Between winter 2008 and summer 2014, we performed five measurement campaigns at various locations across Europe. In Table 1 a summary of the different campaigns, their locations (latitude, longitude, height above sea level) and the time difference between UTC and local noon is given. The location of the different campaigns is documented in Fig. 1. The Diel Oxidant Mechanism in relation to Nitrogen Oxides (DOMINO) campaign was carried out at the El Arenosillo station (31.7∘ N, 6.7∘ W; 40 m a.s.l.) in the period between 21 November and 8 December 2008. El Arenosillo is located in the south-west of Spain approximately 200 m from the Atlantic Ocean. The site itself is situated in a national park. The city of Huelva, a large industrial complex, is situated 26 km to the north-west and the Seville metropolitan area is 75 km to the north-east. Back-trajectory calculations indicate air-mass origins from Huelva and Portugal, the continental north, Seville and the marine sectors, with an occurrence frequency of 42 %, 30 %, 7 % and 21 %, respectively. Maximum temperatures decreased from 23 ∘C in the beginning of the campaign to less than 16 ∘C towards the end. Typical wind speeds ranged between 1 and 4 m s-1. The boundary layer height varied between approximately 200 m during nighttime and 1400 m during the afternoon. Details of the site and an extensive discussion of the meteorological conditions, including a characterisation of air-mass origins, can be found in Adame et al. (2014).

The Hyytiälä United Measurements of Photochemistry and Particles – Comprehensive Organic Particle and Environmental Chemistry (HUMPPA-COPEC) campaign was conducted at the SMEAR II (Station for Measuring Ecosystem–Atmosphere Relation) boreal forest research station in Hyytiälä, Finland (61.5∘ N, 24.17∘ E; 181 m a.s.l.), from 12 July to 12 August 2010. The site is situated in a large boreal forest, with the next major urban setting being Tampere approximately 50 km to the south-west of the site. Back-trajectory calculations indicate air-mass origins from the Tampere (Finland) area (south-west) and the continental north and south-east (Russia) with occurrence frequencies of 53 %, 10 % and 21 %, respectively. Maximum temperatures varied between 16 and 30 ∘C. Precipitation was low with the exception of 3 days (15 and 27 July, 4 August). Typical wind speeds ranged between 1 and 3 m s-1. The boundary layer height varied between approximately 200 m during nighttime and 1500 m during the afternoon. Details of the site, the meteorology during HUMPPA and air-mass origins can be found in Williams et al. (2011).

The PArticles and RAdicals Diel observations of the impact of urban and biogenic Emissions (PARADE) campaign was conducted at the Taunus Observatory on the Kleiner Feldberg mountain (50.22∘ N, 8.45∘ E; 825 m a.s.l.) in south-western Germany between 15 August and 9 September 2011. The site is close to the Rhine–Main area, with the cities of Mainz 25 km to the south-south-west, Wiesbaden 20 km to the south-west and Frankfurt 30 km to the south-east. The first part of the campaign (15–26 August) was characterized by relatively high temperatures up to 25 ∘C, an air-mass origin from the south-west and a wind speed of the order of 5 m s-1. After the arrival of a series of cold fronts from the Atlantic temperatures dropped to maximum values between 10 and 22 ∘C, while wind speed increased to ∼10 m s-1. During the passage of the cold fronts on 27 August and 4 September rainfall occurred at the site. The boundary layer height varied between approximately 175 m during nighttime and 1300 m during the afternoon. Details of the site, the meteorology during PARADE and air-mass origins can be found in Li et al. (2015) and Sobanski et al. (2016).

The HOhenpeißenberg Photochemistry Experiment (HOPE 2012) was conducted at the Hohenpeißenberg Global Atmospheric Watch (GAW) Meteorological Observatory (47.48∘ N, 11∘ E; 988.8 m a.s.l.) in southern Germany between 11 June and 13 July 2012. This hilltop observatory operated by the German Weather Service is situated approximately 80 km south-west of the Bavarian capital of Munich in a rural area. Maximum temperatures during the campaign varied between 20 and 30 ∘C, while wind speeds between 2 and 5 m s-1 were measured. The main wind direction varied between south-east and south-west. Unfortunately, observations of the boundary layer height above the site were not made. Details of the site and trace gas measurements from HOPE 2012 can be found in Novelli et al. (2017).

