Following Cariolle et al. (2009), a passive tracer (from the perspective of the usual model chemistry) is added to the CTM to represent NOx emitted by lightning. The LNOx tracer initial mass corresponds to the NOx mass at the start time of the simulation. Rather than increasing the concentration of NOx within the CTM, lightning NOx emissions now increase the concentration of this new passive tracer, which is transported in the standard way by advection and turbulence. Plume chemistry is considered to be significant when the mixing ratio of the lightning NOx tracer is higher than the critical NOx content, hereafter denoted rl. Above this value the lightning NOx tracer is transferred to the normal NOx tracer at a rate described by a plume lifetime (τ), which is an exponential decay constant. This corresponds to an exchange timescale between the lightning NOx plume and the background NOx. The continuity equation related to the tracer evolution is detailed by Eq. (1). ∂rLNOx‾∂t+<FLNOx>=I-1τ⋅rLNOx‾, where rLNOx‾ is the mixing ratio (in ppb) of the NOx lightning tracer in the model grid (note that all overlined terms refer to grid average quantities in the CTM), FLNOx≡∇×(rLNOx‾u)+∇×(Dt∇rLNOx‾) and corresponds to the flux divergence related to the large-scale transport of the tracer (advection and turbulent diffusion, in molecules cm-2 s-1), I is the injection rate of LNOx (in s-1), and τ is the plume lifetime (in seconds).

The calculation of τ requires evaluating the mass fraction of the lightning NOx (M(t)) corresponding to the undiluted fraction of the plume and characterized by an NOx mixing ratio above the rl critical value. In other words, the plume boundary is defined by the critical value rl depending on the time of day. The NOx mass, M(t), decreases monotonically to zero until t=Tl for which the tracer mixing ratio is everywhere below the rl threshold. The plume lifetime is obtained by an exponential function depending on the mass (Eqs. 2 and 3): M(t)=∫Vpρ⋅rp⋅dV,τ=∫t0=0+∞exp⁡(-t/τ)⋅dt=1M(t0)∫t0=0TlM(t)⋅dt. Where Vp is the volume of the plume, ρ is the density of the air, rp is the NOx mixing ratio within the plume (in ppb), and Tl is the time for which the mixing ratio rp is below the critical value rl everywhere. The calculation of the plume lifetime, by simple plume dispersion simulations, depends on (i) the initial emissions of NOx by lightning, (ii) the rl value, and (iii) the dispersion properties of the atmosphere (related to the horizontal diffusion coefficient, Dh) and is detailed in Sect. 3.2.3. Note that the mean dispersion properties of the atmosphere were associated with the horizontal diffusion only. The lightning NOx emissions occur in the convective part of clouds where the vertical diffusion is strong. Therefore, the vertical diffusion coefficient is a determining parameter for the LNOx distribution in the cloud. As mentioned in Sect. 2.1, the vertical distribution of LNOx is calculated a priori from as a reverse C-shaped profile. The LNOx plume parameterization is applied a posteriori; after that, lightning NOx is vertically prescribed and concerns convective outflow where NOx is detrained in the troposphere. In this region of detrainment, the horizontal dispersion may be more efficient than the vertical one as discussed in .

Once the lightning NOx is emitted, it is transferred to model's background NOx based on the lifetime of the plume (τ). Thus, the continuity equation for the NOx species emitted in the plume and released to the large scale can be deduced as described by Eq. (4). ∂rNOx‾∂t+<FNOx>=+1τ⋅rLNOx‾⋅αNOx+Lss, where rNOx‾ is the mixing ratio of NOx (in ppb) in the model grid, αNOx is the molecular mass ratio between the air and NOx species, and Lss is the large-scale sources and sinks (in molecules cm-2 s-1), such as natural and anthropogenic emissions, photochemical reaction, mixing, and conversion to reservoir species.

