Assessing and improving cloud-height based parameterisations of global lightning flash rate, and their impact on lightning-produced NOx and tropospheric composition

Although lightning-generated oxides of nitrogen (LNOx) account for only approximately 10% of the global NOx source, it has a disproportionately large impact on tropospheric photochemistry due to the conducive conditions in the tropical upper troposphere where lightning is mostly discharged. In most global composition models, lightning flash rates used to calculate LNOx are expressed in terms of convective cloud-top height via the Price and Rind (1992) (PR92) parameterisations for land and ocean. We conduct a critical assessment of flash-rate parameterisations that are based on 15 cloud-top height and validate them within the ACCESS-UKCA global chemistry-climate model using the LIS/OTD satellite data. While the PR92 parameterisation for land yields satisfactory predictions, the oceanic parameterisation underestimates the observed flash-rate density severely, yielding a global average of 0.33 flashes s-1 compared to the observed 9.16 flashes s-1 over the ocean and leading to LNOx being underestimated proportionally. We formulate new/alternative flash-rate parameterisations following Boccippio’s (2002) scaling relationships between thunderstorm electrical generator power and 20 storm geometry coupled with available data. While the new parameterisation for land performs very similar to the corresponding PR92 one as would be expected, the new oceanic parameterisation simulates the flash-rate observations more accurately, giving a global average of 8.84 flashes s-1. The use of the improved flash-rate parameterisations in ACCESSUKCA changes the modelled tropospheric composition—global LNOx increases from 4.8 to 6.6 Tg N yr-1; the ozone (O3) burden increases by 8.5%; there is an increase in the midto upper-tropospheric NOx by as much as 40 ppt; a 13% increase 25 in the global hydroxyl (OH); a decrease in the methane lifetime by 6.7%; and a decrease in the lower tropospheric carbon monoxide (CO) by 3–7%. Overall, the modelled tropospheric NOx and ozone are improved compared to observations, particularly in the Southern Hemisphere and over the ocean. https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
Oxides of nitrogen (NOx ≡ NO (nitric oxide) + NO2 (nitrogen dioxide)) play an important role in tropospheric chemistry by acting as a precursor to ozone (O3) and the hydroxyl (OH) radical, which are the principal tropospheric oxidants (Labrador et al., 2005). As a greenhouse gas, O3 is most potent in the upper troposphere, whereas near the Earth's surface it is an air pollutant, adversely impacting human health and plant productivity. The OH radical plays a critical role in the chemical 5 cycles of many trace gases, such as methane (CH4), in the atmosphere.
Lightning is the dominant source of NOx in the middle to upper troposphere, and the only direct natural source remote from the Earth's surface Banerjee et al., 2014). Lightning predominantly occurs over land in the tropics with deep atmospheric convection. The extreme heat in a lightning flash channel in the atmosphere, which can extend over tens of kilometres, allows for the dissociation of nitrogen (N2) and oxygen (O2) molecules. The dissociation products 10 combine to form nitric oxide (NO) which quickly oxidises to form nitrogen dioxide (NO2), and an equilibrium between NO and NO2 is reached (Finney et al., 2014). A large uncertainty in the amount of NOx produced by lightning has been reported, with most global estimates ranging between 2 and 8 Tg nitrogen (N) per year .
Although lightning accounts for only approximately 10% of the global NOx source, the lightning-generated NOx (referred to as LNOx) has a disproportionately large contribution to the tropospheric burdens of O3 and OH (Murray, 2016). For example , 15 although LNOx emissions are of similar magnitude as those from biomass burning or soils, their contribution to the total tropospheric ozone column is about three times larger (Dahlmann et al., 2011). This is because in the middle to upper troposphere where LNOx is directly released, the O3 production efficiency per unit NOx is much higher (∼ 100 molecules O3 per molecule NOx) than that near the surface (∼ 10-30 molecules O3 per molecule NOx) as a result of the higher amount of UV radiance, lower concentrations and longer lifetimes of NOx (a few days rather than hours), and lower temperatures 20 affecting ozone loss chemistry at such altitudes (e.g. Williams, 2005;Dahlmann et al., 2011). Of any major emission source, variability in global mean OH is most sensitive to LNOx (Murray, 2016). Using a global chemistry transport model, Labrador et al. (2005) observed marked sensitivity of NOx, O3, OH, nitric acid (HNO3) and peroxyacetyl-nitrate (PAN) to the magnitude and vertical distribution of LNOx. Modelling studies by Grewe et al. (2007) and Dahlmann et al. (2011) found that of all the major sources of NOx, LNOx is the dominant source for tropospheric ozone (up to 40%) in the tropics and 25 Southern Hemisphere.
LNOx is also important when studying natural variability of tropospheric composition because lightning occurrence is influenced by natural climate variability drivers such as El Niño and La Niña in the tropics. Similarly, potential changes in deep convection as a result of future climatic change has a bearing on LNOx and thus tropospheric ozone and associated radiative feedbacks, and some of these have been explored through modelling (e.g. Banerjee at al., 2014Banerjee at al., , 2018Iglesias-30 Suarez et al., 2018). In addition, lightning intensity and distribution, and its uncertainty, in a future climate has implications for projections of lightning-induced fire activity (Krause et al., 2014). https://doi.org /10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.
A realistic representation of LNOx source strength and its global distribution is thus of vital importance for understanding tropospheric chemistry and its impact. In most global circulation models used for climate applications, convection is diagnosed/parameterised (i.e. clouds are not explicitly resolved) with limited cloud microphysics. A pragmatic way to predict lightning flash rates in these models is to use parameterisations based on simple physics of electrical charge and correlations between the flash rate and appropriate parameters representing convection. 5 The most common conceptual model used to compute the amount of LNOx in global models is where F is the lightning flash rate and is the amount of NO produced per flash. This calculation is carried out in atmospheric models by first calculating the lightning flash rate within a model grid column at every model time step, partitioning it into intra-cloud (IC) and cloud-to-cloud (CC) flash-rate components, applying an amount of NO mass produced per flash, and then vertically distributing the calculated NO mass in the column. 10 Various approaches to estimate lightning flash rate in global models have been followed in the past. Assuming an electric dipole structure for a thunderstorm with two equal but opposite charge volumes, separated by a distance of the order the vertical cloud dimension as developed by Vonnegut (1963) and Williams (1985), Price and Rind (1992, hereafter PR92) developed simple empirical parameterisations for calculating lightning flash rate in terms of convective cloud-top height over land and ocean. Flash-rate parameterisations based on convection parameters other than cloud-top height have also been 15 developed, e.g. convective precipitation and upward mass flux (Allen and Pickering, 2002); convective available potential energy (CAPE) (Choi et al., 2005), cold-cloud depth (Futyan and Del Genio, 2007), maximum vertical velocity and updraft volume (Deierling and Petersen, 2008), upward cloud ice flux (Finney et al., 2014;2016), product of CAPE and precipitation rate (Romps et al., 2014;Zhu et al., 2019), and multi-parameter regression fits (Luo et al., 2017).
The PR92 parameterisations are by far the most widely used ones by default in global chemistry transport models (CTMs) 20 and coupled chemistry-climate models, such as GEOS-Chem (Hudman et al., 2007), MOZART (Emmons et al., 2020), CAM-Chem (Lamarque et al., 2012), ECHAM5/MESSy (Jöckel et al., 2006), and UM-UKCA (Archibald et al., 2020), perhaps primarily because they are based on convective cloud-top height which can be easily diagnosed from a model's convection scheme. Additionally, with its use of an electric dipole structure for a thunderstorm, the framework underlying the PR92 parameterisations has some theoretical support. The PR92 parameterisations also perform reasonably well. For 25 example, Clark et al. (2017) tested flash-rate parameterisations based on cloud-top height, cold cloud depth, mass flux, convective precipitation rate, and cloud-top height with column-integrated cloud droplet number concentration, in a global model, and found that the PR92 parameterisations had the best correlation with the observations, but a higher value of the spatial standard deviation compared to observations due to a large land-ocean contrast in this parameterisation. Finney et al. (2014) found that the PR92 lightning flash parameterisation had considerable biases compared to satellite observations of 30 https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License. spatial flash density but performed 2 nd best (behind their parameterisation based on ice flux) out of the 5 parameterisations tested. A recent comparison by Gordillo-Vázquez et al. (2019) of six flash-rate parameterisation schemes showed a relatively good performance by those based on cloud-top height. However, a number of global modelling studies has demonstrated that the PR92 parameterisations underestimate the lightning flash density over the ocean compared to satellite observations (Allen and Pickering, 2002;Tost et al., 2007;Finney et al., 2014Finney et al., , 2016Clark et al. (2017). The performance of the PR92 5 flash-rate parameterisations has not yet been tested properly for their land and ocean components separately.
In this paper, we critically assess the performance of currently used flash-rate parameterisations for land and ocean based on convective cloud-top height. We also derive new/alternative flash-rate parameterisations following Boccippio's (2002) (Bo02) scaling relationships founded on theory linking thunderstorm electrical generator power and storm geometry applied to the available data. We implement in a global chemistry-climate model, viz. ACCESS-UKCA , 10 (a) these new parameterisations, (b) an oceanic flash-rate parameterisation suggested by Michalon et al. (1999) (Mi99), and (c) use the standard PR92 flash-rate parameterisation as a default. The model results are tested using global satellite data of flash density from the Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) (Cecil et al., 2014), which are available as global climatological, inter-annual and seasonal distributions. The veracity of the new modelled LNOx estimates are examined through comparison of modelled and reanalysis tropospheric NO2 column amounts. The impacts of the 15 modelled LNOx based on the new flash-rate parameterisations on tropospheric composition involving NOx, ozone, the hydroxyl radical, methane lifetime, and carbon monoxide are examined, including comparison with observations where available.