The CYprus PHotochemistry EXperiment (CYPHEX) was conducted on a hilltop site in north-western Cyprus at Ineia (34.96∘ N, 32.37∘ E; 650 m a.s.l.) during the period between 7 July and 4 August 2014. The site is situated in a rural area with no major population centres upwind in the westerly and north-westerly directions. The distance to the Mediterranean Sea shoreline is approximately 10 km. Back-trajectory calculations indicate an air-mass origin from the western Mediterranean during the first half of the campaign, while the second half was characterized by an air-mass origin north of Cyprus over eastern Europe. Maximum temperatures varied between 21 and 28 ∘C. Typically, the wind speeds ranged between 2 and 6 m s-1. The boundary layer height varied between approximately 50 m during nighttime and 250 m during the afternoon. Details about the site, the meteorology during CYPHEX and air-mass origins can be found in Meusel et al. (2016), Hüser et al. (2017) and Derstroff et al. (2017).

During the campaigns discussed here H2O2 was measured with a commercial analyser (AL2001 CA, Aero Laser, Garmisch Partenkirchen, Germany) based on the wet chemical dual-enzyme technique described by Lazarus et al. (1985, 1986). The instrument has been used previously for airborne (Stickler et al., 2007; Klippel et al., 2011) and ship-based (Fischer et al., 2015) measurements, and details of the instrument operation and performance are found in these publications. The detection limit of the instrument is of the order of 25 pptv at a time resolution (10 %–90 %) of 30 s. The total uncertainty is typically of the order of 12 %–15 % (Fischer et al., 2015).

Nitrogen oxides (NO and NO2) were measured with a highly sensitive two-channel chemiluminescence detector (CLD, ECO Physics CLD 790 SR, Duernten, Switzerland) during the DOMINO, HUMPPA, PARADE and CYPHEX campaigns. The instrument has been previously used in a number of airborne and ship-based campaigns and is described in detail in Hosaynali Beygi et al. (2011). The time resolution is 1 s and typical detection limits are in the low pptv range, with a total uncertainty of the order of 3 % and 5 % for NO and NO2, respectively. During HOPE NOx measurements were performed by the German Weather Service with a similar measurement technique.

Ozone was measured during all campaigns using a commercial UV Photometric O3-Analyzer (model 49, Thermo Environment Instruments, USA). The detection limit was typically 2 ppbv and the total uncertainty less than 5 %.

Measurements of OH and HO2 radicals were conducted with the Max Planck Institute for Chemistry HORUS instrument based on laser-induced fluorescence detection (Martinez et al., 2010; Hens et al., 2014). OH is detected directly, while HO2 is measured indirectly as OH following conversion with NO via Reaction (R2). Typical detection limits for OH and HO2 are 9×105 molec cm-3 and 0.4 pptv, respectively. The total uncertainty is of the order of 30 % (Hens et al., 2014). Note that since the HUMPPA campaign in 2010 an inlet pre-injector (IPI) has been used to determine the OH background signal via a chemical modulation (Novelli et al., 2014). This technique was not used during the DOMINO campaign so that OH measurements from this campaign are considered to be an upper limit. Moreover, during PARADE, HOPE and CYPHEX HO2 was measured using reduced amounts of NO sufficient to convert 10 %–30 % of the HO2, but low enough to avoid conversion of RO2 (Fuchs et al., 2011, Whalley et al., 2013). Previous measurements of HO2 reported for DOMINO and HUMPPA are therefore an upper limit as they are affected by a fractional measurement of RO2. Crowley et al. (2018) found in a data-constrained box model study that during HUMPPA at noon 30 % occurred due to RO2, confirming the finding by Hens et al. (2014). For the early morning and nighttime hours RO2 interference was significantly larger. During later campaigns (PARADE, HOPE, CYPHEX) the reduction of the amount of NO used to convert HO2 to OH resulted in RO2 interferences of the order 12 % to 15 % (Mallik et al., 2018).

During PARADE and CYPHEX photolysis rates for a large number of trace gases were measured with a commercial single monochromator spectroradiometer (Meteorologie Consult GmbH, Glashütten, Germany), while in all other campaigns J(NO2) was measured with a filter radiometer (Metorologie Consult GmbH, Glashütten, Germany). Based on a correlation analysis between measured J(NO2) and measured J(H2O2) during PARADE and CYPHEX, a second-order correlation function was determined (J(H2O2) =0.015 J(NO2)2+0.0004 J(NO2) +6×10-9, R2=0.99), which was used to calculate J(H2O2) from measured J(NO2) during DOMINO, HUMPPA and HOPE. We estimate the total uncertainty of the H2O2 photolysis rates obtained by this method to be of the order of 10 %.