We consider a fairly simple chemistry within the plume as described below. The increase in the nitrogen oxide concentration in the upper troposphere leads to ozone production through the reaction of NO with peroxide (HO2), CH3O2, or RO2 radicals from the OH oxidation as shown by Reaction (R1). NO+RO2⟶NO2+RO In the case of large NOx injection by lightning, the NOx content (∼40 ppt in unpolluted atmosphere) becomes close (a few ppb, according to in situ measurements; ) to the surrounding ozone (60 ± 24 ppb) . The ozone evolution within the plume is described by Reactions (R2)–(R6). NO2+hν(λ<400nm)⟶NO+ONO+O3⟶NO2+O2O+O2+M⟶O3+MO+NO2⟶NO+O2O+O3⟶2O2 From these equations we can define an Ox family (Ox≡O+O3+NO2) where the only net loss of Ox is by reactions between atomic oxygen and NO2 or O3. The rate of change of each chemical family is given by Eqs. (5), (6), and (7): . d([O]+[O3])dt=+k2⋅[NO2]-k3⋅[NO]⋅[O3],-k5⋅[O]⋅[NO2]-2⋅k6⋅[O3]⋅[O],d([O]+[O3]+[NO2])dt=-2⋅k5⋅[O]⋅[NO2],-2⋅k6⋅[O3]⋅[O]d([NO]+[NO2])dt=0, where ki corresponds to the rate constants for the Ri reactions.

Thus, two processes occur to O3 in the plume during the daytime. On short timescales Ox is conserved. Lightning emissions of NO in the plume are converted into NO2, but as NO2 is in Ox family, there is net conservation of Ox. However, on long timescales Ox can be destroyed through the reaction of O with NO2 and O3. Both of these processes need to be considered.

The first regime (regime I) occurs at low concentrations of NOx (relative to O3). Under these conditions the Reaction (R5) is slow. There is the rapid equilibrium between NO, NO2, and O3 (Reactions R2, R3, and R4). As a consequence, O3 is converted into NO2 and can be restored later after dilution of the plume depending on the balance between NO and NO2 on a large scale . Overall, Ox is conserved. In this regime emitted NO reacts with the available O3 until the NO to NO2 ratio in the plume reaches that in the background. Thus, the impact on the O3 background concentration is to reduce it by the number of molecules of NO emitted multiplied by the background NO2 to NOx ratio. The effect of the first regime on the ozone burden is expressed by Eq. (8). ∂rO3‾∂t+<FO3>=-1τ⋅rLNOx‾⋅αNOx⋅(NO2‾NOx‾-E)⋅δ+Lss, where rO3‾ is the mixing ratio of O3 (in ppb) in the model grid, E is the NO2NOx ratio in the initial emissions, δ is equal to 1 during the day and 0 during the nighttime, and Lss is the sources and sinks of ozone, such as photochemical production, transport from the stratosphere, surface deposition, photolysis reactions, and photochemical destruction.

The second regime (regime II) occurs at high concentrations of NOx (relative to O3). Under these conditions the rate of R5 is large. The nonlinear chemical interactions between NOx and O3 occur with different rates than in the background atmosphere. To account for this, Cariolle et al. (2009) introduced an effective reaction rate constant (Keff), which is related to the production or the destruction of the odd oxygen (Ox) within the plume. Keff is expressed by Eq. (9). Keff=∫t0Tl∫VpK⋅rNOxP⋅rO3P⋅dVp⋅dtrO3‾⋅∫t0tl(∫VprNOxP)⋅dVp)⋅dt, where rNOxP and rO3P are the mixing ratios of nitrogen oxides and ozone within the plume, rO3‾ is the background ozone mixing ratio averaged in the model grid, and K is the rate of NOx–O3 reaction within the plume.

The analysis of the chemical reactions related to the two regimes shows that [O3]≫[O] and k5×[NO2] is more efficient than k6×[O3] as a sink for Ox . Thus, Eq. (6) is simplified to give Eq. (10). d([O3]+[NO2])dt=-2⋅k5⋅[O]⋅[NO2] Consequently, Keff can be simplified to Eq. (11). Keff=2⋅(∫Tk5⋅O⋅NO2⋅dt)(NOx⋅∫TOx⋅dt) The calculation of Keff is detailed in Sect. 3.2.4. Considering the two regimes related to the sub-grid plume chemistry, the ozone burden is described by Eq. (12) during the daytime and nighttime. Note that during the nighttime there is no direct impact on its burden due to the ozone plume chemistry as δ=0. Only indirect effects are expected from NOy chemistry. ∂rO3‾∂t+<FO3>=-1τ⋅rLNOx‾⋅αNOx⋅(NO2‾NOx‾-E)⋅δ-Keff⋅rLNOx‾⋅ρ⋅αNOx⋅rO3‾⋅δ+Lss