The ACCESS-UKCA global chemistry-climate model
We use the United Kingdom Chemistry and Aerosol (UKCA) global atmospheric composition model (Abraham et al., 2012;20 http://www.ukca.ac.uk) coupled to ACCESS (Australian Community Climate and Earth System Simulator) (Bi et al., 2013;Woodhouse et al., 2015). In our simulations, ACCESS is essentially the same as the U.K. Met Office Unified Model (UM) (vn8.4) since the ACCESS specific ocean and land-surface components are not invoked as the model is run in atmosphereonly mode with prescribed monthly-mean sea surface temperature (SST) and sea ice fields, and the UM's original landsurface scheme (viz. JULES) is used. The atmosphere component of the UM vn8.4 is the Global Atmosphere (GA 4.0) 25 (Walters et al., 2014). The UKCA configuration used here is the so-called StratTrop (or Chemistry of the Stratosphere and Troposphere (CheST)) (Archibald et al., 2020), which, in essence, combines the tropospheric chemistry scheme described by O'Connor et al. (2014) and the stratospheric chemistry as described by Morgenstern et al. (2009). The tropospheric chemistry scheme includes the Ox, HOx and NOx chemical cycles, and the oxidation of CO, methane, and other volatile organic carbon species (e.g. ethane, propane and isoprene). The Fast-JX photolysis scheme (Neu et al. 2007;Telford et al. 30 2013) is used, and ozone is coupled interactively between chemistry and radiation. The aerosol component includes sulphur chemistry. The total number of reactions, including aerosol chemistry, is 306 across 86 species.
The atmospheric model has a horizontal resolution of 1.875° in longitude and 1.25° in latitude, and 85 staggered terrainfollowing hybrid-height levels extending from the surface to 85 km (the so-called N96L85 configuration). The vertical resolution decreases with height, with the lowest 65 levels (up to ∼ 30 km) lying within the troposphere and lower stratosphere. The UKCA timestep is 60 min and the model physics timestep is 20 min. A global monthly-varying emissions database for reactive gases and aerosols is used, which includes both anthropogenic, biomass burning and natural 5 components, whereas for carbon dioxide, methane, nitrous oxide and ozone depleting substances, concentrations are prescribed instead of emissions .
The ACCESS-UKCA setup used here incorporates some additional modifications compared to the base UM-UKCA version 8.4, and these include: • Dry deposition of ozone to the ocean is now based on a process-based scheme developed by Luhar et al. (2018) (the 10 Ranking 1 configuration in their Table 1).
• Dry deposition of all relevant species is applied at the lowest model level, instead of it being distributed through the vertical extent of the atmospheric boundary layer (Luhar et al., 2017).
• The coefficient 8.53 is corrected to 4.8 in the following branching ratio expression used to compute the rate constant k2 (cm 3 molecule -1 s -1 ) for the chemical reaction HO2 + NO → HNO3: 15 where pressure P is in hPa and temperature, T is in K, and k is the rate constant (cm 3 molecule -1 s -1 ) for the chemical reaction HO2 + NO → NO2 + HO. The coefficient 8.53 is correct when P is expressed in Torr (Butkovskaya et al., 2007), but it should be 4.8 when P is in mbar 1 .
• In the parameterisation = × 10 exp(270/ ), the model uses = 3.3 for this reaction, but in the branching ratio Eq.
(2) it uses = 3.6, which we change to 3.3 for consistency. 20 The above changes lead to an increase in the tropospheric ozone burden (the first two changes together by ∼ 7% and the last two together by ∼ 5%).
Another change is that we have backported the LNOx subroutines from a more recent version of the model (at UM vn11.0) to vn8.4. This is to ensure that any refinements that may have occurred in the new version are used in our study. However, it is found that there are no major LNOx parameterisation differences between the two versions, with the new version continuing 25 to use the original PR92 flash-rate parameterisations. 1 This inconsistency stems from a typo in the document "IUPAC Task Group on Atmospheric Chemical Kinetic Data Evaluation -Data Sheet I.A3.45 NOx15" (http://iupac.pole-ether.fr/htdocs/datasheets/pdf/NOx15_HO2_NO.pdf) in which a constant of 8.53 instead of 4.8 is mistakenly specified in the branching ratio expression in the "Rate coefficient data" table.

