The Contribution of Sprite Streamers to the Chemical Composition of the Mesosphere‐Lower Thermosphere

Sprites are mesospheric filamentary discharges that liberate and accelerate large quantities of electrons. They produce local enhancements of some chemical species and fast (millisecond) optical emissions. In this work, we couple a self‐consistent 2‐D model of sprites with an extensive chemical scheme to calculate the injection of chemical species by one sprite streamer in the mesosphere 0.85 ms after its onset. The N, NO, and N2O injections per streamer are about 1021 atoms, 6 × 1019 molecules, and 1018 molecules, respectively. According to our results, longer simulations are necessary to determine the role of sprites in the concentration of N2O in the mesosphere. We also calculate the contribution of sprite glows to space‐based photometers of the Atmosphere‐Space Interactions Monitor and the Tool for the Analysis of RAdiations from lightNIngs and Sprites.

Since their discovery in 1989, several authors have investigated the chemical influence of sprites in the mesosphere using zero-and one-dimensional models (e.g., Evtushenko et al., 2013;Gordillo-Vázquez, 2008Parra-Rojas et al., 2015;Sentman et al., 2008;Winkler & Nothold, 2014). They reported a significant production of NO in the center of sprite streamers due to the oxidation of atomic nitrogen produced by electron-impact processes. Sentman et al. (2008) assumed a streamer nominal diameter of 25 m and a vertical length of 10 km to estimate a production of 5 × 10 19 molecules of NO per streamer between altitudes 65 and 75 km. In the stratosphere, NO x produced by lightning contributes to ozone depletion (Crutzen, 1979;Schumann & Huntrieser, 2007), while its concentration in the mesosphere is very low. Enell et al. (2008) estimated a production of 3 × 10 22 -3 × 10 23 molecules of NO per sprite. Arnone et al. (2014) used these estimated NO x production to calculate, using the Whole Atmosphere Community Climate Model version 4 (WACCM4), the global and regional sprite-induced variations in the concentration of NO x . They found that the perturbation in the tropical concentration of nitrogen oxide by sprite streamers could lie between 0.015 and 0.15 ppbv. These quantities correspond to a perturbation of the background concentration of NO x between less than 1% and up to 20%. Rodger et al. (2008), Arnone et al. (2008), Arnone et al. (2009), and Arnone and Dinelli (2016) reported NO x over thunderstorms through satellite observations. They concluded that sprite-NO x is at the edge of detectability with current instruments.
The third strongest greenhouse gas after CO 2 and CH 4 is N 2 O, having a global-warming potential (GWP) of almost 300 over 100 years and being an important ozone depleting species (Davidson, 2009). The most important source of N 2 O in the atmosphere is from surface emissions (Davidson, 2009). However, Sheese et al. (2016) reported the existence of an atmospheric source of N 2 O based on observations from the satellite instrument "Atmospheric Chemistry Experiment-Fourier Transform Spectrometer" (ACE-FTS). They proposed energetic particle precipitation in the lower thermosphere as the main N 2 O atmospheric source. Kelly et al. (2018) included the production of N 2 O via N 2 (A 3 Σ þ u ) + O 2 in the mesosphere-lower thermosphere (MLT) in WACCM. Their results supported the N 2 O measurements provided by ACE-FTS. However, their simulations produced less N 2 O than observed between 60 and 80 km over middle and low latitudes. Winkler and Nothold (2015) proposed Blue Jets, another type of TLE, as a possible source of N 2 O in the lower stratosphere. Based on results by Winkler and Nothold (2015), Pérez-Invernón et al. (2019) developed the first global parameterization for Blue Jets and implemented it in WACCM4. These authors reported that Blue Jets could contribute to about 38% of the N 2 O between 20 and 40 km. Previously, Gordillo-Vázquez (2008) and Parra-Rojas et al. (2015) had found an important production of N 2 O in sprites due to the chemical reaction N 2 + O − → e + N 2 O with the concentration of O − being previously increased, with respect to background values, due to the action of sprite streamers . According to Parra-Rojas et al. (2015), the production of NO and N 2 O could spread down to 50 km altitude (Parra-Rojas et al., 2015). In particular, the density enhancement of N 2 O molecules due to the streamer channel (scale of seconds) between 50 and 60 km altitudes could be up to 2 orders of magnitude above the background value. There are no global measurements nor estimations on the global chemical impact of sprites in the concentration of N 2 O in the mesosphere. However, modeling results by Gordillo-Vázquez (2008) and Parra-Rojas et al. (2015) suggest that sprites could contribute to the global concentration of N 2 O in the mesosphere, specially over middle and low latitudes where sprites are more frequent (Chen et al., 2008).
According to computational models of streamers, laboratory experiments, and optical measurements, sprites emit light predominantly in the first and second positive systems of the molecular neutral nitrogen (1PS N 2 and the 2PS N 2 , or simply FPS and SPS), the first negative system of the molecular nitrogen ion (N þ 2 -1NS or simply FNS), the Meinel band of the molecular nitrogen ion (Meinel N þ 2 ), and the Lyman-Birge-Hopfield (LBH) band of the molecular neutral nitrogen (e.g., Armstrong et al., 1998;Gordillo-Vázquez et al., 2018;Kanmae et al., 2007;Kuo et al., 2005b;Sato et al., 2015;Stenbaek-Nielsen et al., 2007). Some authors have proposed the use of the ratios FNS to SPS and FPS to SPS to estimate the peak electric field in air discharges (Adachi et al., 2006;Bonaventura et al., 2011;Celestin & Pasko, 2010;Hoder, 2016;Hoder et al., 2012;Kim et al., 2003;Kozlov et al., 2001;Kuo et al., 2005aKuo et al., , 2009Kuo et al., , 2013Liu et al., 2006;Morrill et al., 2002;Paris et al., 2004Paris et al., , 2005Pasko, 2010;Shcherbakov & Sigmond, 2007;Šimek, 2014). Recently, Ihaddadene and Celestin (2017) proposed the measurement of the ratio of the SPS to the LBH band as a possible method to estimate the sprite streamer altitude from space-based photometers, such as the Atmosphere-Space Interactions Monitor (ASIM) Neubert et al., 2019) and the Tool for the Analysis of RAdiations from lightNIngs and Sprites (TARANIS) (Lefeuvre et al., 2008). According for the spatial non-uniformity of streamers, Malagón-Romero et al. (2019) introduced two new methods to estimate the peak electric field in streamer heads.
Recently, Ono and Komuro (2019) validated the use of 2-D self-consistent streamer models to simulate the chemical influence of streamers in air. They compared the simulated enhancement of ozone produced by one streamer at atmospheric pressure with laser spectroscopy measurements. In this work we couple an extensive kinetic model of 131 species interacting through 952 chemical reactions with a 2-D self-consistent sprite streamer electrodynamical model. This 2-D approach allows us to self-consistently calculate the chemical influence of a single sprite streamer between the altitudes 68 and 75 km. The implemented vibrational and electronical kinetics of N 2 enable us to calculate the contribution of single sprite streamers to the photometers of ASIM and TARANIS. According to our results, optical emissions produced in the glow emerging in the streamer channel prevent the estimation of the sprite streamer head altitude from space-based photometers.