In addition, we consider the conversion of NOx into HNO3 within the plume. This conversion takes place in two different ways depending on the day or night atmospheric conditions. During the day, NO2 reacts primarily with OH to give HNO3 directly, and it is characterized by the coefficient β1, while during the nighttime the conversion of NOx to HNO3 occurs mainly through the N2O5 formation followed by a heterogeneous hydrolysis reaction, which corresponds to β2. In other words, the β coefficients are the molar fractions of NOx converted to HNO3 within the plume. These two fractions are unitless.

In summary, the equation system solved on a large scale by the CTM for a lightning NOx source is detailed by Eqs. (13), (14), and (15). ∂rNOx‾∂t+<FNOx>=+1τ⋅rLNOx‾⋅(1-β1⋅δ-β2⋅(1-δ))⋅αNOx+Lss,∂rHNO3‾∂t+<FHNO3>=+1τ⋅rLNOx‾⋅(β1⋅δ+β2⋅(1-δ))⋅αNOx+Lss,∂rO3‾∂t+<FO3>=-(1τ⋅(NO2‾NOx‾-E)+Keff⋅rO3‾⋅ρ)⋅rLNOx‾⋅αNOx⋅δ+Lss, where rNOx‾, rHNO3‾, and rO3‾ correspond to the NOx, HNO3, and O3 mixing ratios averaged over the grid cell of the model, respectively.

In this study, the tropospheric chemistry and especially the LNOx plume chemistry is considered both during the daytime and nighttime since no reactions are initiated during the day. The chemical interactions during the night correspond mainly to the reactions of O3 and O with NO and NO2 as well as the NOx deactivation and the chemistry of the nitrogen reservoir species (here, HNO3 and N2O5) and the nitrate radical (NO3). NO3 is the main oxidant in night conditions and is produced from the slow oxidation of NO2 by O3 (Reaction R7). NO2+O3⟶NO3+O2 The other dominant source of NO3 is the destruction of N2O5 (Reaction R8), but as N2O5 is formed from NO3 (Reaction R9), the two species act in a coupled manner. N2O5+M⟶NO3+NO2+MNO3+NO2+M⟶N2O5+M

As mentioned previously, N2O5 is a determining species for the tropospheric chemistry during the nighttime, allowing the HNO3 formation by the heterogeneous reaction on the particle surface (aerosols and ice crystals). During the day, NO3 rapidly undergoes photolysis to produce NO or NO2. In addition, NO3 reacts very quickly with NO, which is more concentrated during the daytime than during the nighttime (Reaction R10) but NO3 is very low during the daytime. However, this reaction can take place during the night, especially for a plume characterized by high NO mixing ratios (like a plume from lightning emissions) which is transported both during the day and at night. NO3+NO⟶NO2+NO2 Furthermore, the nitrate radical can potentially react with VOCs. The reaction of the unsaturated hydrocarbons such as isoprene, butenes, and monoterpenes with NO3 leads to the HNO3 formation (Reaction R11). NO3+RH⟶HNO3+R Considering NO3 reaction with alkenes, an additional mechanism is found initiating a complex chemistry allowing the formation of NO2 or organic nitrates . Finally, NO3 can initiate VOC oxidation via peroxy radical production (Reaction R12). That way, it can be involved as a chain propagator (Reactions R13 to R17). NO3+organic compound⟶R+productsR+O2+M⟶RO2+MRO2+NO3⟶RO+NO2+O2RO+O2⟶R′R′′CO+HO2HO2+O3⟶OH+2O2HO2+NO3⟶OH+NO+O2 The reactions of HO2 with ozone (R16) or NO3 (Reaction R17) imply OH production. Also, the reaction of ozone with alkenes allows the formation of OH during the night (Reaction R18) . Alkene+O3⟶v1OH+v2HO2+v3RO2 Reaction (R18) occurs when ozone concentrations remain sufficiently high in night conditions, in other words for polluted atmosphere.

