Quantiﬁcation of lightning-produced NO x over the Pyrenees and the Ebro Valley by using different TROPOMI-NO 2 and cloud research products

. Lightning is one of the major sources of nitrogen oxides (NO x ) in the atmosphere, contributing to the tropospheric concentration of ozone and to the oxidising capacity of the atmosphere. Lightning produces between 2-8 Tg N per year globally and on average about 250 ± 150 mol NO x per ﬂash. In this work, we estimate the moles of NO x produced per ﬂash (LNO x production efﬁciency) in the Pyrenees (Spain, France and Andorra) and in the Ebro Valley (Spain) by using nitrogen dioxide (NO 2 ) and cloud properties from the TROPOspheric Monitoring Instrument (TROPOMI) as well as lightning data 5 from the Earth Networks Global Lightning Network (ENGLN) and from the EUropean Co-operation for LIghtning Detection (EUCLID).


Introduction
Lightning is one of the major sources of nitrogen oxides (NO x = NO + NO 2 ) in the upper troposphere (e. g., Schumann and Huntrieser, 2007) and references therein].Lightning channels are formed by plasma reaching several thousands of Kelvin (Wallace, 1964).Such a high temperature produces dissociation of nitrogen and oxygen air molecules (Ripoll et al., 2014b, a;Kieu et al., 2021), contributing to the formation of NO x by the Zeldovich mechanism (Zeldovich et al., 1947).Lightninginduced nitrogen oxides (LNO x ) contribute about 10% to global NO x emissions and play an important role in determining the concentration of ozone and other chemical species in the upper troposphere as well as the oxidising capacity of the atmosphere (e. g., Labrador et al., 2005;Schumann and Huntrieser, 2007;Murray et al., 2012;Gordillo-Vázquez et al., 2019).Lightning produces between 2-8 Tg N per year globally (100-400 mol NO x per flash) and on average about 250 mol NO x per flash Schumann and Huntrieser (2007) .
Reducing the uncertainty of the NO x production by lightning and understanding the factors that influence this production is still a challenge.Aircraft measurements have significantly contributed to determining the production of NO x per flash, or LNO x Production Efficiency (PE) (e. g., Huntrieser et al., 2002Huntrieser et al., , 2016;;Allen et al., 2021b).However, aircraft campaigns cannot provide a continuous monitoring of LNO x and are difficult to carry out in some regions.Nadir-viewing satellite instruments such as the Ozone Monitoring Instrument (OMI), the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) and the TROPOspheric Monitoring Instrument (TROPOMI) measure spectra that are employed to estimate column densities of NO 2 over thunderstorms.Several authors have used OMI NO 2 measurements to estimate the LNO x PE in a case-based approach or systematically over different regions (Beirle et al., 2010;Marais et al., 2018), including midlatitude regions (Bucsela et al., 2019), tropical regions (Allen et al., 2019) and the U.S. (e. g., Pickering et al., 2016;Lapierre et al., 2020;Zhang et al., 2020;Allen et al., 2021a).Satellite-based measurements can help to estimate LNO x amounts over regions where aircraft campaigns are rare or to systematically investigate possible relationships between the characteristics of thunderstorms and LNO x over different geographical regions (Bucsela et al., 2019).However, the opacity of thunderclouds can strongly affect the retrieval of NO 2 (Beirle et al., 2009), while convection can transport NO x released at the surface to the upper troposphere, where it is mixed with freshly produced LNO x .Therefore, the use of atmospheric and radiative models in combination with NO 2 measurements is needed to estimate the NO x Production Efficiency (LNO x PE).
The TROPOMI instrument on board the European Space Agency Sentinel-5 Precursor (S5P) satellite was launched on 13 October 2017.TROPOMI operates from a low Earth polar orbit that provides daily global measurements of several trace gases (including NO 2 ) and cloud properties (Veefkind et al., 2012).The horizontal resolution at nadir is 3.6 km × 7.2 km before 6 August 2019, while it is 3.6 km × 5.6 km thereafter.This unprecedented spatial resolution represents a unique opportunity to investigate the LNO x PE from satellite measurements.Recently, Allen et al. (2021a) used, for the first time, TROPOMI measurements to estimate the LNO x PE for 29 cases in the USA lightning data from the Earth Network Global Lightning Network (ENGLN) and from the Geostationary Lightning Mapper (GLM) aboard the Geostationary Operational lightning activity in the area reaches its maximum over the mountains and is driven by solar heating (Esteban et al., 2006;Pineda et al., 2010).Therefore, we expect that during this time of the year a number of thunderstorms are active during the TROPOMI overpass (∼13:30 LT).We combine two TROPOMI research products with lightning data from the ENGLN (Zhu et al., 2017;Lapierre et al., 2020) and the EUropean Co-operation for LIghtning Detection (EUCLID) systems (Schulz et al., 2016).Apart from providing new valuable estimates of LNO x for Europe, this analysis will enable us to quantify the influence of using different lightning data sets and different TROPOMI NO 2 and cloud research products for the estimates of LNO x PE.
It is important to emphasize that the analyzed thunderstorms are not confined to the Pyrenees, but include lightning in adjacent regions where significant boundary layer pollution can be present.Therefore, a careful analysis of the background NO x is stil needed to estimate the LNO x for the analyzed cases.
2 Data sets and methods