Implementation of lightning flash-rate parameterisation in the model
In ACCESS-UKCA, convective cloud bottom level (Hb) and top level (H) are diagnosed from the UM convection scheme.
This scheme represents the sub-grid scale transport of heat, moisture and momentum associated with cumulus clouds within a grid box. The scheme uses a mass flux convection scheme based on Gregory and Rowntree (1990) with various extensions to include downdraughts and convective momentum transport (Walters et al., 2014). The scheme consists of three stages: (a) 5 diagnosis to determine whether convection is possible from the boundary layer, (b) a call to the shallow or deep convection scheme for all points diagnosed deep or shallow by the first step, and (c) a call to the mid-level convection scheme for all grid points. Examples of evaluation of the distribution of cloud depths simulated by the UM include those by Klein et al. (2013) and Hardiman et al. (2015).
A minimum convective cloud thickness ( − ) of 5 km is required for the lightning NOx to be activated (the use of 5 km 10 is based on the range of data used to develop the flash-rate formulas by PR92), and the model diagnosed H is used in the flash-rate parameterisations, which calculate the lightning flash rate (F, flashes per minute) as a function of and H (km) (see Section 3.2).
The PR92 flash-rate expressions (discusses later in Section 3.2) were developed based on observations of individual thunderstorms. Price and Rind (1994) developed a spatial calibration factor (c) to adjust these expressions for varying model 15 resolutions: where is the longitudinal resolution and is the latitudinal resolution of the model (in degrees).
The total flash rate (f) within a grid cell (flashes per minute per grid box) is then calculated as where A is the model grid box area (which is a function of latitude), is the area of model grid box centred at 30°N (Allen and Pickering, 2002), and the subscripts L and O to refer to land/continental and ocean/marine, respectively. 20 The total flash rate , is then divided into proportion of flashes that are cloud-to-ground (CG) and those that are intracloud (IC) using the method suggested by Price and Rind (1993) based on the thickness of the cold cloud region (0°C to cloud top) in thunderstorms which in turn is parameterised in terms of latitude. CG flashes are about 20-25% of the total (Barthe and Barth, 2008;Price and Rind, 1994), which we find is also the case with our model.

Production of NO per flash 25
Both the moles of NO produced per flash, , and the variation of this parameter between CG and IC flashes are poorly constrained by atmospheric observations. The overall rate, , regulates the amount of nitrogen oxides produced by https://doi.org/10.5194/acp-2020-885 Preprint. In bottom-up models, in addition to flash rate, is a key source of uncertainty, with a review by Schumann and Huntrieser (2007) suggesting a range of ∼ 33-660 and an average of 250 moles NO per flash. This large range, in part, reflects spatial variation in the frequency and uncertainty in the relative yield of CG and IC flashes, which may involve a varying level of dependencies on environmental variables such as peak current, rate of energy dissipation, channel length, air density, and strokes per flash (Murray et al., 2016). For example, some modelling studies consider that the less frequent CG flashes yield 10 a greater amount of NO per flash than IC flashes (Price et al., 1997;Luo et al., 2017), whereas in others both CG and IC flashes yield the same amount of NO on average (DeCaria et al., 2005;Ott et al., 2007). A few studies suggest that may not be constant over the globe, with higher production rates in extratropics than tropics (Murray et al., 2012) and globally variable production rates (Miyazaki et al., 2014). Details about and global LNOx reported in previous studies are given in Section 3.7.1. 15

Flash-rate parameterisations based on convective cloud-top height and LNOx
The approach of parameterising lightning flash frequency in terms of cloud-top height has its origins in the simple scaling relationships suggested by Vonnegut (1963) for the electrical power output of a thundercloud with the cloud size. Vonnegut's model assumes an electric dipole structure with two equal but opposite charge volumes, separated by a distance on the order of the vertical cloud dimension, and a cloud aspect ratio of approximately unity. The charge transport velocity 20 (charging current) that supports the dipole, flows in the vertical and is assumed to exist across the horizontal cross-section of the cloud. The electrical power generated is proportional to the fifth power of cloud dimension and the lightning flash rate is proportional to the electrical power generated. Williams (1985) extended this work using Vonnegut's (1963) model and available atmospheric observations over land to demonstrate from observations that (a) the convective velocity for clouds ranging in size from a few kilometres to 17 km is proportional to the size of the cloud and (b) cloud height and flash-rate 25 data from three US locations (New England, Florida and New Mexico) are in good agreement with the predicted slope of 5 from Vonnegut (1963). An important consequence of the last finding is that charge transport velocity must scale with cloud dimension, in the same way as convective velocity does. However, as Williams (1985) writes, this does not establish whether convective motion or falling precipitation is directly responsible for the charge separation.
https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License. Boccippio (2002) presents a systematic physical account of Vonnegut's (1963) model and the subsequent work on this issue by Williams (1985), PR92 and others. Boccippio (2002), using the laws of electricity, derived a fundamental scaling relationship between thunderstorm electrical generator power and storm geometry, which provides a possible theoretical basis for linking lightning to thunderstorm dynamics, microphysics, and geometry. Boccippio (2002) takes Vonnegut's 5 conceptualized thunderstorm of a quasi-steady state electrical dipole, with the horizontal and vertical scales of the two dipole charge centres comparable and varying with storm scale. The storm generator current is conceptualized as a net charge transport velocity, which maintains the dipoles. The electrical generator power (watts) is calculated as the generator current multiplied by the potential drop between the dipoles. The generator power is further expressed by assuming tangential spherical charge centres with volumetric charge density (±ρ) and radius R, maintained by a generator current density (= 10 charge density × charge transport velocity). Scale similarity between horizontal and vertical dimensions is invoked, and the dipole separation and size of the spherical charge centres are assumed to vary linearly with cloud-top height, a more readily observable parameter. The lightning flash rate is taken to vary linearly with lightning power dissipation, the latter is assumed to vary monotonically with generator power. A further significant and explicit simplification replaces charge transport velocity with storm updraft velocity w. With the assumptions above, the flash rate F scaling relation is 15

