A parameterization of Long-Continuing-Current (LCC) lightning in the lightning submodel LNOX (version 3.0) of the Modular Earth Submodel System (MESSy, version 2.54)

Lightning flashes can produce a discharge in which a continuing electrical current flows for more than 40 ms. This type of :::: Such : flashes are proposed to be the main precursors of lightning-ignited wildfires and also to trigger sprite discharges in the mesosphere. However, lightning parameterizations implemented in global atmospheric models do not include information about the continuing electrical current of flashes. The continuing current of lightning flashes cannot be detected by conventional lightning location systems. Instead, these so-called Long-Continuing-Current (LCC) flashes are commonly 5 observed by Extreme Low Frequency (ELF) sensors and by optical instruments located in space. Previous reports :::::: Reports of LCC lightning flashes tend to occur in winter and oceanic thunderstorms, which suggests a connection between weak convection and the occurrence of this type of discharge. In this study, we develop a parameterization of LCC lightning flashes based on a climatology derived from optical lightning measurements reported by the Lightning Imaging Sensor (LIS) on-board the International Space Station (ISS) between March 1

1 Introduction 20 Lightning flashes are formed by electrical discharges with duration ranging between a few hundred of microseconds and hundreds of milliseconds (Rakov and Uman, 2003). Lightning flashes containing a discharge in which a continuing electrical current flows during more than 40 ms are usually referred to as Long-Continuing-Current lightning (LCC-lightning) (Brook et al., 1962). LCC-lightning has been associated with lightning-ignited fires (e.g., Fuquay et al., 1967;Latham and Williams, 2001;Pineda et al., 2014;Pérez-Invernón et al., 2021b), as the long duration of the discharge can favor ignition. This assumption 25 is supported by laboratory experiments (e.g., McEachron and Hagenguth, 1942;Feng et al., 2019;Zhang et al., 2021).
However, the process of separation of electrical charges :::::: electric :::::: charge :::::::: separation : that produces lightning is highly influenced by dynamic and thermodynamic processes (Showalter, 1953). Therefore, lightning and TLE activity are parameterized in global 55 atmospheric models using meteorological variables as proxies (e.g., Tost et al., 2007;Murray et al., 2012;Pérez-Invernón et al., 2019;Gordillo-Vázquez et al., 2019). In the same way, relating the occurrence of LCC-lightning activity to large scale meteorological parameters could be helpful to improve the parameterization of lightning-ignited fires in global climate models and to ::: (to) : implement the occurrence of sprites. In this study, we present a simple LCC-lightning parameterization which relates the ratio of LCC-lightning to typical :::: total lightning in thunderstorms with the updraft strength at a specific altitude. We We use the method proposed by Bitzer (2017) to produce global climatologies of LCC(>9 ms) and LCC(>18 ms) lightning flashes based on ISS-LIS lightning measurements between March 2017 and March 2020.
The fourth panel of Fig. 1 :: (d) : shows that the spatial distribution of the ratio of LCC(>18 ms)-lightning to all lightning flashes is nearly similar to the spatial distribution of the ratio of LCC(>9 ms)-lightning to all lightning flashes, as both ratios are higher over ocean than over land, and show maxima over the same continental areas. ::: This ::::::::: agreement :::::::: indicates :::: that

Meteorological data
Thunderstorm electrification processes are highly influenced by meteorological conditions producing the rising of moist air reaching the level of free convection below the 500 hPa level (Showalter, 1953). Several of the most used lightning parameterizations are based on meteorological variables at the 440 hPa pressure level that are related with convection. For example, the parameterizations by Allen and Pickering (2002) and Finney et al. (2014) use the updraft strength at 440 hPa pressure level and the cloud ice flux at 440 hPa to estimate the lightning activity, respectively. The 440 hPa pressure level is typically chosen 125 to parameterize lightning because temperature is about -25 • , favoring supersaturation and the co-existence of a mixture of ice particles and liquid droplets (Korolev and Mazin, 2003) that contributes to electrification (Khain et al., 2012). Other lightning parameterizations employ some meteorological variables that are also related with convection, such as the parameterization by Grewe et al. (2001), that uses the updraft velocity in clouds as a proxy for lightning activity, or the parameterizations by Price and Rind (1992) and Luhar et al. (2021) ::::::::::::::: Luhar et al. (2021), that use the Cloud Top Height (CTH).