In this context, we consider different values during the daytime and nighttime for the plume lifetime, the effective reaction rate constant, and the fraction of NOx conversion into HNO3 within the plume. Distinguishing day and night chemistry is linked with the fluctuation of the critical rl value (below which the sub-grid plume chemistry is negligible), depending on atmospheric conditions. Therefore, if rl changes with sunlight, the plume lifetime also changes. Note that except for the β2 fraction, this night chemistry is not considered by the initial plume approach developed by Cariolle et al. (2009), which considers NOx plumes from aircraft exhausts only during the daytime.

Figure 1 summarizes all elements which define the plume approach and how it has been adapted and implemented into the model.

The horizontal diffusion coefficient (Dh) is a key parameter of the atmospheric dynamical conditions in determining the dispersion of the lightning NOx plume. Dh is used as the dispersion constraint for the simple plume dispersion simulations carried out in order to estimate the plume lifetime and the effective reaction rate constant. The diffusion coefficient was determined in two different ways. A first estimate of the horizontal diffusion was performed by running the 3-D mesoscale Meso-NH model. Then, the Dh coefficient was calculated using in situ measurements in a thunderstorm anvil.

The Meso-NH mesoscale model was used (see Sect. 2.2) to investigate Dh. A simple convective cell forced by a warm bubble and initialized by a radiosounding at the simulation start was run as an ideal case. Simulations were realized for a domain of 24 km in the two horizontal directions, and the grid horizontal resolution is Δx=Δy=1 km and Δz=500 m. The convective cell is located at 43.29∘ N latitude and 0∘ longitude . Simulations of 6 h were performed, allowing the complete development and the dissipation of the convective cell. Dh was calculated within the anvil using the mixing length diagnostic variable, hereafter denoted L, as described by Eq. (16) . Dh=23×L4×exp⁡12 At the mature stage of the cell, Dh was calculated as 100 m2 s-1 within the upper levels of the convective cell (i.e., in the anvil, defined empirically).

In addition to the modeling estimate, we used in situ measurements to calculate Dh. Turbulence measurements were performed by a B-757 commercial aircraft along a flight from the west of Kansas to the north of Missouri and corresponding to a trajectory of more than 500 km . These in situ measurements were carried out from 07:00 to 10:00 UTC on 17 June 2005, during the development of a mesoscale convective system (MCS). This MCS is associated with a turbulence event characterized by the measurement of the atmospheric eddy dissipation rate (ϵ) and the turbulence kinetic energy (TKE) above and within the cloud anvil. The higher values of ϵ (ϵ1/3∼0,4 m2/3 s-1) were recorded between 11.3 and 11.6 km altitude, corresponding to the cloud anvil levels. In addition, for this MCS, the TKE was about 1 m2 s-2 at the locations of the highest ϵ values.

According to these observations, the turbulent diffusivity (Eq. 17) was estimated above the anvil of the MCS (http://www.ral.ucar.edu/projects/turb_char/), such that Dh> 0.1 m2 s-2. Then, Dh was calculated within the anvil such that Dh=15 m2 s-1 using the same formulation (Eq. 17). This last estimate seems to be the most common value compared to the diffusion coefficient value of 20 m2 s-1 used by , close to the tropopause level and the Dh value calculated for contrails (15 m2 s-1) in the upper troposphere . Dh=(TKE)2ϵ The Dh estimate using the Meso-NH model is high compared to the results from measurements, corresponds to the upper limit of the calculated diffusion coefficients, and may be associated with the turbulence in the convective cloud. However, it is important to note that usually most numerical simulations are performed with 1-D turbulence models. What is interesting in the use of Meso-NH in this study is that the 3-D turbulence is solved. This simulation provides an additional estimate of Dh, allowing a comparison with the calculation from in situ measurements. Moreover, studies on the diffusivity in cloud anvils are uncommon. It is necessary to conduct additional work in the future on that issue, again constrained with new in situ measurements of the atmospheric turbulence in the anvil.

It is important to note that the 3-D turbulence is not solved online in the GEOS-Chem model because of the fine scale characterizing this process but is prescribed by the GEOS-5 met fields. Therefore, the global variability of Dh is not calculated by the CTM, and it is beyond the scope of this study.