Diel variations have been calculated for NOx, O3, OH, HO2, H2O2, and J(NO2) by binning the data into 30 min bins and calculating median values, 25 % and 75 % quartiles and minimum and maximum values for each bin (Figs. S1–S5 in the Supplement). We use the medians instead of means to be less sensitive to outlier values, e.g. due to measurements below the detection limit or rain events. For the same reason, we use quartiles instead of standard deviations. Table S1 in the Supplement lists the data coverage (in %) for each species measured during the individual campaigns. Complete coverage (100 %) refers to uninterrupted measurements throughout the campaign time given in Table 1. In general, data coverage is less than 100 % due to calibrations, instrument maintenance and failure. Figure 2 shows the H2O2 diel variations and solar elevation angle for DOMINO, HUMPPA, PARADE, HOPE and CYPHEX, respectively. Visual inspection of the H2O2 diel variations indicates two groups with different behaviour: sites on flat terrain like those encountered during DOMINO (Fig. 2a) and HUMPPA (Fig. 2b) versus hilltop sites probed during PARADE (Fig. 2c), HOPE (Fig. 2d) and CYPHEX (Fig. 2e). The first group (flat terrain) exhibits local minima in the early morning hours between 05:30 and 08:30 UTC during DOMINO and between 04:30 and 07:30 UTC during HUMPPA, corresponding to local times between 06:00 and 09:00. Sunrise during DOMINO and HUMPPA was around 07:30 and 04:00 UTC, respectively. These minima are followed by steep increases in the H2O2 mixing ratios, reaching broad maxima between local noon and the early afternoon (DOMINO: 12:00–16:00 UTC; HUMPPA: 12:00–18:00 UTC), followed by a slow decrease during the late afternoon into the night. At these sites the daytime H2O2 mixing ratios are significantly higher than during the night, and the diel variations are similar to those observed for O3 (Figs. S1b and S2b). This is typical of the behaviour of a photochemically produced species in the continental boundary layer at a site with no significant orographic features. It is due to the interplay between net photochemical production during the day and strong deposition loss, scaling inversely with the variation of the boundary layer height.

The second group of sites is situated on hilltops and shows different characteristics. Although H2O2 mixing ratios during PARADE (Fig. 2c), HOPE (Fig. 2d) and CYPHEX (Fig. 2e) exhibit similar local minima in the early morning hours and increasing mixing ratios afterwards with maximum values between noon and the early afternoon, the nighttime mixing ratios are often higher than during the day. A similar evolution was observed for O3 (Figs. S3b–S5b) and is typical of mountainous sites with upslope air flow during the day due to local heating of the mountain slopes and descending air flow due to cooling during the night (Zaveri et al., 1995). Comparable H2O2 diel profiles have been described previously during observations at Mauna Loa, Hawaii (Heikes, 1992), and at Izana, Tenerife (de Reus et al., 2005). The higher mixing ratios of H2O2 and O3 during the night are generally due to sampling from higher altitudes (the nocturnal residual layer or the free troposphere), where mixing ratios for both species are expected to be higher as deposition losses are negligible.

Median H2O2 mixing ratios averaged across the diel cycle vastly differ from site to site. Here we investigate the causes of these differences by plotting campaign median (25–75 % quartiles) H2O2 mixing ratios versus median (and quartiles) HO2 and NOx, respectively (Figs. 3 and 4). The lowest H2O2 mixing ratios are observed for DOMINO, with median values (25 % to 75 % quartiles given in parentheses) of 58 pptv (37–91 pptv) for 24 h averages. Daytime mixing ratios (filtered by J(NO2) > 10-3 s-1) are slightly higher: 72 pptv (49–94 pptv). This was expected since DOMINO is the only campaign that took place in the early winter, when HOx levels and thus the oxidizing capacity of the atmosphere are generally lower. Higher mixing ratios are obtained during HOPE, 169 pptv (108–267 pptv), PARADE, 270 pptv (148–585 pptv), HUMPPA, 382 pptv (209–786 pptv), and CYPHEX, 601 pptv (420–936 pptv). Daytime-only values during HUMPPA are higher than the 24 h averages (473 pptv (227–907 pptv)), similar to observations at DOMINO. This is in line with the discussion of the diel variations in Sect. 3.1, where it was found that flat-terrain sites exhibit higher H2O2 mixing ratios during the day compared to the night. For the mountainous sites, there is no significant difference between the 24 h averages listed above and the daytime-only values: HOPE 155 pptv (103–241 pptv), PARADE 230 pptv (153–452), and CYPHEX 596 pptv (444–762 pptv).