TROPOMI NO 2 and cloud research products
We use TROPOMI NO 2 and cloud research products for eight deep convective systems in the Pyrenees and adjacent regions between April and May 2018.TROPOMI is a passive imaging spectrometer with eight spectral bands covering the ultraviolet (UV), visible (VIS), near infrared (NIR), and short-wavelength IR (SWIR) spectral regions (Veefkind et al., 2012).TROPOMI provides spectral data that is combined with different methods/algorithms to retrieve NO 2 column densities and cloud properties (e.g., Wang et al., 2008;Loyola et al., 2018;Marais et al., 2021;Liu et al., 2021a).In this work, we use two different sets of TROPOMI research products.The variables extracted from the TROPOMI products are the Slant Column Density (SCD) NO 2 , the error of the SCD NO 2 , the quality assurance (QA) value, the stratospheric Vertical Column Density (VCD) of NO 2 , the stratospheric Air Mass Factor (AMF), the Cloud Fraction (CF) and the Optical Centroid Pressure (OCP).
The first set of TROPOMI research products are here referred to as the Royal Netherlands Meteorological Institute (KNMI) version 2.1 research product (Allen et al., 2021a;van Geffen et al., 2022;Zhang et al., 2021) (TROP-KNMI) based on the official TROPOMI NO 2 Algorithm Theoretical Basis Document (ATBD) (van Geffen et al., 2021).This product is not au-tomatically produced for all the TROPOMI orbits.We produce it on a case-by-case basis as needed to analyze particular thunderstorms.The TROP-KNMI cloud research product is based on the Fast Retrieval Scheme for Clouds from the Oxygen A-band-S (FRESCO-S) algorithm with a Cloud as Reflecting Boundaries (CRB) model of clouds (Koelemeijer et al., 2001).
In the CRB model, clouds are described as a Lambertian reflecting boundary.The separation of the contribution of the troposphere and stratosphere to the NO 2 column density for the TROP-KNMI NO 2 research product is based on a priori chemical profiles from the chemistry transport model TM5-MP (Williams et al., 2017;Myriokefalitakis et al., 2020).We use the version 2.1_test of this product, a modified NO 2 product that increases the data coverage over bright pixels over deep convective clouds and includes a spike removal to better deal with saturation and blooming effects in the radiance spectra (Williams et al., 2017;Ludewig et al., 2020;Allen et al., 2021a).The reflectance value at 440 nm is reconstructed from the Differential Optical Absorption Spectroscopy (DOAS) method polynomial and the Ring correction as input to the routine that calculates the cloud (radiance) fraction in the NO 2 window.We refer to van Geffen et al. (2021b) and Allen et al. (2021a) for a detailed description of the TROP-KNMI NO 2 and cloud research products.Following Allen et al. (2021a), we use pixels with a quality assurance value above 0.28 (fair or better quality).This selection ensures that the SCD NO 2 error is less than 2 × 10 19 molec m −2 .
We refer to the second set of TROPOMI research products as the Deutsches Zentrum für Luft-und Raumfahrt (DLR) research product (TROP-DLR).The TROP-DLR cloud research product uses the OCRA/ROCINN algorithms for retrieving cloud properties (Loyola et al., 2018).The cloud properties provided by ROCINN uses the Clouds-As-Layers (CAL) model (Loyola et al., 2018).In the CAL model, clouds are treated as optically uniform layers using a more realistic cloud scattering model than the CRB model (Lindfors et al., 2018).::: This ::::::: product :: is :::::::: produced ::: on : a ::::::::::: case-by-case ::::: basis :: as ::::::: needed :: to ::::::: analyze Mainz (DSTREAM) to separate the contribution of the troposphere and stratosphere to the NO 2 column density (Liu et al., 2021b).This method does not require any input from atmospheric models.The DSTREAM method does not distinguish free tropospheric diffuse NO 2 from stratospheric NO 2 .This is different in the TROP-KNMI approach, where a free tropospheric column is derived from the TM5-MP profiles.In the case of TROP-KNMI, the stratospheric NO 2 retrieval does not include free tropospheric NO 2 , while it does include free tropospheric NO 2 in the case of the TROP-DLR product.So, we expect the tropospheric background to be substantially higher in the TROP-KNMI product than in the TROP-DLR product.The detailed description of the TROP-DLR NO 2 research product can be found in (Liu et al., 2021b).In this work, we use pixels with a SCD NO 2 error lower than 2 × 10 19 molec m −2 to be consistent with the QA threshold defined for the TROP-KNMI product.
Pixels with deep convection are defined as pixels in which the effective cloud fraction is greater than 0.95 (Allen et al., 2021a) and the OCP value is lower than a threshold.The threshold is defined as the averaged OCP for all lightning flashes included in this study.We calculate it using OCP values for all pixels containing lightning flashes during the 5 h period before the TROPOMI overpass according to the TROPOMI cloud products, providing that the OCP value is not undefined.The averaged OCP for the TROP-KNMI and the TROP-DLR products are 523 hPa and 534 hPa, respectively.These pressures are slightly higher than the 500 hPa threshold employed by Pickering et al. (2016) and Allen et al. (2021a) for deep convective systems over the USA. Figure 1 shows the distributions of OCP values for TROP-KNMI and TROP-DLR using ENGLN lightning data over all the studied cases.Both distributions peak around 400 hPa, while there are more lightning flashes taking place in pixels with OCP values between 650 hPa and 500 hPa in the case of the TROP-DLR product than the TROP-KNMI product (3923 versus 3489 pixels).We have calculated the T-test for the means of the OCP distributions plotted in Figure 1, obtaining a p-value lower than 0.05.This p-value indicates that differences in the mean OCP derived from the TROP-KNMI and the TROP-DLR products are statistically significant.

Lightning measurements
We apply lightning data provided by two lightning location systems, ENGLN and EUCLID, to calculate the amount of LNO x produced per flash (or LNO x PE).
The ENGLN is a global network composed of both broadband sensors from the Earth Networks Total Lightning Network (Liu et al., 2014) and Very Low Frequency (VLF) sensors from the World Wide Lightning Location Network (Hutchins et al., 2012) that provide the position, time of occurrence, polarity and peak current of lightning strokes.ENGLN has a Detection Efficiency (DE) of about 90% for Cloud-to-Ground (CG) strokes over the USA (Marchand et al., 2019).In this work, we use the flash product provided by ENGLN.This product is based on the flash criteria proposed by Liu and Heckman (2011), to cluster these strokes into flashes, in which two strokes are part of the same flash if they occur in a 0.7 s temporal window and in a 10 km spatial window.
We use lightning data from the Lightning Imaging Sensor (LIS) onboard the International Space Station (ISS) (Blakeslee et al., 2020) to estimate the DE of ENGLN over the Pyrenees.ISS-LIS detects optical emissions from lightning with a frame integration time of 1.79 ms with a spatial resolution of 4 km (Bitzer and Christian, 2015;Blakeslee et al., 2020).LIS sorts contiguous events into groups, and clusters groups into flashes with a temporal criteria of 330 ms and a spatial criteria of 5.5 km (Mach et al., 2007).ISS-LIS has a spatially uniform DE of about 60%.We compare ENGLN and ISS-LIS lightning data over the Pyrenees using the Bayesian approach proposed by Bitzer et al. (2016) with 330 ms and 25 km as the matching criteria.
The Bayesian approach is more accurate than direct comparison between lightning data, as neither of the detection systems can be characterized as the truth.We show in Figure 2