Boccippio's (2002) extension of Vonnegut's model and derivation of scaling relationships for land and ocean
where H is cloud-top height (m), w is updraft velocity (m s -1 ), ρ is charge density (coulomb m -3 ), ε is permittivity constant (coulomb 2 joule -1 m -1 ), and the coefficient γ has units of joule -1 . The variability in the charge density of the dominant dipole regions is taken to be small, and thus can be treated as a prescribed constant.
In all the following parameterisations, FL,O is in flashes per minute, H is in km, and w is in m s -1 .
It is apparent that in the above approach, flash rate is set by storm dimension, with a small direct contribution from generator 20 current density (which is taken to vary linearly with updraft velocity). In the case where ( ) for land and ocean are considered to be power law fits of H, i.e. , = , , , the above approach based on Eq. (5) leads to the following self-consistent scaling relationships, where the coefficient k1 (~ ) is (supposed to be) invariant, and , and , are other coefficients for land and ocean (Boccippio, 2002): These self-consistent scaling relationships are central to this study. 25 https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.
Using these scaling relationships, the data of Williams (1985), PR92 and LIS satellite data, Boccippio (2002) (note there is a negative sign missing in the first exponent of this equation in Boccippio (2002)), and = 4.09 × 10 . , where = 1.4314 × 10 was used in deriving the relationships (9) and (10), which are plotted in Figure 1.
There were no direct F vs. H data to fit a relationship similar to Eq. (11) for the marine environment. Therefore, PR92 made the assumption that the charge separation velocity and the convective updraft velocity are equal, noted that an increase in the intensity of convective updrafts enhances cloud electrification, and derived empirical relations based on observations 10 between maximum updraft velocity (w, m s -1 ) and H (km) for continental and marine clouds = 1.49 . , = 2.86 . .
Eliminating H from Eqs. (11) and (12) Now, PR92 made the crucial assumption that Eq. (14) is independent of location, so is valid for the marine environment too.
(Our calculation suggests that the coefficient 6.4 in the above equation should actually be 5.94.) The relationships (11) and 15 (15) are plotted in Figure 1, which show that the oceanic flash frequencies that are roughly 2 to 3 orders of magnitude smaller than those obtained for continental clouds.
The PR92 parameterisations (11) and (15) are widely used in global chemistry transport models and coupled chemistryclimate models.  Michalon et al. (1999) identified that the PR92 parameterisation, when used in global models, was producing lightning flash 10 frequencies that did not agree with observations. To address this, they proposed that cloud electrification is directly related to cloud droplet concentration (N) and droplet size, and derived = / , where A is a proportionality constant. They retained the continental PR92 expression (11)  values, and used it for the ocean by multiplying it with a factor of ( / ) / assuming that cloud droplet concentrations for continental (NL) and marine (NO) clouds are different:

Michalon et al.'s (1999) ocean parameterisation
where two "standard" continental and maritime cloud droplet concentrations of NL = 600 and NO = 50 per mg of air, respectively, were used. Eq. (16) is plotted in Figure 1. One factor for a smaller droplet concentration in marine clouds is suggested to be more intense droplet coalescence in such clouds (Rosenfeld and Lensky, 1998). 5 In the above approach, the values of NL and NO are not well constrained. There is a large variability in cloud droplet concentration over land and ocean, as reflected in values observed in field experiments as well as those prescribed in cloud microphysics schemes in global models (convective cloud droplet concentrations are not usually predicted in global climate models) (Rosenfeld and Lensky, 1998;Gultepe and Isaac, 2004). Boccippio (2002) cautions against this approach, and we suggest that given the uncertainty in the mean droplet concentrations, the approach of Michalon et al. (1999) is essentially 10 empirical.

This study: Alternative flash-rate parameterisations
The following includes (a) the reanalysis of the Williams (1985) and PR92 data for lightning flashes versus cloud top height over land into the self-consistent scaling relationships framework of Boccippio (2002) At this stage is undetermined. We proceed by fitting Eq. (17) directly to the F vs. H data for land reported by Williams (1985) and compiled by PR92 (which are reproduced in Figure 1 as blue solid circles). This gives = 1.612 × 10 and 20 The relationships PR92 Eq. (11), Boccippio (2002) Eq. (9) and this study (TS) Eq. (18) are presented in Figure 1 along with the F vs. H data just discussed. Although these behaviours look almost identical and are well within the scatter of the data, Eq. (18)  Concerning the oceanic parameterisation: there are limited data on flash rate versus cloud-top height for marine environments. Figure 1 presents Ushio et al.'s (2001) (Us01) data over the ocean in the tropics and extratropics (their Figure   3b and 3d), which they obtained by averaging flash rates every 1 km in cloud height. These are shown as triangles in Figure  5 1. Also shown are the Molinié and Pontikis' (1995) (MP95) flash-rate data over French Guyana coastal zone which we averaged over every 1 km in cloud height for heights greater than 10 km (below this height, the number of data points is not sufficient for averaging). Because these are coastal observations, it is possible that the air masses in which the thunderstorm clouds developed could be mixed air masses (i.e. both continental and marine). However, these data do show a qualitative agreement with the Ushio et al. (2001) data in Figure 1. 10 Applying the scaling relationships (Boccippio 2002) to obtain an equivalent relationship for marine clouds involves equating Eq. (6) with the observed oceanic convective updraft velocity versus cloud top height from PR92 given in Eq. (13). This yields = 2.86 and = 0.38. Substituting these into the scaling relationship Eq. (7) gives For this study, fitting Eq. (19) to the ocean data leads to = 2 × 10 (which gives = 0.7 × 10 ) and This marine parameterisation yields flash rates that are approximately an order of magnitude smaller than the PR92 15 continental formula and roughly two orders of magnitude larger than the PR92 marine parameterisation. In Figure 1 are shown the relationships for lightning flash rates and associated cloud-top height over the ocean for PR92, Boccippio's (2002) Eq. (10), Michalon et al. (1999) and this study (TS) Eq. (20). Clearly the PR92 ocean equation is unrealistic, and the relationship of Boccippio (2002) gives marine flash rates that are twice as large as Eq. (20) and are not supported by the data plotted. The relationships of Michalon et al (1999) and this study group together around the oceanic data. 20 The values of implicit in Eqs. (18) and (20) are different for land and ocean, although as per Boccippio's (2002) theory, they should be the same (as used in deriving Eqs. (9) and (10)). This difference may suggest possible differences in cloud microphysics between land and ocean, which Boccippio's (2002) generator power framework does not include. If we use the same logic as by Michalon et al. (1999) in deriving Eq. (16), then the different values of in Eqs. (18) and (20) for land and ocean can be interpreted in terms of the values of and being different. 25 https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.

