. LI-7500, Li-Cor, USA), and a chemiluminescence ozone fast analyzer based on coumarin-47 dry targets (mod. COFA, Ecometrics, I) which is a clone of the GFAS sensor (Güsten et al. 1992). The COFA was located 1 m apart and 2 m below the sonic anemometer, and the air was drawn from the sonic anemometer to the fast ozone analyzer at 100 L min −1 through a 2.5 m long pipe with a 30 mm inner diameter. A conventional UV photometer (mod. O 3 42 M, Environnement, F) was used as a reference for the chemiluminescence O 3 analyzer.
Conventional probes for air temperature and relative humidity (mod. E2-ACT, Rotronic, D), air pressure (mod. PTB101B, Vaisala, FI), and other common meteorological parameters were installed at the top of the tower and along the vertical profile of the tower every 8 m up to the top. Details can be found in Gerosa et al. (2022).
The instrumentation for fluxes was sampled at 20 Hz, and raw data were stored in separate files every 30 min. Slow sensors were sampled every 30 s by CR1000 dataloggers (Campbell sci., USA), and half-hour averages of every parameter were stored.
Fluxes were calculated on the 30-min raw data files by the eddy covariance (EC) technique (Lee et al. 2004). Raw data were despiked (Vickers and Mahrt 1997), gapfilled with splines, double rotated (Lee et al. 2004), and linearly detrended (Aubinet et al. 2012). Then, the covariances between the fast vertical wind speed (w) and the sonic temperature, water, and ozone molar fraction were calculated to get the kinematic fluxes of heat (w'T'), water w ′ r ′ , and ozone w ′ O ′ 3 . In these calculations, the water and the ozone time series were shifted with respect to the w series, and the lag time that maximized the covariances was chosen. Covariances with lag times that differed from the mode by more than 10% were discarded.
The covariances were then corrected for high-frequency flux losses. The correction factors, which were identified by means of the ogive analysis (Rummel et al. 2007), ranged from a min of 0% to a max of 1.5%, with an average value of 1.02%. Details on this calculation chain can be found in Finco et al. (2018) and Gerosa et al. (2022).
Then, the Boylan's correction (Boylan et al. 2014) and the WPL correction (Webb et al. 1980) were applied. The parameter for Eq. 2 was estimated by linear regressing 1∕f on the water vapor mixing ratio, with f representing the correction factor of Schurath et al. (1991) calculated with the Eq. 1, correction factor which is the ratio between the sensitivity of coumarin based chemiluminescence to ozone in humid air humid (volt/ ppb) and in dry air dry (volt/ppb), i.e., the ratio between the ozone signal measured in humid air O 3,r (volt) and in dry air O 3,0 (volt): The slope of the regression, reported in Fig. 1, was − 3.898·10 −3 for the parameter (R 2 = 0.992, p < 0.001).
Once the parameter was identified, the Boylan's corrected ozone fluxes ( F O3,corr ) were obtained with Eq. 3.
Finally, the WPL correction was applied to the Boylan's corrected fluxes to get the final value. Rannik et al. (1997) showed that for a closed-path sensor, a sampling tube length 1000 times that of the inner diameter of the tube is enough to reduce the temperature fluctuations to a fraction of less than 1% of the initial temperature. Based on that work and referring to the instruments for the measurement of the fluxes of CO 2 and H 2 O, Ibrom et al. (2007) concluded that the WPL correction for a closed-path instrument should be limited to the dilution term, and the expansion term should be omitted because the fluctuations of temperature are damped inside the sampling tube.
Following the Rannik et al. (1997) conclusions, the length of the tube required for our fast ozone analyzer to neglect the heat fluctuations should have been at least 30 m. Since it was only 2.5 m, we did not meet the condition to neglect the expansion term, and thus, the WPL correction formula was applied in its original "full" formulation (Eq. 4).
Ultimately, the corrected kinematic ozone fluxes (nmol mol −1 m s −1 ) were converted to ozone flux densities (nmol m −2 s −1 ) by multiplying them for P∕(ℜT) , with P (Pa) and T (K) the air pressure and temperature, respectively, and ℜ (J mol −1 K −1 ) the universal gas constant.