Meteorological and chemistry data
As we will describe in section 2.4, estimating the tropospheric background concentration of NO x (NO x that is not produced by lightning) is essential for the calculation of LNO x .Although the Pyrenees are an area with relatively low background-NO x concentration (Vinken et al., 2014), tropospheric background-NO x can be transported from the boundary layer to the upper troposphere by convection or advected from the Ebro Valley or the city of Barcelona.Therefore, we cannot neglect the background-NO x and have to subtract it from the VCD satellite measurements.To account for this, we use a combination of meteorological and chemical data as described below.
We use meteorological data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5reanalysis data set.In this work, we use the 1-hourly ERA5 horizontal wind averaged between 200 hPa and 500 hPa pressure levels with a horizontal resolution of 0.25 • .For each TROPOMI pixel containing lightning flashes prior to the TROPOMI overpass, we use the wind velocity and direction to estimate the advection of LNO x .All the pixels that satisfy the deep convection constraint and that are not influenced by the spreading of LNO x , are then considered as non-flashing pixels and employed to estimate the background-NO x . of the Atmosphere Based on an Instrument Container (CARIBIC) NO measurements (Brenninkmeijer et al., 2007).On 22 June, 2005, a CARIBIC flight passed over a convective system in the Pyrenees.Unfortunately, we do not have access to lightning data for that day, only cloud satellite products.However, the measured ratio NO/NO y can be used to estimate the age of the freshly produced NO x (Huntrieser et al., 2002).The measured ratio of NO to NO y (about 0.1) during the passage over the convective system suggests no impact of fresh LNO x .The measured mixing ratio of CO can be used as a proxy for upward 175 transport of NO from the boundary layer (Huntrieser et al., 2002).Measured simultaneous increases of CO and NO on 22 June, 2005 flight suggest upward transport of polluted boundary layer air, confirming that the airplane passed across a convective system.The measured mixing ratio of NO at 12 km altitude during the passage over the convective system was 0.3 ± 0.1 ppb, in agreement with previous airborne NO measurements over convective systems without lightning in Europe during the EULINOX campaign (Huntrieser et al., 2002).We assume a NO/NO 2 ratio in the upper troposphere of 2 mol mol −1 (Silvern et al., 2018).Therefore, we use 0.45 ppb as an alternative to the estimation of the background-NO x from non-flashing pixels.
We can estimate the VCD of NO x using CARIBIC measurement at 12 km.We assume that the shape of the vertical profile of NO x of the 22 June, 2005 convective system case is similar to the mean vertical profile of NO x reported by Huntrieser et al. (2002) in Europe (Fig. 7a in (Huntrieser et al., 2002)).Using the shape of the EULINOX profile and the CARIBIC measurement at 12 km, we can estimate the mixing ratio of NO x between the surface and 12 km level.Finally, we can integrate the vertical profile to obtain the VCD of NO x , resulting in 0.75 × 10 19 molec m −2 .
2.4 Calculation of the LNO x Air Mass Factor TROPOMI provides total SCD NO 2 .In the case of cloudy pixels, TROPOMI provides the SCD NO 2 over the cloud top and in the upper parts of the clouds.As we will see in section 2.5, our LNO x PE algorithm requires the VCD LNO x to be determined from the SCD NO 2 .The ratio to convert SCD NO 2 to VCD LNO x is called the AMF LN Ox and its calculation requires a priori estimations of the mean LNO 2 and LNO x profiles over the studied region (Pickering et al., 2016) and of the absorption of the atmosphere (Beirle et al., 2009;Bucsela et al., 2013).The AMF LN Ox is obtained by calculating the scattering weights for each of the eight studied cases using the viewing geometry and the cloud properties for each pixel.It is important to note that a conversion of NO 2 SCD into NO 2 VCDs using an overall AMF followed by a conversion of VCD NO 2 into VCD NO x using a mean NO 2 to NO x ratio is not appropriate, as explained by Beirle et al. (2009).
We employ the ECMWF -Hamburg (ECHAM)/Modular Earth Submodel System (MESSy version 2.54.0)Atmospheric Chemistry (EMAC) model (Jöckel et al., 2016) to extract the mean LNO 2 and LNO x profiles over the studied area by performing two simulations (with and without lightning).We perform the simulations following the Quasi Chemistry-Transport Model (QCTM) mode proposed by Deckert et al. (2011).Firstly, we perform a one year global simulation (January 1, 2018 to January 1, 2019) without lightning nudged towards ERA-Interim reanalysis meteorological fields.Secondly, we perform a second simulation with lightning for the same period using numerically identical meteorological fields as the simulation without lightning.The QCTM mode decouples the dynamics from the chemistry in order to operate the model as a chemistry-transport model, implying that small chemical perturbations do not alter the simulated meteorology by introducing noise (Deckert et al., 2011).The simulations are conducted in T42L90MA resolution, i.e. with a quadratic Gaussian grid of 2.8 • ×2.8 • in latitude and longitude with 90 vertical levels reaching up to the 0.01 hPa pressure level and with 720 s time steps (Jöckel et al., 2016).
LNO x is calculated by using the MESSy submodel LNOX (Tost et al., 2007).Lightning is parameterized according to the updraft velocity (Grewe et al., 2001) and using a scaling factor that ensures a global lightning occurrence rate of ∼45 flashes per second (Christian et al., 2003;Cecil et al., 2014).We set the production of NO x per flash following Price et al. (1997) and employ the C-shaped vertical profiles of LNO x reported by Pickering et al. (1998).We use the same chemical setup and chemical mechanism as described by Jöckel et al. (2016) for RC1 simulations.
We extract the vertical profiles of NO and NO 2 with and without lightning for May 2018 coincident with the TROPOMI overpass time to calculate the LNO 2 and LNO x vertical profiles.We obtain that the day in May 2018 with the highest LNO x column density is May 13, 2018.Figure 3 shows the vertical profiles obtained from the EMAC simulations.Both LNO x and LNO 2 vertical profiles peak between 300 hPa and 250 hPa pressure levels (between ∼9 and 11 km altitude), while the vertical profiles of LNO x and LNO 2 calculated by Pickering et al. (2016) over the Gulf of Mexico peak at about 150 hPa.The reason for this difference is that thunderstorms are taller at sub-tropical latitudes than at mid-latitudes.Non-negligible values of LNO x and LNO 2 values between 100 and 200 hPa (Figure 3) may have been transported to the Pyrenees from tropical latitudes.
We use the LNO 2 and LNO x vertical profiles from the simulations to calculate the AM F LN Ox following Bucsela et al. (2013).We use the TOMRAD forward vector radiative transfer model (Dave, 1965) to calculate the scattering weights for each of the 8 studied cases using the viewing geometry and the cloud properties for each pixel, which depend on the TROPOMI cloud product.We obtained AM F LN Ox values ranging between 0.28 and 0.71.