Global model runs with various flash-rate parameterisations
In order to assess the above flash-rate parameterisations against global lightning flash observations, and to investigate how they influence tropospheric composition via their impact on LNOx generation, we conduct the following four runs of the ACCESS-UKCA global chemistry-climate model incorporating the five specified flash-rate parameterisations: • Run 1 (PR92): The default PR92 parameterisations: continental Eq. (11) and marine Eq. (15) ACCESS-UKCA was setup as a free running simulation for 2 years (2005)(2006), and the simulation was started using model initial conditions taken from a previously spun-up, nudged model run. The first year was used as a spin-up period and 10 the model output for the year 2006 used for analysis.

Comparison of the modelled lightning flash rates with satellite observations
We analyse the global gridded lightning flash data from the Optical Transient Detector (OTD) on the OrbView-1 (formerly MicroLab-1) satellite and the Lightning Imaging Sensor (LIS) on the Tropical Rainfall Measuring Mission (TRMM) satellite, which are described by Cecil et al. (2014) and available from https://lightning.nsstc.nasa.gov/data/data_lis-otd- frequency compared to the data. In contrast, the new flash-rate parameterisations (Run 2, Eqs. (18) and (20)) greatly improve the estimation of flash frequency over the ocean, with some overestimation (by ∼ 15%) of the climatology and giving nearly the same value as the year 2006 observational data. There is an improvement over land too compared to the PR92 formula.
Globally, the new parameterisations yield almost the same flash frequency as the data. Both the PR92 and the new parameterisations lead to an almost equal partitioning of flashes in the Northern and Southern hemispheres, compared to ∼ 5 55% in the Northern Hemisphere indicated by the data. As expected, the Run 3 flash rate is nearly the same as that for Run 1 for land, and that for Run 2 for the ocean. For Run 4, with the PR92 continental Eq. (11) and Michalon et al.'s (1999) marine Eq. (16), the flash rate over land is almost the same as Run 1, whereas for the ocean Run 4 gives a flash rate that is about 50% higher than the climatology and 23% higher than the data for 2006.

Modelled flashes per second
Modelled flashes per second The monthly variation of the observed and modelled flash rates is shown in Figure 3. The observed variation for the year 5 2006 is very similar to the climatological variation, mostly within the one standard deviation climatological variability shown. The model runs underpredict in spring in both hemispheres and overpredict in autumn in the Southern Hemisphere.
In the Northern Hemisphere (Figure 3a), the model simulates the observed variation qualitatively with a peak in July, but while Run 1 underestimates the observed flash rate for all months, the other Runs mostly underestimate during February -May and do well for the other months. In the Southern Hemisphere (Figure 3b), again the model is able to simulate the 10 observed variation well qualitatively, but a significant overprediction for January -April and an underprediction for August -October is apparent. In the global plot (Figure 3c), while Run 1 always underestimates, which is mostly because of its underprediction of the flash rate over the ocean (Figure 3e), the other Runs underestimate in the first three months of the year and overestimates during September -November, and these differences can be explained in terms of the hemispheric differences shown above. The nature of monthly variation in Figure 3d for land-based flash rates is very similar to Figure 3c, 15 indicating that continental flashes dominate the global total. The large underprediction by the PR92 scheme in Run 1 and an overprediction in Run 4 over the ocean can be seen in Figure 3e; there are also differences in the monthly variation.
https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.  Table 2 for the globe, land and ocean. Also given are the values of fractional bias FB = 2( − )/( + ), which varies between -2 (overestimation) and +2 (underestimation). These values confirm, as shown in Figure 2, that the Run 2 flash-rate parameterisations from this study yield the best comparison 10 with the data.    Allen and Pickering, 2002;Tost et al., 2007). Another potential factor could be greater vertical wind shear 15 outside the tropics which extends the horizontal lightning channel length (Huntrieser et al., 2008), which is not accounted for in the cloud-top height-based approaches.

Figure 4: Observed and modelled zonal mean flash densities (flashes km -2 yr -1 ) from the four model runs over the (a) globe, (b) land and (c) ocean. The observations are the LIS/OTD climatology and the LIS data for the year 2006.
Hereafter, we only present plots from Run 1 (default) and Run 2 (new), but the results from Runs 3 and 4 are included in all 5 comparison Tables except Table 5. latitudes. There is also some significant flash density over the ocean at these latitudes, particularly over the Pacific, western Atlantic, western Indian Ocean near southern Africa, and the seas around the maritime continent (i.e., largely Indonesia, the Philippines and Papua New Guinea). The distribution modelled using ACCESS-UKCA with the default PR92 flash-rate scheme (Run 1) shown in Figure 5c is very similar to other global modelling studies that use the same PR92 scheme, e.g. Allen and Pickering (2002)

parameterisations (Run 1), and (d) model simulation with the new flash-rate parameterisations from this study (Run 2).
The area-weighted NMSE, FB and correlation coefficient (r) comparing the spatial patterns of the observed climatology presented in Figure 5a with the annually-averaged modelled patterns of flash rate are given in Table 3 for the four model runs. The NMSE and FB values clearly show that Run 1 performs the worst, a result dominated by the oceanic component. 10 While the NMSE values are nearly the same for Runs 2-4, Run 2 has the best FB values. The spatial pattern correlation stays essentially the same for all Runs (presumably because the underlying independent model variable, the cloud-top height, is the same in all model runs), and it is lower for the ocean -suggesting that further understanding of convection and lightning processes and their parameterisations are needed. The global correlations in Table 3 are very similar to those reported by Gordillo-Vazquez et al. (2019) for cloud-height based schemes, but those for the ocean are lower in our study. 15 Based on the above flash-rate comparisons, Run 2 (TS1) performs the best, followed by Run 3 (TS2), Run 4 (Mi99) and Run 1 (PR92).
Modelled flash rates depend critically on modelled convection parameters (e.g. the cloud-top height) used by flash-rate parameterisations and on the representativeness of these parameterisations themselves. Thus, it is common in a global model to match the globally averaged modelled lightning flash rate to the observed value, e.g. that based on the LIS/OTD 20 total global LNOx amount, as per Eq. (1).) In the present study, no scaling factor was applied/necessary.