To compare the magnitude of the corrections, the absolute differences (nmolO 3 m −2 s −1 ) between corrected and uncorrected fluxes were calculated, and the relative corrections (%) were calculated as the ratio between the absolute differences and the uncorrected flux ( [(F corr − F uncorr )∕F uncorr ] • 100 ), all with their respective sign (i.e., negative for deposition fluxes and positive for emission fluxes).
(5) f = humid ∕ dry = O 3,r ∕O 3,0 Fig. 1 Ratio between the sensitivity of coumarin dye to ozone in dry air (O 3,0 ) and in humid air (O 3,r ) at increasing air humidity (r), according to Schurath et al. (1991). The slope of the linear regression is the alpha value for the Boylan's correction (2014)

Results and discussion
In the 8-year period, the average kinematic ozone flux in the summer season (when ozone concentration is maximum in the Boreal hemisphere) was − 0.25 nmol mol −1 m s −1 , and the mean ozone mole fraction in the same season was 56 nmol mol −1 . In these average conditions of ozone concentration and flux, the Boylan's relative correction calculated for air humidity and water vapor flux values ranging from min to max observed at our site spans from − 20% to + 30% (Fig. 2), a magnitude which is in line with those reported by Bariteau et al. (2010). However, if we insert in Eq. 3 the average conditions of humidity and water vapor flux of the summer season at our site (mean water flux = 0.054 mmol mol −1 m s −1 ; mean water vapor mixing ratio = 20.74 mmol mol −1 ), the Boylan's correction to the ozone fluxes is around − 3%. Please note that a positive relative correction means that the absolute (unsigned) value of the corrected flux is greater than the absolute value of the uncorrected one. For a deposition flux such as that of ozone, which is negative since the transport of matter is directed downward, a positive relative correction means that the corrected flux is more negative (i.e., more intense) than the uncorrected one. The opposite is for a negative relative correction. Figure 2 shows that the corrected ozone fluxes are greater than the uncorrected ones for low and moderate humidity (positive correction), but they turn to be lower than the uncorrected fluxes in high humidity conditions (negative correction), and at increasing water vapor fluxes corrections turn to be positive from negative.
When we applied the Boylan's correction to all the half-hourly samples of the 8 years of measurements, i.e., for all the real conditions of ozone and water, concentrations, and fluxes found in the field, the average relative correction was − 0.05% in summer, − 2.8% in winter, − 1.1% in spring, − 2.9% in autumn, and − 1.3% on the whole year (Table 1). Hence, the Boylan's correction reduces the intensity of the uncorrected fluxes, on average.
The correction varies during the hours of the day (Fig. 3) and with the season. For example, in summer, the relative correction is negative during the night and the morning, and positive at noon and in the afternoon (Fig. 3a) when the intensity of the corrected fluxes exceeds up to 5.8% of that of the uncorrected ones. However, in absolute values, the flux corrections are one order of magnitude lower than the uncorrected fluxes and never exceed few decimals of nmol m −2 s −1 (maximum − 0.55 nmol m −2 s −1 ) (Fig. 3b).   In autumn and winter, the relative corrections were always negative, and the intensity of the corrected fluxes resulted lower than the measured ones.
The WPL correction is almost an order of magnitude higher than the Boylan's correction. The mean daily cycle of this correction (Fig. 4a) appears to mirror that of Boylan but, on average, also the WPL correction acted in reducing the intensity of the ozone fluxes. In fact, the mean relative WPL corrections were − 8.8% in summer, − 1.2% in winter, − 7.1% in spring, − 2.8% in autumn, and − 6.2% on the whole year (Table 1). The intensity of the correction peaks in the first hours of the afternoon where, on average, it reaches its maximum absolute value of 1.86 nmol m −2 s −1 in summer (− 15.8%) and 1.26 nmol m −2 s −1 in spring (− 16.8%). The magnitude of the correction decreases from summer to winter, and it is negligible in absolute value during the night (Fig. 4b), when water fluxes are very low.
When the Boylan's correction and the WPL correction are applied in sequence, the net result is a reduction of the intensity of the uncorrected fluxes, with average daily corrections of − 6.6% on annual basis and − 7.5% in spring and summer when the corrections are higher (Table 1). The greater daily correction occurs in spring in the first hours of the afternoon (− 13.6%) (Fig. 5a), and its absolute value is about 1 nmol m −2 s −1 (Fig. 5b).