Streamer Model
To study the propagation of a sprite streamer and the latter evolution of the channel, we use a 2-D cylindrically symmetric model. We describe the time evolution of the electron density n e and ion densities n i with the drift-diffusion-reaction equations coupled to Poisson's equation as follows: where the i indexes the different types of ions, μ e is the electron mobility, D e is the electron diffusion coefficient, E is the electric field, and C e,i are the net production of electrons and ions due to chemical reactions. In the present model we consider ions motionless over the short time scales (of a few milliseconds) that we study and therefore we neglect their mobility and diffusion. We use the local field approximation, and, consequently, transport coefficients are derived from the electron energy distribution function (EEDF) that only depends on the local electric field. The symbol δ is the Kronecker delta, and S ph is the photoionization term that only applies to electrons and O þ 2 . As for Poisson's Equation 1c, ϕ is the electrostatic potential, the sum extends over all the charged species s, q s is the charge of the species s, with s running over ions as well as electrons, and ϵ 0 is the vacuum permittivity.
Finite volume methods coupled to hyperbolic methods are suitable to solve the set of Equations 1a and 1b. To solve these equations we have used CLAWPACK/PETCLAW (Alghamdi et al., 2011;Clawpack Development Team, 2017;LeVeque, 2002). PETCLAW is built upon PETSc (Balay et al., 2016b(Balay et al., , 2016a and allows us to split the simulation domain into different subdomains (problems) that can be solved in parallel. Poisson's equation is solved using the generalized minimal residual method and the geometric algebraic multigrid preconditioner, both from the PETSc numerical library.
We consider that the streamer is completely formed between altitudes 74.82 and 68 km, and we calculate its chemical influence and optical emissions in this range of altitudes. This approach allows us to ensure that the seed does not excessively influence our results.