Calculation of the LNO x PE
We use the TROPOMI LNO x PE method proposed by Allen et al. (2021a).Figure4 shows an overview graphic indicating the variables that are included in the calculation of LNO x PE, while Appendix 5 indicates the list of acronyms.The source of these variables are TROPOMI products, lightning data, simulations and parameters that are introduced based on literature.The LNO x PE is calculated as where P E are the moles of NO x produced per flash, V tropLN Ox is the tropospheric column of NO x produced by recent lightning (molec cm −2 ) and that is calculated from the TROP-NO 2 , A is the area (cm −2 ) of the thunderstorm with deep convection or with undefined OCP, N A is the Avogadro's number (molec mol −1 ), DE is the detection efficiency of ENGLN or EUCLID and τ is the lifetime of NO x in the near field of convection, assumed as 3 hours (Nault et al., 2017;Allen et al., 2021a).The lifetime is uncertain and can vary between 2 hours and 2 days (e.g., Pickering et al., 1998;Beirle et al., 2010;Nault et al., 2017, and references therein), as it depends on the height where LNO x is emitted, the proximity to deep convection and how it is transported by convection in each particular thunderstorm.t i is the age of individual flashes at the time of the overpass (the time since the flash occurred) and F is the total number of flashes 5 hours prior to the TROPOMI overpass of each pixel.We use a 5 h flash window because it is larger than the assumed 3 hours lifetime of NO x in the near field of convection.
Sensitivity studies using other flash windows are performed in Section 3.3.V tropLN Ox is calculated as where V tropNOx is the vector containing the VCD NO x over pixels with deep convection or with undefined cloud fraction and V tropbck is the background-NO x .We use the median instead of the mean of V tropNOx in order to remove the influence of possible outlier pixels.V tropNOx is defined as where S NO2 is the vector containing the SCD of NO 2 , V stratNO2 is the vector containing the stratospheric VCD of NO 2 and AMF strat is the vector of stratospheric AMF.As previously explained by Allen et al. (2021a), values of V stratNO2 and AMF strat are sometimes missing over pixels affected by deep convection.Therefore, using the average V stratNO2 ×

245
AMF strat product increases the number of pixels available to estimate V tropN Ox .
Following Allen et al. (2021a), we calculate V tropbck as the 30 th and the 10 th percentile of V tropNOx over non-flashing pixels with deep convection.These percentiles are in agreement with airborne measurements during the EULINOX campaign ( Huntrieser et al., 2002).Alternatively, we calculate the background as the mean V tropNOx concentration averaged over three days with low lightning activity over the Pyrenees from TROPOMI data and using CARIBIC measurements in a convective system with low lightning activity over the Pyrenees (as described in section 2.3).Several events are outside the Pyrenees, with considerably higher background NO x .Thus, the local tropospheric background estimate over the clean Pyrenees can be considered as a lower limit.

Calculation of the background-NO x based on days with low lightning activity
Apart from calculating the background-NO x from non-flashing pixels in a case-based approach, we have selected three cases with low lightning activity before the TROPOMI overpass to estimate the mean background-NO x over convective systems.
In particular, we have used TROPOMI measurements on 8 April, 12 April and 13 April 2018 in the region between 41  3)) or the tropospheric background is exceeding the signal (eq.( 2)).The average background V tropN Ox for the TROP-KNMI and the TROP-DLR research products were, respectively, 1.06 × 10 19 molec m −2 , and 0.37 × 10 19 molec m −2 .These estimates are, respectively, slightly above and below the background VCD of NO x estimated using CARIBIC measurements (0.75 × 10 19 molec m −2 ).

Results
In this section we present LNO x estimates for eight selected cases.We describe the TROPOMI product for the selected cases in Section 3.1.The LNO x PE estimates are presented in Sections 3.2, while a sensitivity analysis of the results is discussed in Section 3.3.