These mixing ratios are consistent with previous observations over Europe, which indicated a general tendency for the highest mixing ratios in the summer season and lowest during winter; e.g. Morgan and Jackson (2002) observed a mean mixing ratio of 1.58 ppbv in June 1999 at Mace Head (Ireland) during the PARFORCE campaign and 0.23 ppbv in September 1998. This kind of seasonal variation is also observed at higher altitudes: Fels and Junkermann (1994) observed an average concentration of approximately 750 pptv of H2O2 in the summer of 1990 at an Alpine mountain station (Wank, Germany), while lower values of 185±233 pptv were reported for February/March 2006 at the neighbouring Jungfraujoch (Switzerland) (Walker et al., 2006). Airborne observations in the continental boundary layer (below 2 km) over Europe confirm this tendency, with mean (±1σ, standard deviation) mixing ratios of 0.55±0.37, 1.72±1.34, 1.74±0.75 and 0.92±0.47 ppbv during March 2004, July 2003, July 2007 and October 2006, respectively (Klippel et al., 2011).

With respect to diel variations, previous studies confirm the differences found here between mountainous sites and those at flat terrain. Fischer et al. (1998) reported higher H2O2 mixing ratios at night (∼2.4 ppbv) than during the day (2.1 ppbv) at high-altitude site Izana (Tenerife) during July/August 1993. This result was confirmed in July/August 2002 at the same side by de Reus et al. (2005). Average daytime mixing ratios were 1.24ppbv±0.38 ppbv, increasing to 1.72±0.55 ppbv during the night. Contrary to mountainous and flat continental sites, coastal sites often exhibit no or only weak diel variations (e.g. Sauer et al., 1997; Morgan and Jackson, 2002) in line with the observations during DOMINO. Strong diel variations with daytime maxima have been reported for Tabua (Portugal) in June/July 1994 (night: < 15 pptv; day: 0.45±0.33 ppbv) (Sauer et al., 2001), Zagreb (Croatia) in the summer of 2004 (night: 0.2±0.35 ppbv; day: 0.4±0.56 ppbv) (Acker et al., 2008), and Waldstein (Germany) in July/August 2001 (night: ∼0.1 ppbv; day: ∼0.6 ppbv) (Ganzeveld et al., 2006; Valverde-Canossa et al., 2006). In general, the H2O2 mixing ratios and diel variations reported in this study are in good agreement with previous observations for similar locations.