Global LNOx
The modelled global lightning-generated NOx using the various lightning flash-rate schemes are presented in Table 4. With the new flash-rate parameterisations (Run 2), the modelled global LNOx increases to 6.6 Tg N yr -1 from 4.8 Tg N yr -1 for 15 Run 1, an increase of 38%, most of which is due to the change in the oceanic flash-rate component. Of the total global LNOx, about 20% is generated over the ocean in Run 2, compared to ∼ 1% in Run 1. The partitioning into NH and SH is almost equal for both schemes. The Run 3 and Run 4 total LNOx emissions are similar to the Run 2 value. Given the same value of NO emitted per flash used for both IC and CG flashes, the partitioning of the global LNOx into NH, SH, and Land and Ocean for all Runs in Table 4 is very similar to the partitioning of flash rate for the corresponding Runs in Table 1. 20 . https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License. The amount of global LNOx produced, (Tg N yr -1 ), is a function of the global average flash rate, (flash s -1 ), and the moles of NO produced per flash, : 5 If the climatological average = 46.5 flash s -1 based on the LIS/OTD satellite data is used, then = 20.5 × 10 .
The values in Table 4 Boersma et al. (2005) analysed above-cloud tropospheric NO2 column retrievals from the GOME satellite observations for the year 1997 for cloudy scenes over tropical oceans and continents, and found that the above-cloud annual-mean NO2 20 https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License. column increases sharply with convective cloud-top height (H)-as . for continents and . for oceans, where H > 6.5 km. Considering that these above-cloud NO2 columns primarily consist of contributions from lightning-generated NOx, which is a direct function of flash rate, there is a very good agreement between these power-law exponents and those in the flash-rate relationships (11) and (18) for continents, and (20) for oceans. The analysis of Boersma et al. (2005) demonstrates that the exponent of 1.73 in the PR92 oceanic flash-rate relationship (15)

Vertical distribution
The vertical distribution of LNOX in the model at a grid point location is a parameter (see Section 2.1) that is essentially unconstrained by observations. Figure 7    https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.

Tropospheric NO2 verification
As lightning impacts atmospheric NOx directly, the changes in the modelled tropospheric NOx can be examined and compared with observations. We use data from the global reanalysis of atmospheric composition produced by the https://ads.atmosphere.copernicus.eu/cdsapp#!/dataset/cams-global-reanalysis-eac4-monthly) for comparison with the 5 monthly-averaged modelled NO2. The reanalysis was produced by assimilating space observations of aerosols and reactive gases using a 4D-Var method in an ECMWF global atmospheric model with 60 pressure levels (from 1000 to 1 hPa) and a horizontal resolution of 0.75° × 0.75°. For NO2, the model assimilated the tropospheric column retrievals from the SCIAMACHY, OMI, and GOME-2 satellite overpasses at ∼ 10:00 local time (LT), 13:30 LT and 09:30 LT, respectively (for the year 2006, only SCIAMACHY and OMI data were available for assimilation). Monthly-averaged total vertical column 10 NO2 reanalysis data (version -ECMWF Atmospheric Composition Reanalysis 4) are available and used here as follows.
The CAMS total NO2 columns ( ) are converted to tropospheric columns , by subtracting the total NO2 columns over the Pacific (180°W) ( , ) from the NO2 columns at all longitudes. This is a common approach used with the satellite data to separate the tropospheric and stratospheric amounts (Inness et al., 2019), and assumes a longitudinal homogeneity of the stratospheric NO2 column amounts (uncertainty < 1 × 10 15 molecules cm -2 ) and a constant and negligibly small tropospheric 15 NO2 column amounts over the reference 180°W longitude ( , , ) (uncertainty < 0.5 × 10 15 molecules cm -2 ) (Lauer et al., 2002). Thus where , ,  0. In Figure 8, we plot , , for the year 2006 obtained from the model Runs 1 and 2. While these modelled values are smaller or comparable to the limit of above uncertainty value, they are neither constant nor negligibly small compared to the , (as shown below) and would reflect contributions from sources such as lightning, aviation, 20 shipping, and possibly regional transport. It is also clear in Figure 8 that the column amounts are higher for Run 2 within the latitudes ± 30° mainly due to higher flash rates over the ocean.

5
As , , is not available from the satellite data as it is implicitly neglected, we take the average of the two curves in Northern Hemisphere dominated by surface NO2 emissions. In Figure 9b for the ocean, the agreement with the data is again very good, but it is apparent that the CAMS NO2 is better simulated by the model with the new oceanic flash rate within the tropics than with the PR92 oceanic flash-rate parameterisation, whereas the two model curves are almost the same for the other latitudes. For land (Figure 9c), the two model curves are nearly identical, with the model overestimating the CAMS NO2 column amounts in the southern tropical region. The results in Figure 9 demonstrate that the use of the new oceanic 15 flash-rate improves the tropospheric NO2, and they also imply that the value 330 moles NO per flash used is appropriate, except perhaps a slightly lower value over land in the southern tropic. Obviously, there are uncertainties associated with the CAMS reanalysis and the assimilated satellite columns, which are documented in the appropriate references cited above, as well as those associated with model inputs (e.g. emissions) and processes.

5
In Table 5 for latitudes between ± 30º, the performance measures show a good improvement in the simulation of the reanalysis NO2 columns with Run 2 (TS1) over the default scheme Run 1 (PR92) for the ocean, but for land there is a very slight deterioration in the performance.

Table 5: Normalised mean square error (NMSE), fractional bias (FB) and correlation (r) for the observed and modelled NO2
10 columns shown in Figure 9 for latitudes between ± 30º.

Impact on tropospheric composition
We present the impact of LNOx determined from the flash-rate parameterisations from Runs 1 and 2 on tropospheric composition. 15

Oxides of nitrogen (NOx)
The modelled tropospheric NO2 columns and their comparison with observations have already been presented in Section 3.7.3. Figure 10 presents the zonal distribution of NOx (as NO2) from the two model simulations and the difference between the two. In the lower troposphere, the two modelled distributions of the zonal annual-mean NOx (as NO2) are virtually Overall, the increase in the volume-weighted global tropospheric NOx is by 8.7 ppt (15.7%), and it is by 9.9 ppt (28.0%) over 5 the ocean and by 6.3 ppt (6.7%) over land.