Chemical Model
We use a modified version of the set of chemical reactions for halos and elves collected in the Appendix of Pérez-Invernón et al. (2016a), based on sprite and halo models developed by previous studies (Gordillo-Vázquez, 2008Parra-Rojas et al., 2013. In addition, the chemical reactions of the 2-D model of streamers developed by Malagón-Romero and Luqoue (2018) are added to the model. As sprite streamers take place in the upper mesosphere where the concentration of water is negligible, we do not include chemical reactions involving water in our simulation. Vibrational chemistry of CO 2 is not considered in this study.
We use the software QtPlaskin, developed by Luque (2011), to analyze the main chemical processes that contribute to the concentration of each chemical species as a function of time in our simulation.

Initial and Boundary Conditions
Sprites are high-altitude discharges made of many streamers that propagate through a varying air density. In our model, we have set as initial state of the atmosphere the chemical profiles of Figure 1 of ; that is, we set the air density profile and composition at nighttime conditions in November from the Whole Atmosphere Community Climate Model (WACCM) (Marsh et al., 2013) for a latitude of 38°and a longitude of 0°relaxed for 6.5 s under the presence of cosmic ray ionization (Thomas, 1974). The concentration of N is negligible, and the humidity is set to zero (dry air conditions). We also set a background electron density following the Wait-Spies profile (Hu et al., 2007) In order to start the streamer we set a gaussian seed with an e-folding radius of 40 m and a peak density of 5 × 10 10 m −3 . This initial electron density is neutralized by an identical density of positive ions. In order to solve Poisson's equation we impose Dirichlet boundary conditions at z=z min and free boundary conditions at r=r max = 600 m and z=z max according to the method described by Malagón-Romero and Luqoue (2018). These free boundary conditions are consistent with the density charge inside the domain and with a potential decaying far away from the source.
We have simulated a positive streamer propagating in a background electric field of 100 V/m, which correspond to 120 Td at 74.23 km. The simulated domain extends from 67 to 75 km in the vertical direction, and the grid resolution is 1 m. They proposed electron-ion dissociative recombination processes as the main mechanism producing an enhancement of N in the streamer channel. According to our results, the production of N by direct electron-impact dissociation of N 2 driven by the electric field in the streamer channel is 4 orders of magnitude above the production of N by electron-ion dissociative recombination processes. This apparent disagreement could be due to a lower importance of recombination processes at low density than at atmospheric conditions. In addition, the characteristic time of recombination processes is larger than the time simulated. The density of O 3 is reduced in the streamer channel due to the electron attachment process e + O 3 → O − + O 2 . For a more detailed discussion of the main chemical mechanisms involved in this simulation, we refer to Parra-Rojas et al. (2015) and .

Chemical Influence of Sprite Streamers in the MLT
In Figure 2 we show the vertically and horizontally integrated radial density enhancement of some chemical species produced by a simulated sprite streamer 0.85 ms after its onset. This figure shows for the first time the radial dependence of the production of NO and N 2 O by a sprite streamer. The production of chemical species in the simulated streamer decays radially around 2 orders of magnitude between the center of the streamer and 400 m. The production of N, NO, and electrons increases during the downward propagation of the streamer head. The maximum production of N 2 O takes place in the glow (above 72 km).