In order to cover all horizontal diffusivity estimates discussed in this section, values of 0.1, 15, and 100 m2 s-1 were used. The horizontal coefficient is constant for all lightning NOx plumes which are considered in the GEOS-Chem model. Hereafter, the results are detailed for the central value Dh=15 m2 s-1. Sensitivity tests depending on the uncertainty associated with the parameter estimate are performed and presented later in Sect. 4.3.

The rl critical value is the NOx mixing ratio within the undiluted phase of the plume below which the nonlinear chemistry can be neglected (Sect. 3.1). It has been estimated using the 0-D DSMACC box model (Sect. 2.2). Initial conditions for simulations carried out with the DSMACC box model are from outputs of the GEOS-Chem model. In particular, initial atmospheric parameters and atmospheric background concentrations of species correspond to the average of the GEOS-Chem outputs (i) from 8 to 11 km, (ii) for two latitude regions (tropics and midlatitudes), and (iii) for the year 2006 (Table 1). The altitude range refers to the detrainment region estimated by GEOS-Chem using the GEOS-5 met fields (Sect. 2.1) both in the tropics and in the midlatitudes. Note that this range can vary depending on the met fields and the convection parameterization. In addition, the LNOx plume parameterization should have an impact outside of this altitude range, mainly between 6 and 12 km, but to a lesser extent.

In order to focus on chemistry interactions only between chemical species of interest and on removing the mixing influence and sunlight fluctuations, short simulations (i.e., 1 h each) were run with the DSMACC model. The effects of the day or night conditions were carefully considered, carrying out separate simulations during the daytime and nighttime. Simulations were run for a large range of initial NO mixing ratios from 0.01 ppb to 1 ppm. The rl value is defined from the NO value, for which the ∂Oxdt trend is perturbed. In other words, rl is associated with the second derivative of Ox, i.e., the curve optimums on Fig. 2. The rl threshold was defined to be 0.1 and 0.25 ppb during the day and at night for midlatitudes and 0.1 and 0.75 ppb during the day and at night in the tropics (Fig. 2).

Note that the midlatitudes and the tropics were separated because of the large differences in LNOx emissions between the two regions in terms of the number of flashes in a particular convective cell, which is higher in the tropics according to the LIS–OTD climatologies . This last point is important for the plume lifetime estimate detailed in the following section.

The plume lifetime (τ) depends directly on (i) the initial NO pulse from lightning emissions, (ii) the rl critical value, and (iii) the diffusion properties of the atmosphere. The plume lifetime also depends on the initial size of the plume. Here we use a width of 500 m in order to include an ensemble of spikes on the cloud scale (i.e., each plume is defined from several electrical discharges on a convective cell scale). τ is crucial for the physical description of the NOx plumes, and it has been computed by carrying out dispersion simulations of a simple plume assumed to be cylindrical. In this model, the standard atmospheric conditions are represented by temperature, pressure, and species concentrations of the background atmosphere, which are similar to the initial conditions used for the DSMACC simulations. As a reminder, initial conditions are from GEOS-Chem outputs averaged (i) from 8 to 11 km, (ii) for two latitude regions (tropics and midlatitudes), and (iii) for the year 2006 (Table 1). Simulations are initialized by an NO pulse from lightning emissions (hereafter denoted NOi), and the plume dispersion depends on the Dh value estimated in Sect. 3.2.1.

The initial tracer concentration NOi related to lightning NO emissions on the scale of a convective cell (gathering several flashes together) in the midlatitudes was defined according to previous aircraft measurement campaigns. In particular, the STERAO (Stratospheric–Tropospheric experiment: radiation, aerosols, and ozone) campaign recorded NO spikes of a magnitude from 1 to 10 ppb related to lightning activity in thunderstorms and occurring from 9 to 10 July 1996 over northern Colorado . measured NO spikes of 3.5 ppb during the STREAM (Stratosphere–Troposphere Experiment by Aircraft Measurements) campaign associated with a matured storm over Ontario. Several peaks of NO mixing ratios from 0.7 to 6 ppb were also observed during EULINOX (European Lightning Nitrogen Oxides Project; ) over Germany in July 1998. The LINOX (Lightning NOx) aircraft campaign recorded NO spikes from 0.75 to 1.25 ppb related to thunderstorms over Europe on 30 July 1996. From these studies, the NO concentration associated with the electrical activity in thunderstorms occurring over the midlatitudes was determined as NOimean, Midlats= 3.4 ppb (NOimin, Midlats= 0.7 ppb and NOimax, Midlats=10 ppb). Because there are much fewer LNOx measurements in the tropics and in order to be consistent with the LNOx emissions defined in the GEOS-Chem model, the ratio RLNOx=LNOxMidlatitudesLNOxTropics was defined as in the CTM. During the year 2006, the relative midlatitude and tropics LNOx contribution was about RLNOx=0.33. This result is in agreement with higher LNOx emissions in these regions rather than in the midlatitudes. The value of the NO mixing ratio injected by lightning into the tropics was estimated as NOimean, Tropics=10.2 ppb (NOimin, Tropics=2.8 ppb and NOimax, Tropics=29.7 ppb).