Based on airborne measurements in the continental boundary layer over Europe, Klippel et al. (2011) reported a significant latitudinal gradient of H2O2, with decreasing mixing ratios at increasing latitude, reflecting decreasing HOx and photochemical activity. This behaviour is only partly reproduced in the present study, indicating that other local effects have a strong influence on the mixing ratio of H2O2 at ground level. A suitable measure for the photochemical activity (or the oxidizing power of the lower troposphere) is the HO2 concentration during the day, which is also a precursor of H2O2 according to Reaction (R1). In Fig. 3 we therefore plot the daytime median H2O2 and HO2 mixing ratios against each other at the five measurement locations. The 25 % and 75 % percentiles are also plotted. In general, the range of mixing ratios for an individual site is too small to yield significant correlations, but by comparing different environments, this limitation is removed. Figure 3 indicates a strong positive correlation between H2O2 mixing ratios and its precursor HO2. Due to the quadratic dependency of the H2O2 production rate on [HO2] (Reaction R1), one expects that the mixing ratio of H2O2 will exhibit a quadratic relation as well. The data in Fig. 3 can be subdivided into two groups at median HO2 between 3 and 6 pptv (DOMINO, PARADE and HOPE) and those at higher HO2 levels (18–24 pptv during CYPHEX and HUMPPA). Visual inspection suggests a roughly linear relation between H2O2 and HO2. This is confirmed by a linear regression analysis based on median values, which yields a regression coefficient R2 of 0.73. Plotting H2O2 versus (HO2)2 (not shown) yields a smaller R2 of 0.61. This lower R2 is largely due to the HUMPPA data point whereby a lower H2O2 mixing ratio was measured at higher HO2 compared to CYPHEX. As reported by Hens et al. (2014), HO2 measurements with the HORUS instrument are prone to interferences from peroxy radicals, in particular from alkene-based peroxy radicals, which are expected to be most abundant in forest environments, e.g. during HUMPPA. In a recent modelling study, Crowley et al. (2018) determined the contribution of RO2 to the measured HO2 during the daylight hours to be of the order of 30 % around noon and close to 100 % around sunrise and sunset. If we correct the HUMPPA data by a weighted all-day value of 50 % for this potential interference, median daytime HO2 is reduced from 24 pptv (14 to 35 pptv for the 25 %–75 % percentiles) to 12 pptv (7–17.5 pptv). Thus, the data point for HUMPPA in Fig. 3 shifts to the left of the CYPHEX data point. A regression analysis of H2O2 versus (HO2)2 (not shown) with the reduced HUMPPA HO2 results in R2 of 0.9, yielding much better agreement with the hypothesis that the measured H2O2 follows a quadratic dependence on HO2. For further calculations on the HUMPPA data set, we have used the corrected HO2 data. For DOMINO the HO2 observations that were also measured at high NO additions were not corrected due to very low concentrations of biogenic VOCs (Sinha et al., 2012).

Since the concentration of H2O2 according to Eq. (4) depends strongly on HO2, it is to be expected that the competing reaction of HO2 with NO (Reaction R3) will also have an effect. In Fig. 4, we therefore plot the median mixing ratio (25th–75th percentiles) of H2O2 versus the median mixing ratio (25th–75th percentiles) of NOx at the five measurement locations. Please note that, contrary to Fig. 3, we use data obtained during both day and night. Restriction of the analysis to daytime data only, as has been done in Fig. 3, will not change the results. As can be expected, there is a negative correlation between H2O2 and NOx, with the highest H2O2 mixing ratio observed at the lowest NOx values.

Besides being dependent on HO2 and NOx, H2O2 mixing ratios also show a positive (linear) correlation with O3 (Fig. S6), which is an indication of the dependence of H2O2 on photochemical activity. It is expected that higher O3 will be accompanied by higher HOx levels and thus an increasing H2O2 production rate.

Overall, it can be concluded that the H2O2 mixing ratios strongly depend on local oxidation rates represented by HOx and O3 levels. Higher photochemical activity leads to higher concentrations of H2O2. Nitrogen oxides play a key role in modulating the HOx partitioning and thus affect H2O2 levels indirectly by influencing the HO2 concentrations available. In order to study the role of physical processes (deposition and transport) in local H2O2 mixing ratio levels, we will next evaluate the H2O2 budget according to Eq. (1).

Equation (1) describes the temporal evolution of H2O2 neglecting scavenging by particles, cloud processing and wet deposition. Rain events and cloud processing that could result in total H2O2 removal were rare during the campaigns. Median values and 25 % and 75 % percentiles do not include such events. Therefore, we can neglect wet deposition in the analysis of Eq. (1). In the following, we concentrate on the observed increases in H2O2 during the period between sunrise and midday. During this period, net photochemical production, dry deposition and vertical entrainment associated with the growth of the boundary layer are expected to influence the observed change in H2O2. Based on a comparison of the mean observed change (dH2O2/dt in pptv s-1) with calculations of the mean net production rate (Pchem–Lchem) and the deposition loss, we estimate potential entrainment rates during the growth of the boundary layer, neglecting horizontal advection. Please note that horizontal advection reflecting different air-mass origins will affect the absolute values of hydrogen peroxide, while the relative increase between sunrise and noon is mainly affected by local processes.