10.1029/2020GL088578
In Table 1 we show the most important productions of atoms and molecules in the mesosphere by a sprite streamer 0.85 ms after its onset in a cylindrical volume with a radius of 0.45 km and altitudes ranging from 67 up to 74.82 km. Computational limitations of this self-consistent electrodynamical model do not allow us to extend the simulation to longer times. We obtain streamer diameters of hundreds of meters, in agreement with previous observation (Cummer et al., 2006;Stenbaek-Nielsen et al., 2013) and modeling results (Luque & Ebert, 2009) of sprite streamers before bifurcation. We have obtained an injection of 5.9 × 10 19 NO molecules per sprite streamer, consistent with the production of 5 × 10 19 NO reported by Sentman et al. (2008) using a zero-dimensional model. The ratio of produced O atoms to NO molecules is about 5 in agreement with Sentman et al. (2008). According to our calculations, a sprite streamer could produce about 10 18 N 2 O molecules between 68 and 74.82 km.
Let us now estimate the chemical influence of a sprite composed by several streamers in the MLT using measured optical signatures of sprites. Armstrong et al. (1998) reported the maximum brightness of a complete sprite to be about 150 kR using a ground-based photometer covering 6°of field of view (FOV), centered at 399.4 nm, and sampling at 750 Hz. The wavelength of the SPS that contributes to this photometer is 399.7 nm (Gilmore, 1992). The maximum brightness is reached in the first millisecond. In addition, Figure 5 of Armstrong et al. (1998) shows that the FOV of the photometer covers a significant part of the sprite. Therefore, we can compare the maximum brightness reported by these authors with the maximum brightness of the complete sprite in the total simulated time 0.85 ms. We use the density of N 2 (C 3 Π u ,v) in our simulated single streamer, the atmospheric absorption calculated using the software MODTRANS 5 (Berk et al., 2005) between the sprite and the observer, and the system response of the photometer employed by Armstrong   (1998) to estimate the optical signature, obtaining a maximum brightness of 3 kR. Therefore, the simulated brightness of a streamer is about 50 times less than the reported optical emissions of a complete sprite.
On the other hand, the Global Lightning and Sprite Measurements on Japanese Experiment Module (JEM-GLIMS) reported absolute peak intensity of a complete sprite of about 3 × 10 −6 W/m 2 with a photometer sampling at 20 kHz in a range of wavelengths between 150 and 280 nm at 410 km altitude (Sato et al., 2016). We use the density of N 2 (a 1 Π g , v) in our simulated streamer to estimate the optical signature in the photometer of JEM-GLIMS, obtaining a peak intensity of 1.6 × 10 −7 W/m 2 . Therefore, we can assume that a complete sprite would produce between 18 and 50 times more optical emissions and production of chemical species than the simulated single streamer. We will use factor 18, which is calculated from space-based measurements that are not significantly influenced by the absorption of the atmosphere. We have compared the maximum brightness of simulated and reported sprites in the first millisecond after their onset to estimate the production of chemical species by a complete sprite in about 1 ms. During this time, the streamers travel about 7 km downward. According to this comparison, a complete sprite would produce about 2 × 10 19 molecules of N 2 O and 10 21 molecules of NO between about 68 and 75 km. Assuming a global sprite occurrence of 0.5 per minute (Chen et al., 2008), sprites could inject about 10 25 N 2 O and 10 27 NO molecules in the MLT annually. Since the average concentration of N 2 O in the MLT is about 1 ppbv (Kelly et al., 2018;Sheese et al., 2016), the total number of molecules of N 2 O contained between 68 and 75 km is about 3 × 10 30 . Therefore, the injection of N 2 O molecules by sprites would contribute to the latitude-height profiles of N 2 O measured by ACE-FTS (Kelly et al., 2018;Sheese et al., 2016) by less than 0.003% of the total population per year for a sprite simulation up to 0.85 ms. Hence, the chemical effect of sprite seems to be not enough to explain the disagreement between the concentration of N 2 O in the MLT over middle and low latitudes measured by ACE-FTS (Sheese et al., 2016) and concentrations simulated by using WACCM4 (Kelly et al., 2018).
Our results correspond, however, to a simulation of 0.85 ms. The present computational capabilities do not allow more extensive spatiotemporal simulations with 2-D models. This means that we are only reporting the complete chemical influence of a sprite streamer head between altitudes 68 and 74.82 km and the influence of the first millisecond evolution of the streamer channel and the glow. The production of N 2 O and NO in the glow is still active at the end of the simulation. However, the 0-D simulation by Parra-Rojas et al. (2015) shows that the chemical influence of one sprite between 68 and 74.82 km altitudes would not significantly change between 0.85 ms and 100 s after the onset of the sprite streamer (see Figures 8 and 15 of Parra-Rojas et al., 2015).