Selected case studies
The eight selected cases correspond to eight thunderstorms that were active no more than 5 hours before the TROPOMI Figure 5 shows the ENGLN lightning data and some of the variables from the TROP-DLR product for the case 29 April 2018., suggesting that the LNO x signal is detectable by TROPOMI.There are also high SCD-NO 2 values near the city of Barcelona, a highly populated area producing high emissions of NO x .However, pixels near Barcelona do not satisfy the deep convective constraint.
The center left and right panels show the stratospheric VCD of NO 2 and the calculated AMF LN OX , respectively.The VCD stratN O2 from the TROP-DLR product is slightly larger than from the TROP-KNMI product, while both, the stratospheric VCD of NO 2 and the stratospheric AMF of NO 2 , are more homogeneous for the TROP-DLR product than for the TROP-KNMI product.The method to separate the contribution of the troposphere and stratosphere to the NO 2 column density are different for each product, which can affect the spatial distribution of the VCD stratN O2 and the AMF stratN O2 .The TROP-KNMI NO 2 product uses a priori chemical profiles from the chemistry transport model TM5-MP (Myriokefalitakis et al., 2020), while the TROP-DLR NO 2 product uses the DSTREAM method to separate the contribution of the troposphere and stratosphere to the NO 2 column density (Liu et al., 2021b), (see section 2).Inhomogeneities in the TROP-KNMI product are due to jumps in the tropopause level associated with thunderstorms (Pan et al., 2014).The TROP-KNMI product uses the temperature of the tropopause, which may jump up and down by a few levels linked to horizontal changes in temperature gradients.The STREAM model used in the TROP-DLR product will absorb free tropospheric NO 2 into the stratosphere, while the free tropospheric background may be larger in the TM5-MP model which is used to estimate the stratospheric column in the TROP-KNMI product (Boersma et al., 2018).As the obtained values of AMF are different for each product because they depend on the cloud information.
Finally, the lower panels show that there are not significant differences between the cloud products, except for some pixels in which the TROP-DLR product estimates larger cloud fractions.The existence of more pixels with high cloud fractions in the TROP-DLR product than in the TROP-KNMI product can influence the total number of pixels labeled as cloud convective pixels.The values of AMF LN Ox for each product differ because they depend on details of the cloud product.
We present in Figures 7 and 8 similar plots for the case 7 May.As in the case 29 April, lightning activity is distributed between the Ebro Valley, the Pyrenees and the French coast.Areas with high lightning activity coincide with areas with high SCD-NO 2 , while there are also also high SCD-NO 2 values near the city of Barcelona.We can see the same differences between the TROP-KNMI and the TROP-DLR products as in the case 29 April.

LNO x PE estimates
In this section, we present the LNO x PE estimates for the selected cases using two different methods to estimate the background-NO x .The first method (subsection 3.2.1) is exclusively based on case by case TROPOMI measurements, as it uses non-flashing In this section, we present the LNO x PE estimates for the selected cases by using the 30 th and the 10 th percentile of V tropN Ox over non-flashing pixels with deep convection as background-NO x estimations.Table 1 shows the results for eight cases in the Pyrenees using the described method and the TROP-KNMI research product, while Table 2 shows the results using the 335 TROP-DLR research product.Here we have used a 5 h time window before the TROPOMI overpass and a chemical lifetime of NO x (τ ) of 3 h for all the cases shown in these tables.We have chosen these values for the flash window and τ as reference values to show the LNO x estimates in Table 1.However, later in Section 3.3, we perform a sensitivity analysis using different values for flash window and τ .The case-based averaged age of individual flashes ranges between 0.9 hours for 7 May and 2.3 hours for 26 May.
340 measurements over convective systems with low lightning activity (1.06 × 10 19 molec m −2 for the TROP-KNMI product and 0.37 molec cm -2 for the TROP-DLR research product), as detailed in Section 2.6.
The LNO x PE for each case using ENGLN and EUCLID lightning data are shown in column 9 and 10 of Tables 1 and 2, respectively.We have used the standard deviation over all cases in order to estimate the error of the mean PE.We can see a factor of ∼2 difference between the LNO x PE using different backgrounds for most of the cases, indicating that the method to estimate the background introduces a significant uncertainty of the results.Using the TROP-KNMI research product, we obtain lower LNO x PE for ENGLN than for EUCLID (47 ± 33 mol NO x per flash vs 69 ± 34 mol NO x per flash).On the contrary, we obtain slightly higher LNO x PE for ENGLN than for EUCLID when using the TROP-DLR product (58 ± 33 mol NO x per flash vs 51 ± 25 mol NO x per flash).The mean LNO x PE values averaged over ENGLN and EUCLID for the TROP-KNMI and the TROP-DLR products are 58 and 54.5 mol NO x per flash, respectively.The LNO x PE value using the TROP-KNMI product is then higher than the value using the TROP-DLR product.We suggest that this slight difference is caused by the higher stratospheric VCD NO 2 value in the TROP-DLR product.
The standard deviations of the LNO x PE derived from the TROP-DLR and the TROP-KNMI products are rather similar, suggesting that the variability in the column densities of NO 2 provided by the TROP-DLR NO 2 product is similar to the variability provided by the TROP-KNMI product.
The average number of pixels with deep convection and satisfying the quality criterion using the TROP-KNMI product is 370, while it is 758 for the TROP-DLR product.This difference is a consequence of the cut-off employed for both the retrieved cloud fraction and OCP.The cloud fraction over the studied cases is about 30% larger for the TROP-DLR product than for the TROP-KNMI product, while the OCP is about 10% lower for the TROP-DLR product than for the TROP-KNMI product, leading to more pixels with deep convection in the case of TROP-DLR product than in the case of TROP-KNMI product.
We have found that using 650 hPa as OCP threshold for the TROP-KNMI product instead of 523 hPa produces a similar total number of pixels with deep convection and satisfying the quality criterium using the TROP-KNMI and the TROP-DLR products.This change in the OCP threshold for the TROP-KNMI product produces a change of only +14% in the LNO x PE estimates, as more pixels with low convection would be included in the estimation of the background-NO x .