Ozone (O3)
Tropospheric ozone is a by-product of the oxidation of carbon monoxide (CO), CH4 and other volatile organic compounds in the presence of NOx and is thus impacted by LNOx. 15 With the new flash-rate parameterisations (Run 2), the modelled tropospheric O3 burden increases from 284 to 308 Tg O3, a rise of 8.5% over the default PR92 scheme (Run 1). The new burden is closer to a the ACCMIP (Atmospheric Chemistry and Climate Model Intercomparison Project) multi-model mean of 337 ± 23 Tg O3 reported by Young et al. (2013), the latter value is consistent with measurement climatologies (this, however, does not necessarily mean that LNOx in these models is represented correctly). The Run 3 and Run 4 ozone burdens are 306 and 308 Tg, respectively. 20 The mean relative difference (%) between the global ozone mixing ratios predicted using the new lightning flash-rate parameterisations and the default PR92 parameterisations is shown in Figure 11. Near the surface (Figure 11a

10
In Figure 12, we compare the modelled monthly averaged ozone with ground-based in-situ observations from the World Data Centre for Reactive Gases (GAW-WDCRG, http://ebas.nilu.no; https://www.gaw-wdcrg.org;) for the year 2006 at five stations. The site selection was based on these sites being either oceanic or coastal along with data availability. The sites are Ushuaia (54.85ºS,68.31ºW),Cape Grim (40.68ºS,144.69ºE),Mauna Loa (19.54ºN,155.58ºW),Minamitorishima (24.29ºN,15 153.98ºE),and Mace Head (53.33ºN,9.90 ºW), which cover a range of latitudes. The hourly data were averaged to monthly values, and only those observational months were considered for which there were more than 75% valid hourly data points.
The model simulates the observed monthly variation well, at least qualitatively. While the new flash-rate parameterisations do not fully explain the differences between the modelled variation and the observed one, particularly at Mauna Loa and Mace Head, overall there is a slight improvement in the correlation coefficient (r) and normalised mean square error 20 (NMSE) with the new parameterisations over the PR92 scheme at all sites, which in turn suggests a slight improvement in the prediction of seasonal variation of ground-level ozone and its magnitude. The modelled zonal annual-mean tropospheric O3 from the two Runs and the difference between the two are presented in Figure 13. In the lower troposphere, the modelled ozone is smaller over the Southern Hemisphere than over the Northern Hemisphere ( Figure 13a and Figure 13b). The new flash-rate parameterisations result in O3 increases everywhere ( Figure  10 13c). Closer to the surface, the increase is approximately 2 ppb (by volume) in the Southern Hemisphere and 0.5-2 ppb in the Northern Hemisphere. The largest increases are nearly 8 ppb in the tropics at altitudes ∼ 9 km.

Ozone (ppb)
Ozone ( The modelled zonal ozone distribution can be compared with observations. We use the monthly mean vertical ozone profile 5 data for the year 2006, given as zonal means, from the publicly-available Bodeker Scientific database (http://www.bodekerscientific.com/data/monthly-mean-global-vertically-resolved-ozone) which combines measurements from several satellite-based instruments and ozone profile measurements from the global ozone-sonde network. The database spans the period 1979 to 2016 with 5º latitude resolution and 70 altitude levels (1 to 70 km). Different 'Tiers' of data are provided, and we used the highest Tier 1.4 (vn1.0) data. For comparison with the model predictions, these monthly profile 10 data were regridded to the model resolution. The modelled monthly tropospheric mask was zonal averaged and then applied to the monthly regridded data.
There is an agreement, both in magnitude and distribution, between the modelled zonal ozone in Figure 13a and b, and the data plotted in Figure 14a. The model reproduces the observed lower levels of tropospheric ozone in the Southern Hemisphere. The observed high levels just below the tropopause within 10-40ºN are somewhat better reproduced by the new 15 flash-rate parameterisations. Figure 14b and c represent the differences between the modelled and observed ozone for the PR92 scheme and the new parameterisations, respectively. Overall, the model underestimation in the Southern Hemisphere has reduced with the new parameterisations. In the Northern Hemisphere, the new scheme tends to overestimate ozone within 10-50 ºN below ∼ 9 km the Northern Hemisphere, but with a slight improvement for higher latitudes. Obviously, there are additional factors that influence tropospheric ozone distribution in the model, such as dynamics, including inter-20 hemispheric mixing and stratosphere-to-troposphere exchange, and how chemical mechanisms are represented. However, it is evident that the new flash-rate parameterisations lead the modelled ozone closer to the observations. Getting ozone in the upper troposphere correct is climatically important as surface temperature is more sensitive to changes in ozone in the upper troposphere and near the tropopause than those in the lower atmosphere (Forster and Shine, 1997) and, similarly, radiative forcing due to tropospheric ozone is more sensitive to ozone abundance in the upper troposphere (Worden et al., 2011). Overall, the increase in the volume-weighted global tropospheric O3 is by 4.1 ppb (8.0%), and it is by 4.4 ppb (9.1%) over the ocean and by 3.6 ppb (6.3%) over land.

Hydroxyl (OH) radical 10
The hydroxyl radical (OH) is the dominant oxidizing (and cleansing) agent in the global troposphere and controls the atmospheric abundance and chemical lifetime of most natural and anthropogenic gases, such as methane (CH4). The tropospheric abundance of OH is determined by a complex series of chemical reactions involving tropospheric ozone, methane, carbon monoxide (CO), non-methane volatile organic compounds (NMVOCs), and NOx, and also the amount of solar radiation and humidity (Naik et al., 2013). Through these reactions, the amount of LNOx produced also impacts OH. 15 The modelled zonal annual mean tropospheric OH in Figure 15 shows highest OH concentrations near the surface in the tropics, with values as high as (25 -30) × 10 5 molecules cm -3 at ∼ 20º N. The concentrations decrease with altitude, but there is a secondary maximum in the upper troposphere at around 13 km. There is an increase in the OH concentration using the new flash-rate parameterisations (Figure 15c), particularly in the upper troposphere in the tropics, by as much as 5 × 10 5 molecules cm -3 . 20
the Southern Hemisphere, and these for February are 8.8 ± 2.1 × 10 5 and 11.4 ± 2.8 × 10 5 , respectively. These can be compared with the corresponding modelled values 16.9, 7.3, 8.0 and 11.6 × 10 5 using the PR92 scheme, and 18.7, 8. 5, 9.2 and 13.5 × 10 5 using the new scheme. Clearly, the model value in the Northern Hemisphere in August is considerably larger than the observation even with the PR92 scheme. It is known that the UKCA StratTrop configuration yields substantially larger OH in the Northern Tropics at low altitudes compared to observations and to the ACCMIP multi-model estimates 5 (Archibald et al., 2020).
With an overall increase in OH using the new flash-rate parameterisations in ACCESS-UKCA, the global annual mean lifetime of CH4 against loss by tropospheric OH ( _ , defined as the division of the global total atmospheric CH4 burden and the globally integrated CH4 loss rate by reaction with tropospheric OH) decreases by 6.7%, from 7.5 to 7.0 years.