Optical Signature From Space-Based Photometers
Our chemical model incorporates all mechanisms that influence the population of excited species that emit observable radiation. Figure 3 shows an analysis of the contribution of a simulated sprite streamer optical signature to the photometers of ASIM and TARANIS. We plot in the first and second panels of Figure 3 the altitude and maximum electric field of the downward propagating streamer head, respectively. The third panel of Figure 3 shows the ratio of the contributions of the simulated sprite streamer optical emissions to the different photometers of ASIM and TARANIS. Comparison of the three uppermost panels of Figure 3 shows that the photometer ratios do not provide information about the altitude of the streamer head. This is due to the significant contribution of the glow discharge to the total optical emissions of the sprite streamer. In addition, the temporal evolution of the vibrational distribution function (VDF) of the most populated vibrational states of N 2 (a 1 Π g , v) (Kirillov, 2011) showed in the fourth panel of Figure 3 is not constant during the temporal evolution of the simulated sprite streamer. The transient behavior of the N 2 (a 1 Π g , v) VDF is influenced by the radiative decay of the electronically excited N 2 (w 1 Δ u , v) to N 2 (a 1 Π g , v = 0)-with a characteristic time of 0.6 ms (Gilmore, 1992)-within the streamer channel. This cascading process breaks the assumption of a constant VDF of the N 2 (a 1 Π g , v) levels, which is required to calculate the contribution of the LBH into the photometer band and to estimate the altitude of the streamer head (Pérez-Invernón et al., 2018).

Summary and Conclusions
We have calculated the chemical influence and optical emissions of a sprite streamer at altitudes between 68 and 74.82 km and during 0.85 ms using a self-consistent 2-D model coupled with a kinetic scheme of 131 species interacting through 952 chemical reactions. Our results suggest that the injection of N 2 O by sprites in the MLT over midlatitudes and low latitudes is not enough to account for the disagreement between satellite observations and simulations. Future improvements in computational capabilities will allow more extensive spatiotemporal simulations to confirm this conclusion. The obtained injection of NO, N, and O molecules is in agreement with previous results based on 0-D and 1-D models. We have also estimated the contribution of the optical emissions of a simulated sprite streamer to the photometers of ASIM and TARANIS, concluding that the altitude of the streamer head cannot be estimated from space-based optical measurements operating at nadir.
The main conclusions of this work are as follows: 10.1029/2020GL088578 1. Single non-bifurcated sprite streamers can inject 9.7 × 10 20 atoms of N, 5.9 × 10 19 molecules of NO, and 1.2 × 10 18 molecules of N 2 O between the altitudes 68 and 74.82 km during 0.85 ms after its onset. 2. We have calculated for the first time the radial dependence of the production of NO and N 2 O by a single sprite streamer. 3. We have estimated the contribution of the sprite streamer optical signature to the ratio between optical signals recorded by different photometric recordings of ASIM and TARANIS. 4. According to our model, the LBH band optical emissions from the glow and the transient N 2 (a 1 Π g , v) VDF influenced by the radiative decay of N 2 (w 1 Δ u , v) to N 2 (a 1 Π g , v = 0) prevent the estimation of the sprite streamer head altitude from space-based photometric recordings.

Data Availability Statement
Data presented here are available at the IAA repository (https://cloud.iaa.csic.es/public.php?service=fil-es&t=cb269d94561c81cdcdd5061f57cd86f0). The code developed for the simulation of sprite streamers is available at the repository (https://gitlab.com/amaro/streamer2d).