LNO x PE estimates using fixed background-NO x values
Let us now estimate the average LNO x PE over all cases using the background-NO x based on days with low lightning activity as calculated in Section 2.6.Instead of using the V tropbck values of Tables 1 and 2, we use 1.06 × 10 19 molec m −2 , and 0.37 × 10 19 molec m −2 for estimations of the LNO x PE based on the TROP-KNMI and the TROP-DLR research products, respectively.We obtain 86 ± 63 mol NO x per flash by using the TROP-KNMI product with ENGLN lightning data, 160 ± 102 mol NO x per flash by using the TROP-KNMI product with EUCLID lightning data.These values are larger than the mean LNO x PE using non-flashing pixels (47 ± 33 and 69 ±34 mol NO x per flash).By using the background-NO x based on days with low lightning activity, we calculate 44 ± 61 mol NO x per flash by using the TROP-DLR product with ENGLN lightning data and 53 ± 59 mol NO x per flash using the TROP-DLR product with EUCLID lightning data.The LNO x PE estimates based on the TROP-DLR product for the two cases of 7 May and 12 May are negative when using the background-NO x The LNO x PE estimates by using different TROPOMI products (KNMI versus DLR) are not similar, as obtained in section 3.2.1.There is a 23% difference between the LNO x PE estimates using both TROPOMI products and ENGLN lightning data, and a 35% difference when using EUCLID lightning data.The difference is reduced when using only ENGLN lightning data, whose DE is higher than for EUCLID.The total uncertainty introduced by the choice of the TROPOMI product based on the means LNO x PE per flash between ENGLN and EUCLID lightning data is only 3%.We obtain a p-value of 0.44 by calculating the T-test for the means of the LNO x PE estimates when using TROP-KNMI and TROP-DLR, indicating that differences in LNO x PE using different TROPOMI products are not statistically significant.
As shown in Tables 1 and 2, the estimation of the background-NO x as the 30 th or as the 10 th percentile of V tropN Ox over non-flashing pixels with deep convection can significantly influence the LNO x PE estimates.The average LNO x PE between both TROPOMI products using the 30 th percentile of V tropN Ox is 42 mol NO x per flash, while it is 70 mol NO x per flash using the 10 th percentile of V tropN Ox .Therefore, the choice of the background-NO x method contributes to the uncertainty of 29%.The p-value obtained by calculating the T-test for the means of the LNO x PE estimates by using the 30 th or the 10 th percentile of V tropN Ox over non-flashing pixels with deep convection as background-NO x is lower than 0.05, which indicates that differences in LNO x PE using different methods to estimate the background-NO x products are statistically significant.
The DE of the used LLS can also contribute to the uncertainty of the LNO x PE estimates.As explained in section 2.2, we obtain a DE for ENGLN over the Pyrenees of 0.676 ± 0.12 (ranging between 0.556 and 0.769 ).The obtained mean LNO x PE using both TROPOMI products and a DE of 0.769 is 59 mol NO x per flash, while it is 43 mol NO x per flash when using a DE of 0.556.Therefore, the uncertainty of the DE of ENGLN contributes to a LNO x PE uncertainty of 17%.For EUCLID, we obtain a DE of 0.27 ± 0.12.The obtained mean LNO x PE using EUCLID data corrected by a DE of 0.40 is 86 mol NO x per flash, while it is 33 mol NO x per flash when using a DE of 0.15.Therefore, the uncertainty of the DE of EUCLID contributes to a LNO x PE uncertainty of 62%.The contribution of the DE of EUCLID to the uncertainty is higher than the contribution of the DE of ENGLN because the DE of EUCLID is significantly lower than the DE of ENGLN.
The lifetime of NO x in the near field of convection (τ ) is another parameter that can introduce uncertainty to the LNO x PE estimates.We have used 3 h, but it can vary between 2 and ::::: several :::: days :::::::::::::::::::::::::::::::::::::::::::::::: (Penner et al., 1998;Nault et al., 2017;Allen et al., 2021a) : . reported ::: that :: it ::: can :::: vary :::::::: between : 2 :: h ::: and : 12h (Nault et al., 2017;Allen et al., 2021a).We ::: h.The time window before the TROPOMI overpass, that is used to count the total number of lightning flashes contributing to freshly produced LNO x , can also be a source of uncertainty.We have calculated the LNO x PE estimates using a time window of 1 h instead of 5 h in order to get an estimation of the uncertainty introduced by the time window.We receive 88 mol NO x per flash as the mean value by using the TROP-KNMI and the TROP-DLR products and ENGLN lightning data.The LNO x Table 3. Sources of differences in the mean LNOx PE estimates.
Source of difference Influence on the LNOx PE estimate Lightning data set (ENGLN or EUCLID) 7% TROPOMI product (DLR or KNMI v2.1) 3% Background-NOx estimation (10% or 30% of non-flashing pixels) 29% Lightning detection system DE using ENGLN 17% Lightning detection system DE using EUCLID 62% Lifetime of NOx in the near field of convection (τ ) 18% Time window before the TROPOMI overpass 29% Other (lightning parameterization, scattering weights, deep convection definition) 30% Overall uncertainty using ENGLN 57% Overall uncertainty using EUCLID 83% PE estimations uses the same TROPOMI products and lightning data with a time window of 5 h was 52.5 mol NO x per flash.
According to our estimations, the time window contribution to the uncertainty of the LNO x PE is about 29%.We do not perform calculations using a larger time window, because studying the transport of LNO x at longer time scales is out of the scope of this work.
The sources of differences in the LNO x PE estimation evaluated in this study are summarized in Table 3.As discussed in previous studies (e.g., Pickering et al., 2016;Allen et al., 2019;Lapierre et al., 2020;Zhang et al., 2020;Allen et al., 2021a), there are other possible sources of uncertainty, such as the calculation of the AM F (LNO x profile type and lightning parameterization and NO x /NO 2 ratios in the simulations, scattering weights calculations) contributing to the uncertainty of about 30% or the method to select the OCP to be used for the definition of deep convection, contributing to the uncertainty of about 10%, or other systematic errors in the retrieval algorithms of TROPOMI.However, estimates of the influence of these parameters for the uncertainty of LNO x PE on the particular area of the Pyrenees is out of the scope of this paper, as we do not expect them to be dependent on the studied area.
We can estimate the overall LNO x PE uncertainty by summing the uncertainties in PE collected in Table 3.We obtain an overall LNO x PE uncertainty of 57% using ENGLN lightning data and 83% using EUCLID lightning data.

