Although lightning-generated oxides of nitrogen
(LNOx) account for only approximately 10 % of the global NOx
source, they have 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, where the oceanic parameterisation is
known to greatly underestimate flash rates. We conduct a critical assessment
of flash-rate parameterisations that are based on cloud-top height and
validate them within the Australian Community Climate and Earth System
Simulator – United Kingdom Chemistry and Aerosol (ACCESS-UKCA) global chemistry–climate model using
the Lightning Imaging Sensor and Optical Transient Detector
(LIS/OTD) satellite data. While the PR92 parameterisation for land yields
satisfactory predictions, the oceanic parameterisation, as expected,
underestimates the observed flash-rate density severely, yielding a global
average over the ocean of 0.33 flashes s-1 compared to the observed
9.16 flashes s-1 and leading to LNOx being underestimated
proportionally. We formulate new flash-rate parameterisations
following Boccippio's (2002) scaling relationships between thunderstorm
electrical generator power and storm geometry coupled with available data.
The new parameterisation for land performs very similarly to the corresponding
PR92 one, as would be expected, whereas the new oceanic parameterisation
simulates the flash-rate observations much more accurately, giving a global
average over the ocean of 8.84 flashes s-1. The use of the improved
flash-rate parameterisations in ACCESS-UKCA 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 mid- to upper-tropospheric NOx by as much as 40 pptv,
a 13 % increase in the global hydroxyl radical (OH), a decrease in the
methane lifetime by 6.7 %, and a decrease in the lower-tropospheric carbon
monoxide (CO) by 3 %–7 %. Compared to observations, the modelled
tropospheric NOx and ozone in the Southern Hemisphere and over the
ocean are improved by this new flash-rate parameterisation.
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 radical (OH),
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. OH plays a critical role in the
chemical cycles of many trace gases, including methane (CH4) and carbon
monoxide (CO), 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 (Schumann and Huntrieser, 2007; Banerjee et al., 2014). Lightning
predominantly occurs over land in the tropics associated 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 into free
N and O within the flash channel. These in turn react with ambient N2
and O2 to produce NO, which remains after the lightning channel cools.
There is a conversion between NO and NO2, during which ozone is
generated in the presence of HO2 and organic peroxy radicals,
collectively called RO2 (Bucsela et al., 2019). 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 (Schumann
and Huntrieser, 2007).
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, although LNOx emissions are
of similar magnitude to those from biomass burning or soils, their
contribution to the total tropospheric ozone column is about 3 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 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 (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 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 have 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., 2014, 2018;
Iglesias-Suarez et al., 2018). In addition, lightning intensity and
distribution, and its uncertainty, in a future climate have implications for
projections of lightning-induced fire activity (Krause et al., 2014).
A realistic representation of LNOx source strength and its global
distribution is thus of vital importance for understanding tropospheric
chemistry and its impacts. 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.
The most common conceptual model used to compute the amount of LNOx in
global models is
LNOx=F×PNO,
where F is the lightning flash rate and PNO 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 intracloud (IC) and cloud-to-ground
(CG) flash-rate components, applying an amount of NO mass produced per
flash, and then vertically distributing the calculated NO mass in the
column.
Various approaches to estimate lightning flash rate in global models have
been followed in the past. 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. The model of PR92
was based on the assumption of 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). Flash-rate parameterisations based on convection
parameters other than cloud-top height have also been 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; Yoshida et al., 2009), 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) and coupled chemistry–climate
models, such as the Goddard Earth Observing System with chemistry (GEOS-Chem)
(Hudman et al., 2007), Model for OZone And Related chemical Tracers (MOZART) (Emmons et al.,
2020), Community Atmosphere Model with chemistry (CAM-Chem) (Lamarque et al., 2012),
European Centre Hamburg Modular Earth Submodel System (ECHAM5/MESSy) (Jöckel et al.,
2006), and the UK Met Office Unified Model coupled with the United Kingdom
Chemistry and Aerosol global atmospheric
composition model (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 example, Clark et al. (2017) tested
flash-rate parameterisations based on cloud-top height, cold-cloud depth
(CCD), 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, closely followed by the CCD-based parameterisation of Yoshida
et al. (2009). The PR92 scheme had a higher value of the spatial standard
deviation compared to observations due to a large land–ocean contrast in
this parameterisation. The quantity CCD is defined as the convective
cloud-top height minus the freezing level. The thunderstorm data analysis
presented by Price and Rind (1993) indicates that freezing levels remain
relatively constant compared to CCD values, meaning that it is largely the
cloud-top height that provides the variation in the lightning flash rate in
the CCD-based scheme, which suggests that the cloud-top height and the
CCD-based schemes would perform very similarly. Finney et al. (2014) found that
the PR92 lightning flash parameterisations had considerable biases compared
to satellite observations of spatial flash density but performed second
best (behind their parameterisation based on ice flux) out of the five
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 have 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., 2014, 2016; Clark et al., 2017).
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 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 (Australian Community Climate and Earth System
Simulator – United Kingdom Chemistry and Aerosol; ACCESS-UKCA) (Woodhouse et al., 2015),
(a) these new parameterisations, (b) an oceanic flash-rate parameterisation
suggested by Michalon et al. (1999) (Mi99), and (c) 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, interannual, and seasonal distributions.