Once the NOi estimate was completed, the calculation of the plume lifetime was achieved using the detailed formulation given in Sect. 3.1.1. The results for τ are summarized in Table 2. Hereafter, the results are detailed for NOimean in Sect. 4, and sensitivity tests are carried out using all NOi values for the midlatitudes and the tropics (Sect. 5). Model calculations for NOimean and Dh=15 m2 s-1 provide a minimum plume lifetime of 3 (6) h for the midlatitudes and maximum plume lifetime of 9 (21.3) h for the tropics during the daytime (nighttime).

The nonlinear chemistry within the plume has been considered in calculating the effective reaction rate constant (Keff), which is used to compute the formation of the secondary species (Ox and HNO3) within the plume. Keff is associated with the evolution of odd oxygen depending on the O and O3 reactions with NO2 and NO, and also on the NOx activation (day) or deactivation (night) with the HNO3, N2O5, and PAN chemistry. Note that in the case of lightning emissions, other species like VOCs, HOx, and H2O may be uplifted into the convective region. However, we assumed that the OPE is mainly controlled by NOx in the upper troposphere, as previously showed by . Therefore, the Keff calculation is here mainly dependent on NOx content. Future studies should try to investigate this issue for lightning emissions mixed with strong surface emissions in order to sharpen our parameterization.

Keff is calculated according to Eq. (11) of Sect. 3.1.2 using the same simple plume dispersion simulations as those carried out to define the plume lifetime (Sect. 3.2.3).

Results for Keff are summarized in Table 3. Model calculations using NOimean and Dh=15 m2 s-1 give a Keff value of 5.49×10-19 molecules-1 s-1 cm3 (4.55×10-19 molecules-1 s-1 cm3) in the midlatitudes and 3.64×10-19 molecules-1 s-1 cm3 (2.98×10-19 molecules-1 s-1 cm3) in the tropics during the daytime (during the nighttime).

Our Keff estimates are smaller than those calculated by Cariolle et al. (2009) for the plume chemistry related to aircraft exhausts. In this previous work, Keff varies from 1.0 to 4.2×10-18 molecules-1 s-1 cm3, with a mean value close to 3×10-18 molecules-1 s-1 cm3 depending on the NOx loading. The very low value for Keff indicates that the plume parameterization implies a delay in the production of ozone on a large scale rather than its destruction within the plume.

The fractions β1 and β2 represent the NOx conversion to HNO3 within the plume during the daytime and nighttime, respectively. They were computed using the DSMACC box model.

The β1 coefficient was calculated for day conditions depending mainly on the OH concentration. The conversion of NOx into HNO3 during the nighttime (β2 coefficient) is related to the heterogeneous reaction of N2O5 and so depends on particle (aerosols and ice crystals) concentration and particles' lifetime. This is directly linked with the surface density and the radius of particles in the anvil region of thunderstorms, which is highly uncertain. We defined these values using in situ measurements. The surface area (ST) and the radius (R) for aerosols are defined such that ST=0.28 m-1 and R=1 µm-1 ; for ice, these are ST=0.03 m-1 and R=30 µm-1 . In addition, the reaction probabilities of NOx on aerosols and ice crystals γN2O5aerosols=0.02 and γN2O5ice=0.03 , respectively, were used for our box model simulations. These values correspond to the probability that an N2O5 molecule impacting an aerosol or an ice crystal surface reacted. The results for β1 and β2 coefficients are summarized in Table 4.