The chemical production (Eq. 2) and destruction (Eq. 3) rates for H2O2 in pptv s-1 are shown as a function of local time in Fig. 5a and b, respectively: 2Pchem=k(R1)[HO2]2,3Lchem=(k(R3)[OH]+J(H2O2))[H2O2]. The calculation of the production term according to Eq. (2) is based on the rate coefficient k(R1) following the IUPAC recommendation, which takes into account an enhancement of the rate coefficient by water vapour (Atkinson et al., 2004; http://iupac.pole-ether.fr, last access: 27 August 2019). Measured water vapour concentrations varied between 0.9 % (DOMINO) and 2.2 % (HUMPPA), leading to enhancement factors of the reaction coefficient of Reaction (R)1 between 1.5 and 2.2. However, it is the difference in median HO2 concentrations that leads to the large variability in Pchem derived for the different campaigns (Fig. 5a). Maximum noontime H2O2 production rates were 0.0015 pptv s-1 (DOMINO), 0.004 pptv s-1 (PARADE), 0.017 pptv s-1 (HOPE), 0.04 pptv s-1 (HUMPPA) and 0.13 pptv s-1 (CYPHEX). This variation by 2 orders of magnitude reflects the dependence of Pchem on the HO2 precursor concentrations (Fig. 3), which are highest for those sites with the lowest NOx concentrations (Fig. 4). Median nighttime production was ∼0 pptv s-1 for DOMINO, PARADE, HOPE and CYPHEX, but between 0.01 and 0.02 pptv s-1 during HUMPPA, due to elevated HO2 concentrations during the night (∼20 pptv in Fig. S2d), which is most likely an artefact due to a RO2 interference of the HO2 measurements (Crowley et al. 2018). The total uncertainty is calculated by error propagation: 4Δy=Σ∂y∂x2×Δx2. The largest contribution to the overall uncertainty is from atmospheric variability calculated from the 25 %–75 % percentiles of the input parameters H2O2 and HO2 used to calculate Pchem according to Eq. (2). The uncertainty in the rate constant is neglected, since it is much smaller that the atmospheric variability of the precursors. The uncertainty of Pchem is ±61 %, ±80 %, ±90 %, ±80 %, and ±35 % for PARADE, DOMINO, HUMPPA, HOPE and CYPHEX, respectively.

Absolute differences in the photochemical destruction rates (Eq. 3) for the individual campaigns differ by an order of magnitude. Maximum Lchem values for DOMINO, PARADE, HOPE, HUMPPA and CYPHEX are -0.001, -0.001, -0.0025, -0.0046 and -0.015 pptv s-1, respectively. During the night, photochemical loss was zero during all the campaigns. Photolysis (Reaction R4) is the dominant photochemical H2O2 sink during CYPHEX (∼70 %), HUMPPA (∼75 %) and PARADE (∼90 %). During DOMINO and HOPE, photolysis and reaction with OH (Reaction R3) are of similar magnitude. Calculation of the uncertainty of Lchem according to Eq. (4) based on the atmospheric variability of the variables in Eq. (3) (i.e. H2O2, OH and J(H2O2)) yields ±86 %, ±62 %, ±76 %, ±72 %, and ±39 % for PARADE, DOMINO, HUMPPA, HOPE and CYPHEX, respectively.

Due to the much higher value of Pchem relative to Lchem (at least 1 order of magnitude), the net chemical production rate (NPR = Pchem-Lchem) is similar to Fig. 5a. The only exception is DOMINO, where the photochemical sources and sinks of H2O2 are almost balanced. It is interesting to evaluate observed H2O2 trends according to Eq. (1).

In order to calculate the effect of dry deposition we use two different approaches. The dry deposition of a trace gas depends on its loss at a surface (described by a surface resistance) and transport to the surface, mainly by turbulence. During the night the transport term is small due to low turbulence and thus we expect a low deposition velocity. In a first step, we therefore estimate the deposition loss rate constant from the decrease in H2O2 mixing ratios during the night, when photochemical production and loss as well as vertical entrainment are assumed to be negligible. This estimate of the dry deposition sink is a lower limit, since it neglects thermally driven turbulence and dry deposition due to stomatal uptake by vegetation, which occurs only during the day and does not take into account day–night changes in the rate of turbulent transport to the ground (e.g. Nguyen et al., 2015). In order to account for the contribution of enhanced turbulence and stomatal uptake, as a second step we also estimate dry deposition loss during local noontime. During this time of the day, associated with maximum H2O2 mixing ratios, it can be assumed that the daytime boundary layer is fully established and vertical intrusion is at minimum. Concentrating on periods with d[H2O2]/dt∼0, only net chemical production, dry deposition and horizontal advection will influence the concentration of H2O2.