Discussion
Previous studies have used OMI NO 2 measurements to estimate the LNO x PE over different regions, as shown in Table 4.  from the TROP-KNMI product.The Pyrenees are a low contaminated area, which explains that the tropospheric VCD of NO x is lower than for the 29 cases studied by Allen et al. (2021a) over the USA.We have also found comparable influence of the background-NO x on the uncertainty of our results than Allen et al. (2021a), (29% vs 22.5%).The explanation of this difference could be that Allen et al. (2021a) analyzed 29 cases, while in this study we have analyzed only eight cases.
The obtained LNO x PE are significantly influenced by the TROPOMI (KNMI and DLR) and the lightning (ENGLN and EUCLID) data sets.The difference between the LNO x PE calculated by using the TROP-KNMI and the TROP-DLR products together with the ENGLN lightning data is 3%.There is a factor of 3.5 difference in the estimated median tropospheric VCD of NO x using the TROP-KNMI product (3.5 × 10 19 molec m −2 ) and the TROP-DLR product (0.96 × 10 19 molec m −2 ), while the differences in the provided mean stratospheric VCD of NO 2 over pixels with deep convection is 14% (7.3 and 8.3 × 10 19 molec m −2 for the TROP-KNMI and the TROP-DLR products, respectively).The background-NO x is estimated from nonflashing pixels, leading to a similar V tropLN Ox and LNO x PE values.However, using a fixed value for the background-NO x

Figure 1 .
Figure 1.Distributions of OCP for pixels containing ENGLN flashes 5 hours prior to the TROPOMI overpass for the TROP-KNMI (left panel) and the TROP-DLR (right panel) products for all the studied cases.

Figure 2 .
Figure 2. Spatial distribution of the ENGLN DE (in %) relative to ISS-LIS between March 2017 and December 2018 over Northern Spain, Southern France and Andorra.

Figure 3 .
Figure 3. Vertical mixing ratio profiles of NO (upper left panel), NO2 (upper right panel), NOx (lower left panel), LNOx and LNO2 (lower right panel) extracted from EMAC simulations with (solid lines) and without (dashed lines) lightning (background: bck) on 13 May, 2018 at 12 h LT (close to the TROPOMI overpass).

Figure 4 .
Figure 4. Overview graphic showing the variables that are included in the calculation of LNOx PE.

Figure 6
Figure 6 is similar to Figure 5 but instead showing EUCLID lightning data and some of the variables from the TROP-KNMI product.Lightning activity is distributed between the Ebro Valley, the Pyrenees and the French coast.The upper left panels of Figures5 and 6show the position of lightning flashes and the calculated VCD NO x in pixels with deep convection.A comparison of the upper left maps of Figures5 and 6shows that there are more lightning flashes reported by ENGLN than by EUCLID.The upper right panels show the SCD-NO 2 for each of the used TROPOMI products, indicating that there are not significant differences between them.Areas with high lightning activity coincide with areas with high SCD-NO 2 Figures 9 and 10 show plots for the case 28 May 2018.In this case, lightning activity is limited to the Ebro valley and the Pyrenees.There is a profuse LNO x signal in the SCD-NO 2 map.The stratospheric VCD of NO 2 and the stratospheric AMF of NO 2 provided by the TROP-KNMI product are more homogeneous than in the previous two cases.The rest of the cases analyzed in this study are plotted in the Supplement.

Figure 11
Figure11shows the velocity and direction of the horizontal wind averaged between the 200 hPa and 500 hPa pressure levels for the cases on 29 April, 7 May and 28 May, 2018.The average of the wind velocity is calculated with the values provided by ERA5 on the pressure levels 200 hPa, 250 hPa, 300 hPa, 350 hPa, 400 hPa, 450 hPa and 500 hPa.On 29 April, 2018 strong southerly winds could have transported LNO x to the north, which is in agreement with the relative position of flashes and pixels with high concentration of NO 2 as shown in Figures6 and 5. On 7 May, 2018 northeasterly winds could have transported LNO x to the southwest according to the location of the flashes, in agreement with Figures ?? :7, 8. Finally, the 7, 8. Finally, the wind velocity was weak on 28 May, 2018 and transport of lightning NO x from the the flash positions is unlikely, in agreement with Figures 9 and 10.We have calculated the Pearson correlation coefficient (r) between the SCD of NO 2 in convective cells with flashes and the total number of flashes reported by ENGLN in each cell averaged over all the studied cases.We have obtained r = 0.18 for TROP-DLR and r = 0.11 for TROP-KNMI.These values indicate a positive correlation between the SCD of NO 2 and flashes that is larger for the case of TROP-DLR than for TROP-KNMI.This correlation is larger when we use the tropospheric winds to identify the cells that have been influenced by LNO x .We have copied each flash to the cells that are influenced by the LNO x produced by the flash with the purpose of calculating the upwind correlation coefficient by taking into account the transport of LNO x .With that we obtain r = 0.20 for TROP-DLR and r = 0.15 for TROP-KNMI.The received larger correlation coefficients indicate that accounting for the transport of LNO x can improve the estimation of LNO x PE.

Figure 5 .
Figure 5. TROP-DLR product and ENGLN lightning data for the case 29 April 2018.The upper left panel shows the positions of lightning flashes (red dots) reported by ENGLN during the 5 h period before the TROPOMI overpass and the calculated VCD NOx.The upper right panel shows the SCD of NO2, center left and right panels show the stratospheric VCD of NO2 and the AMFLNOx, respectively.The lower left and right panels show the cloud fraction and the OCP, respectively.

Figure 6 .
Figure 6.TROP-KNMI product and EUCLID lightning data for the case 29 April 2018.The upper left panel shows the positions of lightning flashes (red dots) reported by EUCLID during the 5 h period before the TROPOMI overpass and the calculated VCD NOx.The upper right panel shows the SCD of NO2, center left and right panels show the stratospheric VCD of NO2 and the AMFLNOx, respectively.The lower left and right panels show the cloud fraction and the OCP, respectively.

Figure 7 .
Figure 7. TROP-DLR product and ENGLN lightning data for the case 7 May 2018.The upper left panel shows the positions of lightning flashes (red dots) reported by ENGLN during the 5 h period before the TROPOMI overpass and the calculated VCD NOx.The upper right panel shows the SCD of NO2, center left and right panels show the stratospheric VCD of NO2 and the AMFLNOx, respectively.The lower left and right panels show the cloud fraction and the OCP, respectively.