The estimate of the β1 fraction does not show significant variation, neither between latitudes regions nor depending on NOi. The minimum β1 value is 1.34×10-4 for the tropical regions and NOimin, and the maximum β1 value is 1.88×10-4 for the midlatitudes and NOimax. The study of production and destruction rates for day conditions taking into account all reactions pathways (not shown here) demonstrates that the production of HNO3 during the day is mainly determined by the reaction of NO3 with formaldehyde (HCHO) and acetaldehyde (CH3CHO). Surprisingly, the HNO3 formation via the NO2+OH reaction seems to be less efficient. This result may be explained by the low initial concentrations of OH used for the DSMACC simulations, and it is in agreement with the small β1 values. The averaged β2 coefficient is higher by a factor 10 compared to β1 with a minimum value of 0.24×10-3 in the tropics for NOimax and a maximum estimate of 14.4×10-3 in the midlatitudes for NOimin. The analysis of the production and the destruction rates for night conditions taking into account all reaction pathways shows that the predominant reaction in the HNO3 evolution is N2O5+H2O (or the heterogeneous reaction on the aerosol and ice crystal surfaces).

Figure 3 displays the geographical distributions of the 9 km lightning NOx emissions (a), the related LNOx tracer distributions (b), and the LNOx tracer zonal average (c) in January (top panels) and in July (bottom panels), reproduced by the CTM from the P1 experiment. These results are shown for an approximate detrainment level (9 km altitude) where the detrainment of LNOx is the largest. In January, the highest emissions of NOx from lightning (4–6 ×109 molecules cm-2 s-1) are located in the Southern Hemisphere around the tropics over west Australia and central–southern Africa. Also, the model gives low LNOx emissions (<3×109 molecules cm-2 s-1) over South America and North America, especially over the Gulf of Mexico. In July, the highest LNOx emissions (4–6 ×109 molecules cm-2 s-1) are calculated in the Northern Hemisphere over North America, the north of India, central Africa, and the Sahel. In addition, LNOx emissions are modeled over Europe and over east Asia, but to a lesser extent (<2×109 molecules cm-2 s-1).

The lightning NOx tracer introduced into the model represents the lightning NOx emissions affected by the transport and the exponential decay depending on the plume lifetime. Figure 3 shows that the tracer distribution is consistent with the lightning NOx emissions. However, it is important to note that the plume lifetime is a key factor in the evolution of the LNOx tracer mixing ratio. A long plume lifetime (several hours to several days) allows the intercontinental transport of LNOx plumes. The representation of the sub-grid chemistry and the transport of the nonlinear chemistry effects related to the plume consideration becomes important for the chemistry of the regions located far downwind from source regions. The plume lifetime depends on the latitude because of the different background chemical concentrations and the different amount of NOx emitted from lightning in the tropics and in the midlatitudes. In addition, as mentioned before, we consider the influence of day and night conditions on the plume lifetime estimate.

According to its preliminary calculation (Sect. 3.2.3), the plume lifetime is longer in the tropics (9 and 21.3 h for day and night conditions, respectively) than in the midlatitudes (3 and 6 h, for day and night conditions, respectively). So, the LNOx tracer is characterized by a shorter lifetime as a plume over North America than over central Africa and around the Sahel, while the model simulated fewer emissions over these regions, especially in summer. In boreal winter, the mixing ratio of the lightning NOx tracer calculated by the model is about 0.21 ppb over central and southern Africa, 0.18 ppb over west Australia and 0.11 ppb over South America. In summer, the tracer mixing ratio is simulated as 0.21, 0.32, and 0.16 ppb over central Africa, northern India, and North America, respectively. The lightning NOx tracer is produced at altitudes where lightning NOx is calculated and detrained (in the upper troposphere between ∼500 and 300 hPa) as shown in Fig. 3c.

The difference between the P1 and BC experiments (P3) was calculated in order to quantify the changes in NOx and O3 mixing ratios on the large scale implied by the implementation of the plume-in-grid parameterization in GEOS-Chem. Figures 4 and 5 display the geographical distributions of the NOx, HNO3, PAN, and O3 absolute changes (in ppb) in January and in July, respectively. The 9 km altitude level was chosen because of the most significant variations at this altitude compared to the rest of the troposphere.