For these two cases we calculate an average loss rate kd constant according to 5kd=dH2O2dtH2O2(s-1) and the deposition velocity vd as 6vd=kd×BLHx(cms-1), with BLH the boundary layer height in centimetres. The factor x takes into account a potential gradient in the mixing ratio profile. During the night x=2, assuming a linear increase in the mixing ratio with height in the nocturnal boundary layer (Shepson et al., 1992). During the day, we assume that the boundary layer is well mixed and x is equal to 1.

Table 2 lists the time span over which d[H2O2]/dt was analysed, the change in H2O2 mixing ratio ΔH2O2, the mean d[H2O2]/dt, kd, BLH and vd. Values for the BLH during the night were taken from van Stratum et al. (2012) for DOMINO, Ouwersloot et al. (2012) for HUMPPA, and Berkes et al. (2016) for PARADE. For HOPE boundary layer height measurements are not available, so the nocturnal BLH was estimated to be 200 m, similar to measurements at the other sites. We assign an uncertainty of 20 % to all BLH values. Note that for CYPHEX this method cannot be applied, since the nighttime mixing ratios of H2O2 exhibit a tendency to increase while the hilltop extends into the free troposphere. Here, the observed decrease in H2O2 in the early morning occurs during sunlit hours. For the estimation of the nighttime deposition velocities we follow the approach of Shepson et al. (1992) and Hall and Claiborn (1997), assuming that the deposition loss is a first-order loss process resulting in an exponential decrease in H2O2 (Hall and Claiborn, 1997). Additionally, we assume a linear H2O2 gradient throughout the nocturnal boundary layer (Shepson et al., 1992). Please note that nighttime production of H2O2 due to the ozonolysis of alkenes is neglected in this approach, leading to a potential underestimation of the deposition velocities, in particular in environments with large biogenic emissions such as during HUMPPA. Estimated deposition velocities varied between 0.18 and 0.6 cm s-1 (Table 2) with a total uncertainty between ±53 and ±105 %. These values are similar to values for the H2O2 dry deposition velocity found in the literature. Walcek (1987) reported a value of 1 cm s-1 over the north-east of the USA, while Baer and Nester (1992) estimated an average vd of 1.5 cm s-1 for the upper Rhine Valley (Germany). From airborne measurements over the tropical rainforest in Suriname, Stickler et al. (2007) deduced a H2O2 deposition velocity of 1.35 cm s-1. Higher values of vd up to 5–10 cm s-1 are reported over forested regions due to enhanced uptake by stomatal openings (Hall and Claiborn, 1998; Valverde-Canossa et al., 2006; Nguyen et al., 2015). The nighttime vd values listed in Table 2 can thus be assumed to be lower limits of daytime values, since the effect of vegetation and enhanced turbulence is not accounted for.

The daytime analysis of vd has been performed for periods of the day in which H2O2 can be assumed to be in a photostationary state (dH2O2/dt=0). This criterion is generally met between local noon and the early afternoon when the BLH is highest and vertical entrainment can be neglected. For the calculation of vd in Table 3 we assume that net H2O2 production (NPR =Pchem–Lchem) is balanced by dry deposition loss. The deposition velocities for DOMINO (0.56 cm s-1; uncertainty ±85 %) and PARADE (0.6 cm s-1; uncertainty ±98 %) are about a factor of 2 to 3 higher than the nighttime values for these sites documented in Table 2, while significantly higher daytime vd values (factor of 10 to 20) (Table 3) are calculated for HUMPPA and HOPE. The value of vd (day) for CYPHEX of 2.1 cm s-1 (uncertainty ±50 %) is within the range of observation at other sites both investigated here and those cited in the literature. The daytime vd value obtained for HOPE (6 cm s-1; uncertainty ±93 %) is also within the range of values reported in the literature for forested environments (Hall and Claiborn, 1997; Valverde-Canossa et al., 2006; Nguyen et al., 2015), while the value obtained for HUMPPA (6.04 cm s-1; uncertainty ±100 %) is comparable to the high values reported for a boreal forest in Canada (Hall and Claiborn, 1997). Note that uncertainties were calculated according to Eq. (4), taking into account the variability of all input variables to Eq. (1) derived from the 25 %–75 % range and an uncertainty of 20 % for the boundary layer height.