Carbon monoxide (CO) 10
There is a decrease in the modelled tropospheric carbon monoxide (CO) with the use of the new lightning parameterisations, as evident from the zonal annual-mean difference plot in Figure 17 (this CO reduction is coupled to the OH increase, via the reaction OH + CO → CO2 + H). In the lower troposphere, the decrease is by approximately 4-6 ppb (∼ 7%) in the Southern Hemisphere and 2-4 ppb (∼ 3%) in the Northern Hemisphere. This reduction gets a little larger in the mid to upper troposphere in the tropics. Overall, the reduction in the volume-weighted global CO is by 4.5 ppb (5.6%). Over the ocean is 15 by 4.7 ppb (6.2%) and that over land by 4.0 ppb (4.5%).

20
In Figure 18, we compare the modelled monthly-averaged CO with surface flask observations from the same GAW-WDCRG sites as in Figure 12 (data from Minamitorishima were missing for 4 months, so are not presented). The model is https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License. in qualitative agreement with the data, but generally the differences between the model runs are substantially smaller than the model-data differences. The NMSE and r values suggest a mixed result.

Conclusions
We have critically examined parameterisations of lightning flash rate that are based on the cloud-top height approach. 10 Testing of the widely used Price and Rind (1992) (PR92) parameterisations within the ACCESS-UKCA global chemistryclimate model for the year 2006 using the global LIS/OTD satellite data has revealed that while the parameterisation for land yields satisfactory predictions, with a globally averaged flash rate of 31.03 flashes s -1 compared to the observed 34.92 flashes s -1 , the oceanic parameterisation severely underestimates the observed flash rate, yielding on average 0.33 flashes s -1 compared to the observed 9.16 flashes s -1 . This leads to lightning-generated NOx (LNOx) being underestimated 15 proportionally over the ocean and thus influencing tropospheric composition.
Following Boccippio's (2002) scaling relationships between thunderstorm electrical generator power and storm geometry as the basis, we derived alternative flash-rate parameterisations. While the new parameterisation for land performed slightly better than the corresponding PR92 one, giving a globally averaged flash rate of 34.23 flashes s -1 compared to the observed https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License. 34.92 flashes s -1 , the new parameterisation for ocean performed more accurately, giving a globally averaged flash rate of 8.84 flashes s -1 compared to the observed 9.16 flashes s -1 . We also tested an oceanic parameterisation by Michalon et al. (1999), which gives a global oceanic average of 11.31 flashes s -1 . With the new parameterisations, there was an increase in global LNOx from 4.8 to 6.6 Tg N yr -1 , with the new estimate comparable to 6.3 ± 1.4 Tg N yr −1 obtained by Miyazaki et al. (2014) using an assimilation of multiple satellite datasets into a global CTM. The model's use of 330 moles NO produced 5 per flash is consistent with the average value 310 moles NO per flash determined by Miyazaki et al. (2014).
The use of the new flash-rate parameterisations in ACCESS-UKCA demonstrated a considerable impact on the modelled tropospheric composition compared to the defaults PR92 parameterisations, mainly due to the change in the oceanic flashrate component. In particular, the following impacts were observed: • An increase in the mid-to upper-tropospheric NOx by as much as 40 ppt (as NO2) in the northern tropics. An 10 overall increase in the global NOx by 8.7 ppt (15.7%) and by 9.9 ppt (28.0%) over the ocean. A better agreement of the modelled tropospheric NO2 columns with the CAMS reanalysis data.
• The tropospheric O3 burden increased by 8.5%, from 284 to 308 Tg O3, closer to a multi-model estimate of 337 ± 23 Tg O3 (Young et al., 2013), the latter supported by measurement climatology. Overall, the distribution of the modelled ozone in the troposphere improved compared to the global profile observations and ground stations data. 15 • A 13% increase in the annual-average volume-weighted global tropospheric OH, from 10.6 × 10 5 to 12.0 × 10 5 molecules cm -3 .
• A decrease in the global annual mean methane lifetime against loss by tropospheric OH by 6.7%.
• An overall reduction in the global CO by 4.5 ppb (5.6%).
The approach of parameterising lightning flash rate in terms of convective cloud-top height works well given its simplicity, 20 and continues to be useful in accounting for LNOx in global models, although there were some significant spatial distributional differences in the modelled flash-rate density compared to the satellite data. The approach is also very sensitive due to an almost 5 th power dependence on cloud-top height. With increased computational power in the future, it may be possible to understand and represent global LNOx in a better process-based manner through a cloud-resolving modelling framework with an explicit prediction of the electrical activity in storms. 25 Recent global chemistry-climate modelling studies using flash-rate parameterisations based on the convective cloud-top height show an increase in LNOx emissions in a future warming climate (e.g., Banerjee et al. 2014;Clark et al., 2017;Iglesias-Suarez et al., 2018), primarily as a result of increases in the depth of convection. This is also the case with a CAPE and precipitation rate based parameterisation (Romps et al., 2014). Conversely, it is found that a flash-rate scheme based on convective mass flux (Clark et al., 2017) and that based on upward cloud ice flux (Finney et al., 2018) predict a global 30 decrease in future lightning flash density (under the RCP8.5 scenario). Clearly, there is an existing uncertainty as to which physical parameterisation approach best represents the reality and the feedbacks that are important for lightning under https://doi.org/10.5194/acp-2020-885 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License. climate change, although parameters such as cloud ice content and/or updraught mass flux used in flux-based lightning schemes are perhaps currently not well constrained by available observations.

Data availability
The ACCESS-UKCA global model output data (in NetCDF format) used for analysis and plotting, and the processed model lighting and composition data (in ASCII format) used for comparison with observations can be made available by contacting 5 the corresponding author (Ashok Luhar: ashok.luhar@csiro.au). The observational data used in the present study are available online, as indicated in the text.