In summer, the maximum daily correction is, on average, greater than in spring in absolute value (1.21 nmol m −2 s −1 ), but lower in relative terms (− 9.9%). Instead, the composite correction is positive only in summer evening hours, where it increases the magnitude of the uncorrected ozone fluxes by 2.7%. The effect of the Boylan's correction is relatively small under the real environmental conditions of a typical terrestrial ecosystem, like our deciduous forest. Thus, the assumption of negligibility of this correction for ozone fluxes made originally by Güsten and Günther (1996) seems confirmed in most practical cases. However, the effect of the Boylan's correction may not be completely negligible in absolute value when ozone flux values are cumulated for a long-time period to obtain the amount of ozone deposited on a land surface in a year. In our case study, for example, the Boylan's corrected cumulated quantity of ozone annually deposited on the forest ecosystem was on average 1.33% lower than the uncorrected one, with an absolute difference of 1.565 mmol O 3 m −2 (Fig. 6).
Instead, the WPL correction for the measured ozone fluxes is far from negligible, resulting about one order of magnitude greater than the Boylan's correction. The difference between the WPL corrected and uncorrected ozone fluxes is particularly evident for the cumulated fluxes, where the WPL corrected fluxes cumulated in a year resulted on average 6.2% lower than the uncorrected ones, with an absolute difference of 7.070 mmol O 3 m −2 (Fig. 6).
WPL correction is commonly reported for CO 2 and water flux measurements, but in the case of ozone flux measurements-to our best review-we noticed that it is rarely indicated in the literature whether it is applied (Finco et al. 2018;Gerosa et al. 2022) or not. It is likely that the WPL correction was barely applied to ozone fluxes. Thus, it is important to recommend its application with an explicit indication on the papers.
As an obvious consequence of the magnitude of the WPL correction, also the combination of the two corrections is not negligible, even though in the central part of the day the Boylan's and the WPL correction act in the opposite direction. The left vertical scale is for all the curves except for the uncorrected ozone flux whose vertical axis is on the right. Please note that the right scale is 2 times greater than the left one In any case, the application of both corrections to the measured ozone fluxes is highly recommended, particularly if seasonal or yearly cumulated fluxes are requested.

Conclusions
The aim of this paper was to evaluate the magnitude of the corrections to be applied to ozone flux measurements, performed under real conditions of typical terrestrial ecosystems, to account for fluctuations of water vapor. The corrections arise (i) from the variation of sensitivity of coumarin-47, the dye used to rapidly detect O3 concentrations in EC measurements, to water vapor fluctuations (the Boylan's correction), and (ii) from density fluctuations related to water vapor and sensible heat fluxes (the WPL correction).
The analysis of continuous EC measurements made above a deciduous forest ecosystem from 2013 to 2020 revealed that the Boylan's relative correction was small on an annual basis (− 1.3%). Even when it was maximum (+ 5.8% on summer afternoons), the correction resulted of little importance as it never exceeded few decimals of nmol O 3 m −2 s −1 during the day (maximum − 0.55 nmol O 3 m −2 s −1 ), thus confirming the Güsten and Günther (1996) hypothesis of negligibility in most practical cases.
Instead, the WPL correction was almost an order of magnitude higher than the Boylan's one and acted in reducing the absolute value of the uncorrected fluxes. The mean relative correction was − 6.2% on annual basis and peaked to − 16.8% in the spring afternoons with a maximum correction of around 2 nmol O 3 m −2 s −1 in absolute terms.
The combination of the two corrections resulted in an average reduction of 6.6% of the absolute value of the uncorrected fluxes, with a maximum absolute correction in the first hours of the afternoon around 1 nmol O 3 m −2 s −1 in the spring season (− 13.6%).
Since the combined effect of the two corrections can be remarkable depending on the seasonal period of measurements, the sequential application of both Boylan's and WPL corrections to the measured ozone fluxes is highly recommended, and the indication of them in the future published articles is necessary to allow a direct comparison of ozone flux measurements made on same land covers but in different environmental conditions.