Figure 8 .
Figure 8. TROP-KNMI product and EUCLID lightning data for the case 7 May 2018.The upper left panel shows the positions of lightning flashes (red dots) reported by EUCLID during the 5 h period before the TROPOMI overpass and the calculated VCD NOx.The upper right panel shows the SCD of NO2, center left and right panels show the stratospheric VCD of NO2 and the AMFLNOx, respectively.The lower left and right panels show the cloud fraction and the OCP, respectively.

Figure 9 .
Figure 9. TROP-DLR product and ENGLN lightning data for the case 28 May 2018.The upper left panel shows the positions of lightning flashes (red dots) reported by ENGLN during the 5 h period before the TROPOMI overpass and the calculated VCD NOx.The upper right panel shows the SCD of NO2, center left and right panels show the stratospheric VCD of NO2 and the AMFLNOx, respectively.The lower left and right panels show the cloud fraction and the OCP, respectively.

Figure 10 .Figure 11 .
Figure 10.TROP-KNMI product and EUCLID lightning data for the case 28 May 2018.The upper left panel shows the positions of lightning flashes (red dots) reported by EUCLID during the 5 h period before the TROPOMI overpass and the calculated VCD NOx.The upper right panel shows the SCD of NO2, center left and right panels show the stratospheric VCD of NO2 and the AMFLNOx, respectively.The lower left and right panels show the cloud fraction and the OCP, respectively.
(Poelman and Schulz, 2020)f the obtained ENGLN DE over the Pyrenees.Schulz et al., 2016).Despite the high DE of EUCLID over Europe, the mean DE of EUCLID over the Pyrenees and the Ebro Valley is only about 30-60%(Poelman and Schulz, 2020)because of the low number of stations over that area and in Africa.We have selected two thunderstorms taking place between April and May 2018 over the Pyrenees and the Ebro Valley that were simultaneously detected by EUCLID and ISS-LIS.We have compared the total number of flashes reported by EUCLID and ISS-LIS in both thunderstorms, calculating a DE of 0.40 in the Pyrenees and a DE of 0.15 in the Ebro Valley.We use 27% ± 12% as the DE correction for EUCLID.The significant difference between the DE of EUCLID and ENGLN over the Pyrenees represents a good opportunity to investigate the influence of Lightning Location Systems (LSS) DE on the LNO x PE.
overpass on the following days: 29 April, 7 May, 12 May, 21 May, 22 May, 26 May, 28 May and 30 May 2018.Unfortunately, the TROP-DLR research product was not available for the case on 30 May 2018 because the raw data files are missing.In addition, the thunderstorm taking place on 26 May 2018 had a significant lightning activity between 45 • N and 46 • N, but we do not have access to EUCLID data north of 45 • N.

Table 1 .
Results for the 8 studied cases in 2018 using the TROP-KNMI research product.

Table 2 .
Results for the 7 studied cases in 2018 using the TROP-DLR research product.
pixels with deep convection to estimate the background-NO x .The second method (subsection 3.2.2) uses fixed values for the 330 background-NO x from measurements over days with low lightning activity.3.2.1 LNOx PE estimates using non-flashing pixels to estimate the background-NO x Bucsela et al. (2019)6)reported a LNO x PE of 80 ± 45 mol per flash over the Gulf of Mexico.Bucsela et al. (2019)systematically estimated the LNO x PE over mid-latitudes, obtaining an average LNO x PE of 180 ± 100 mol per flash.Interestingly, Bucsela et al. (2019) (see Table 1) found a lower LNO x PE in Europe (150 ± 90 mol per flash).Allen et al. (2019) reported a mean LNO x PE over the tropics of 170 ± 100 mol per flash.Lapierre et al. (2020) reported a LNO x PE over the USA of ∼24 mol per flash (estimated from mol per stroke calculations), while Zhang et al. (2021) reported 90 ± 50 mol per flash over the Allen et al. (2021a)t al. (2021a)have estimated the LNO x PE in 29 thunderstorms over the USA by using new TROPOMI NO 2 data, finding a LNO x PE of 120 ± 50 mol per flash based on the use of ENGLN lightning data.We have calculated the

Table 4 .
Allen et al. (2021a))6)imates.CNLDN stands for the China National Lightning Detection Network.for the means of the LNO x PE estimates when using ENGLN lightning data together with the TROP-KNMI product and the LNO x PE estimates provided byAllen et al. (2021a)when using ENGLN lightning data, obtaining a p-value lower than 0.05.Therefore, we conclude that differences in LNO x PE between the Pyrenees and the U.S. are statistically significant.We have used the LNO x PE algorithm employed byPickering et al. (2016);Bucsela et al. (2019);Allen et al. (2019)andAllen et al. (2021a)to provide new LNO x PE estimates based on TROPOMI NO 2 measurements over the Pyrenees.We obtain 47 ± 33 (69 ± 34) mol NO x per flash using the TROP-KNMI research product and ENGLN (EUCLID) lightning data and 58 ± 33 (51 ± 25 mol NO x ) mol NO x per flash using TROP-DLR product and ENGLN (EUCLID) lightning data.Our mean LNO Allen et al. (2021a)))ghtly lower than the LNO x PE reported byPickering et al. (e.g., 2016);Allen et al. (e.g., 2019);Zhang   et al. (e.g., 2020);Allen et al. (e.g., 2021a) and a factor of ∼2 higher as determined byLapierre et al. (2020).The employed method uses only TROPOMI measurements over cloudy pixels to estimate fresh-produced LNO x .As a consequence, part of the LNO x produced before the TROPOMI overpass can be overlooked.Consequently, the obtained LNO x PE can be biased low.When comparing our results with TROPOMI-based estimates byAllen et al. (2021a)over the USA using ENGLN lightning data (120 ± 50 mol), we obtain lower LNO x PE estimates, which is in agreement withBucsela et al. (2019), who reported a lower LNO x PE over Europe than over the USA.We estimate a mean tropospheric VCD of NO x of 3.5 × 10 19 molec m −2 from the TROP-KNMI product.Allen et al. (2021a)reported a slightly higher mean VCD of NO x of 4.4 × 10 19 molec m −2