Parameterization of LCC-lightning based on the updraft strength
In this section, we investigate the relationship between the ratios of LCC(>9 ms)-and LCC(>18 ms)-lightning to typical :::: total 170 lightning flashes and the updraft strength from ERA5 reanalysis.
First, we prepare :::::: process the ERA5 reanalysis data before combination with ISS-LIS lightning data. We extract the ::: The global 1-hourly averaged value ::::: values : of the vertical velocity at the 450 hPa level between March 2017 and March 2018.

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We restrict our analysis to groups of flashes that include LCC(>9 ms)-and/or LCC(>18 ms)-lightning flashes and where the sign of the vertical velocity indicates upward transport of air. We assume that the non-observation of LCC-lightning flashes during the fast passage of ISS-LIS over the thunderstorm does not provide enough information to assume that the observed thunderstorm cannot produce LCC-lightning at all. Therefore, we do not include thunderstorms exclusively producing typical :::: total lightning flashes during the passage of ISS-LIS. We consider that grid cells where the movement of air is dominated by 185 downward velocity are not representative of thunderstorms. Applying these criteria, we find 1.6342 × 10 4 and 2.981 × 10 3 groups of flashes including LCC(>9 ms)-lightning and LCC(>18 ms)-lightning, respectively. We plot in Fig. 2 the obtained ratios of LCC(>9 ms)-and LCC(>18 ms)-lightning to typical :::: total lightning flashes versus the updraught mass flux, estimated as the vertical velocity divided by the acceleration of gravity (9.8 m s −2 ). The high dispersion of values shown in Fig. 2 indicates that a possible relationship between the ratios of LCC(>9 ms)-and LCC(>18 ms)-lightning to typical lightning flashes :::: total 190 ::::::: lightning :::::: flashes :::: and :: the ::::::: updraft is not obvious.
Next, we analyze the data presented in Fig. 2. The average value of the updraught mass flux for the studied thunderstorms is 0.108 kg m −2 s −1 . Most of the studied thunderstorms have updraught mass fluxes below 0.2 kg m −2 s −1 . In particular, only 6.9% of the thunderstorms included in the left panel have updraught mass fluxes larger than 0.2 kg m −2 s −1 , while this quantity is reduced to 0.5% for updraught mass fluxes larger than 0.5 kg m −2 s −1 . In the right panel, only 5% and 1.5% of the 195 included thunderstorms have updraught mass fluxes larger than 0.2 and 0.3 kg m −2 s −1 , respectively. In an effort to develop a parameterization of the ratio of LCC-lightning to typical :::: total lightning that is not over-represented by points of Fig. 2 with updraught mass fluxes below 0.2 kg m −2 s −1 , and which is also applicable for projected simulations, we apply a discrete binning of the data using a 2.5×10 −3 kg m −2 s −1 window. Red lines of Fig. 3 show the corresponding binned data.

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In this section we describe the implementation of the LCC-lightning parameterizations described by equations (1) and (2) as a new subroutine called lcc in the LNOX submodel.

Example application
One year simulation was carried out for a demonstration of the developed LCC(>9 ms)-and LCC(>18 ms)-lightning parameterizations. The simulation setup is described in section 4.1. The obtained lightning flash frequency resulting from each 240 parameterization is presented in section 4.2. Finally, the LCC-lightning flash frequency is presented in section 4.3, including a comparison with observational data from ISS-LIS.

Simulation setup
In this example, we apply EMAC in the T42L90MA resolution, i.e. with a quadratic Gaussian grid of 2.8 • × 2.8 • :::::::: quadratic ::::::: Gaussian :::: grid : in latitude and longitude with 90 vertical levels reaching up to the 0.01 hPa pressure level and with 720 s time 245 step length (Jöckel et al., 2016). We employ the namelist setup for purely dynamical simulations (referred to the E5 setup, no chemistry) in the mode of free running simulation. We use the Tiedtke convection scheme (Tiedtke, 1989) implemented in the submodel CONVECT. The simulation period is the same as that used to develop the LCC-lightning parameterization, i.e., between 1 March, 2017 and 28 February, 2018. However, we start the simulation on January, 2017 using ERA-Interim reanalysis meteorological fields (ECMWF, 2011) as initial conditions and considering three months of spin-up time. The 250 lightning flash density, LCC-lightning flash frequencies and LCC-lightning flash densities are output every 5 hour. We do not modify the lightning-produced NO x in the code, as to the best of our knowledge there are no investigations reporting a difference in the production of NO x by LCC-lightning with respect to typical :::: total lightning.