To evaluate Eq. (1) from sunrise to midday during the five campaigns we use the net photochemical production of H2O2 presented in Fig. 5 and calculate the deposition loss during the increase in the boundary layer height. For this calculation, we linearly interpolate the deposition velocity between the nighttime values presented in Table 2 and the noontime values presented in Table 3. For CYPHEX we use an average of all nighttime deposition velocities presented in Table 3. As mentioned before, during this period it is expected that vertical entrainment due to an increasing boundary layer height and horizontal advection will also have an effect on the temporal evolution of H2O2. The mean rate of d[H2O2]/dt is derived from the observed H2O2 mixing ratio increase from the early morning minimum up to the maximum around local noon in Fig. 2. Average net photochemical production rates (Pchem–Lchem) and dry deposition loss rates over the periods for which d[H2O2]/dt was analysed were derived from Eqs. (2), (3) and (7), respectively. 7Ldep=vd[H2O2]BLH The residual (d[H2O2]/dt–((Pchem–Lchem)–Ldep)) according to Eq. (1) is a measure of gain or loss of H2O2 due to the combination of vertical entrainment and horizontal advection. Table 4 lists the time periods over which d[H2O2]/dt was analysed, the mean H2O2 mixing ratio (pptv), mean d[H2O2]/dt (pptv h-1), mean net photochemical production rate (Pchem–Lchem) (pptv h-1), the mean boundary layer height (BLH) (cm), the deposition loss rate (Ldep) (pptv h-1) and the transport rate (Ptrans) (pptv h-1). Uncertainties in percentage were calculated from Eq. (4) based on the variabilities of the input variables. Positive residuals indicate vertical entrainment or advection of higher H2O2 mixing ratios, and negative values indicate dilution. The budget of net photochemical production, deposition loss, observed change in H2O2 mixing ratios from sunrise to noon and the inferred residual transport are graphically shown in Fig. 6. For DOMINO the calculated net photochemical production (1.3 pptv h-1) is of the same order of magnitude as the loss rate due to deposition (Ldep=-0.96 pptv h-1), indicating a balance between sources and sinks of H2O2. Thus the observed increase in H2O2 (7.9 pptv -1h) during the morning is almost completely due to transport (7.6 pptv h-1).

During PARADE the net production is 5.4 pptv h-1, which is also largely balanced by deposition loss (-4.4 pptv h-1), resulting in a positive residual indicating a missing source of the order of 10.5 pptv h-1. Since the PARADE site is on a hilltop it is likely that entrainment from the residual layer is responsible for this transport.

During HUMPPA the net photochemical production of 53.16 pptv h-1 is only slightly smaller than the deposition loss (-56.9 pptv h-1), resulting in a rather large entrainment rate of the order of 114.2 pptv h-1 required to explain the observed H2O2 increase. Since the surrounding area is rather homogeneous (Williams et al., 2011), we assume that this transport is due to vertical entrainment from the residual layer during the rise in the boundary layer height. The deduced entrainment rate of 118.3 pptv h-1 is an upper limit since we most likely underestimate the net production rate of H2O2. Axinte (2016) estimated that the ozonolysis of terpenes in the boreal forest would lead to an additional H2O2 production of the order of 8.3 pptv h-1, enhancing the net production by 7.5 %.

Slightly higher net production compared to deposition losses is observed for HOPE (net production =27.3 pptv h-1, deposition loss =-20.4 pptv h-1). This yields a contribution of 12.9 pptv h-1 from transport. Since HOPE was performed on a mountaintop, we assume that this increase is due to vertical entrainment during the growth of the boundary layer. Contrary to the other sites discussed above where close to 100 % of the morning increase in H2O2 was due to transport, this contribution is only 65 % during HOPE.

During CYPHEX, the net production of 259 pptv h-1 is only partly balanced by a dry deposition loss of -200.7 pptv h-1. Thus, the photochemical production of H2O2 minus deposition (58.3 pptv h-1) is slightly larger than the observed increase during the early morning (31.7 pptv h-1), yielding a negative residual of -26.5 pptv h-1, indicating a dilution. Since CYPHEX was performed at a high-altitude coastal site affected by a land–sea breeze, it is likely that the advection of marine air masses with slightly lower H2O2 mixing ratios is responsible for this dilution effect.

Please note that the error propagation according to Eq. (4) includes measurement uncertainties and atmospheric variability, with the latter being the dominant term. Exclusion of the atmospheric variability would result in much smaller errors. Therefore, the stated values for net production, deposition and transport are best estimates for the median values, while the error bars reflect atmospheric variability and are thus a very conservative measure of the uncertainty.