In boreal winter, LNOx plume chemistry leads to a maximum decrease on a large scale over regions of emissions of 120 ppt for NOx and a decrease of 68 ppt for HNO3 and 16 ppt for PAN over central and southern Africa. These variations are associated with a maximum O3 decrease of 2.8 ppb over regions of emissions. A similar NOx, HNO3, PAN, and O3 reduction is obtained in other areas of high LNOx emissions (i.e., over west Australia and South America). Downwind of LNOx emissions, the opposite effect is observed for NOx and HNO3 species, with a maximum increase of 40 ppt for NOx and 13.5 ppt for HNO3 observed over the South Atlantic and Indian Ocean. Generally, PAN still decreases over oceans but to a lesser extent compared to regions of LNOx emissions, with a maximum reduction of 9 ppt. The O3 response is a maximum increase of 1.13 ppb around the area where the transport is effective and especially over the oceans. In summer, maximum decreases of 140 ppt for NOx, 60 ppt for HNO3, and 24 ppt for PAN are calculated by the CTM, leading to a maximum O3 decrease of 2.4 ppb over central Africa (reduction is also observed over North America and northern India). Downwind of lightning emissions, an increase in NOx and HNO3 is observed, with a maximum value of 30 ppt and 38 ppt, respectively. The PAN reservoir species also still decrease slightly downwind, with 2 ppt changes. Finally, this leads to a maximum O3 increase of 0.7 ppb.

Note that the production of PAN is limited by the supply of NOx or non-methane volatile organic compounds (NMVOCs). Above continental lightning sources regions, NMVOCs are uplifted by deep convection but with lower NOx due to the activation of the plume parameterization. This implies a less efficient PAN production in these regions. Downwind of lightning source regions (oceanic regions), NOx increases because of the LNOx transport in the plume, but there are less NMVOCs available to produce PAN. Therefore, both in regions of LNOx emissions and downwind, PAN production is limited, leading to overall lower PAN mixing ratios on a large scale in the P1 experiment. However, this a more nuanced view of this may be obtained by considering the PAN chemistry in future studies using a similar LNOx plume parameterization and by introducing the PAN and CH3C(O)OO continuity equations and a new term to consider the fraction of NOx converted to PAN within the plume. This should enable PAN production during plume transport, which is inhibited in the current version.

In order to provide a full overview of the effects of the plume parameterization, the relative difference between the P1 and BC experiments (i.e., P3/BC) was calculated integrated throughout the troposphere. Figures 6 and 7 show the zonal average of NOx (upper panels) and O3 (bottom panels) relative changes (in %) integrated throughout the troposphere for the regions of interest for January and July. During boreal winter, the highest NOx (O3) decreases of 10 % (5 %) in west Australia; then 20 % (6 %) in central Africa are calculated. These negative variations are mainly calculated between 400 hPa and the tropopause level for NOx and ozone. South America is characterized by a decrease of 20 % in the nitrogen oxides and 1 % in ozone. Over this region, variations are significant in the entire troposphere for both species. In contrast to the continent decrease, an NOx increase is observed over the major part of the South Atlantic and the Indian Ocean, with a 14 and 20 % maximum, respectively. O3 responds with an increase of 1 % near the tropopause, and it becomes higher by about 4 % close to the surface. In summer, there is an NOx (O3) decrease of 25 % (8 %) over central Africa, 20 % (2 %) over northern India, and 5 % (0.5 %) over North America. Also, the South Atlantic and Indian Ocean (located downwind of lightning NOx emissions) are characterized by a maximum increase of 18 % for NOx and 2 % for O3.

As a result, the sub-grid chemistry associated with the LNOx emissions implies (i) a decrease in the nitrogen oxides and ozone mixing ratios on a large scale over regions characterized by intense lightning emissions and (ii) an increase in these species downwind of emissions. In particular, the plume parameterization related to the lightning NOx leads to

significant effects on the NOx mixing ratio (±20%): these effects on nitrogen oxides are important because NOx is the first criterion which is constrained in a CTM in order to determine the global LNOx production (6 TgN yr-1 in the GEOS-Chem model);