Lightning flash frequency 265
As explained in section 3.3, the developed LCC-lightning parameterizations are based on the lightning parameterization included in the atmospheric model. Therefore, we analyze the lightning density obtained with each of the employed lightning parameterizations first.
We have used a lightning scaling factor for each lightning parameterization in order to fix the annual global lightning flash rate to 45 flashes per second (Christian et al., 2003;Cecil et al., 2014). The lightning scaling factors are shown in Table 1.

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The seasonal observed and simulated ratios of LCC(>9 ms)-lightning and LCC(>18 ms)-lightning to typical :::: total lightning are shown in Figure ::: Fig. 7 and 8, respectively. Lightning data has been gridded in 2.8 • × 2.8 • in latitude and longitude, while differences between the seasonal observed and simulated ratios of LCC(>9 ms)-lightning to typical ::: total : lightning are shown in Figures ::: Fig. 9-12. We include in Figures ::: Fig. 9-12 the globally averaged difference and the spatial correlation coefficients between observation and simulations (r). In general, all the investigated lightning parameterizations produce a fairly good 310 estimation of the ratio of LCC(>9 ms)-lightning to typical :::: total lightning in Central Africa, where the observed ratio reaches its minimum and non-negligible value. However, they tend to underestimate the ratio over the oceans ::: (see :::: Fig Due to the lack of observations, comparison between simulated and observed spatial distributions of the ratio of LCC(>18 ms)lightning to typical :::: total lightning is not so straightforward as in the case of LCC(>9 ms)-lightning. However, Figure ::: Fig. 8 indicates that simulated and observed spatial distribution of the ratio of LCC(>18 ms)-lightning to typical :::: total lightning are 320 nearly in agreement. The simulation tends to underestimate the ratio of f LCC(>18 ms)-lightning to typical ::: total : lightning over South America, the eastern coast of North America, Central Africa and Southeastern Asia.

Discussion
In this section, we analyze the seasonal and spatial distribution of the ratio of LCC(>9 ms)-and LCC(>18 ms)-lightning to typical ::: total : lightning by comparing with observation.
Indication of the observed ratio of LCC(>9 ms)/typical lightning by region and season. High, medium and low values 345 correspond to approximately values greater than 10 −1 , between 3×10 −2 and 10 −1 , and lower than 3×10 −2 , respectively. The symbol -represents no data. In this section we put the results into content by analyzing the seasonal and regional distribution of the ratio of LCC(>9 ms)-lightning 350 to typical lightning showed in Figure 7. We indicate in Table 3 the relative value of the observed ratio of LCC(>9 ms)/typical :::: total lightning by region and season. The ratio of LCC(>9 ms)-lightning to typical :::: total : lightning is high in regions downwind of the continents, which are known to be the preferred regions where cyclones evolve (Eckhardt et al., 2004). In the so-called warm conveyor belt of the cyclones, a broad band of air masses are rapidly ascending from lower levels to higher Table 3. Indication of the observed ratio of LCC(>9 ms)/typical total lightning by region and season. High, medium and low values correspond to values greater than 10 −1 , between 3×10 −2 and 10 −1 , and lower than 3×10 −2 , respectively. The symbol -represents no data. generally weaker than in pre-frontal convective systems :::::::::::::::::: (Eckhardt et al., 2004), supporting the development of LCC-lightning.
The LCC-lightning parameterization developed here reproduces well the observed ratio of LCC(>9 ms)/typical :::: total lightning in regions for intercontinental transport of trace gases with a high occurrence of warm conveyor belts.
During December, January and February a good agreement between the simulated and the observed ratio of LCC(>18 ms)-lightning to typical lightning is achieved in South America, Central and South Africa, Southeastern Asia, Australia, the Gulf of Mexico and the Tornado Alley. These are the regions with the highest lightning activity during DJF. However, the simulated ratio is higher than the observed in Western Europe. addition, ::: we :::: have ::::: found ::: the :::: same :::::::::: seasonality :: as :::::::: described :: in :::: Table :: 3. : Therefore, we conclude that there are not large differences in other years.