The veracity of the new modelled LNOx estimates is examined through
comparison of modelled and reanalysis tropospheric NO2 column amounts.
The impacts of the 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 or appropriate.
ACCESS-UKCA global chemistry–climate model
We use the UKCA global atmospheric
composition model (Abraham et al., 2012; http://www.ukca.ac.uk,
last access: 4 May 2021)
coupled to ACCESS
(Bi et al., 2013; Woodhouse et al., 2015). In our simulations, ACCESS is
essentially the same as the UK 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 atmosphere-only mode with prescribed monthly mean sea
surface temperature (SST) and sea ice fields, and the UM's original
land-surface scheme (Joint UK Land Environment Simulator; JULES) is used. The atmosphere component of the UM
vn8.4 is the Global Atmosphere (GA 4.0) (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., 2013) is used,
and ozone is coupled interactively between chemistry and radiation. The
aerosol component includes sulfur 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
terrain-following 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 model dynamical time step is 20 min,
the UKCA chemical solver is called every 60 min. It is a symbolic
backward Euler solver with Newton–Raphson iteration and runs to convergence,
halving the step when required; see Esentürk et al. (2018) for more
details. A global monthly varying emissions database for reactive gases and
aerosols is used, which includes anthropogenic, biomass burning, and
natural components, whereas for carbon dioxide, methane, nitrous oxide, and
ozone-depleting substances, concentrations are prescribed instead of
emissions (Woodhouse et al., 2015).
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 to use the
original PR92 flash-rate parameterisations, except that the amount of NO
produced per flash is taken to be the same for both IC or CG flashes in the
new version, which leads to small changes in the LNOx production
compared to the old version.
The ACCESS-UKCA setup used here incorporates some additional modifications
compared to the base UM-UKCA version 8.4, and these include the following:
Dry deposition of ozone to the ocean is now based on a process-based scheme
developed by Luhar et al. (2018) (the “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 (cm3 molecule-1 s-1)
for the chemical reaction HO2+ NO → HNO3:k2/k={[(530±10)/T]+4.8×10-4×P-(1.73±0.07)}/100,where pressure P is in hPa and temperature T is in K, and k is the rate
constant (cm3 molecule-1 s-1) for the included 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 hPa
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,
last access: 5 May 2021) in which 8.53 instead of 4.8 is
mistakenly specified in the branching ratio expression in the “Rate
coefficient data” table.
. Additionally, in the parameterisation
k=c0×10-12exp(270/T), the model uses
c0=3.3 for this reaction, but for k in the branching ratio
(Eq. 2) it uses c0=3.6, which we
change to 3.3 for consistency.
The above changes led to an increase in the modelled tropospheric ozone
burden by about 12 % (the first two changes by ∼7 % and the last
by ∼5 %) to 284 Tg O3, and this increase is towards a reported global
modelling average (see Sect. 4.2).
In the model, the tropopause is calculated every time step. In the
extratropics (latitudes ≥|28|∘), the
tropopause is the pressure level of the 2 PVU (potential vorticity unit)
surface, and in the tropics (latitudes ≤|13|∘) it is the pressure level of the 380 K potential temperature isentropic
surface. Between the two regions, a weighted average of the two
definitions is used following the method of Hoerling et al. (1993).
Implementation of lightning flash-rate parameterisation in the model
In ACCESS-UKCA, the convective cloud bottom level (Hb) and top level
(H) are diagnosed on a time step basis from the UM convection scheme. This
scheme represents the subgrid-scale transport of heat, moisture, and
momentum associated with cumulus clouds within a grid box. The scheme (at
GA4.0) is summarised by Walters et al. (2014); it uses a mass flux
convection scheme based on Gregory and Rowntree (1990) with various
extensions to include downdraughts and convective momentum transport. It
consists of three stages: (a) 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.
Hb is taken to be the air parcel ascent start level and H is set to be
the top of the ascent. On each time step, the flash rate is then determined
by using the calculated values of Hb and H at each grid point. 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 scale needs to be specified for it to constitute
a thunderstorm. In our model, a minimum convective cloud thickness
(H-Hb)
of 5 km is required for the lightning NOx to be activated.
The selected threshold of 5 km is very similar to observations of the
smallest vertical scale of thunderstorms presented by several researchers
(Price and Rind, 1992, 1993; Molinié and Pontikis, 1995; and Ushio
et al., 2001). While prescribing a minimum convective cloud thickness
of 5 km for lightning is somewhat arbitrary, having no such threshold value is
unrealistic because then it would be implicitly assumed that a convective
cloud always translates to a thunderstorm, and this would likely lead to
unrealistically high flash rates. (We found that increasing or decreasing
the minimum cloud thickness value by 1 km from 5 km resulted in a change of
-3.2 % and 1.7 %, respectively, in the modelled global flash rate using
the PR92 scheme.)
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
H (km) (see Sect. 3.2).
The PR92 flash-rate expressions (discussed later in Sect. 3.2) were
developed based on observations of individual thunderstorms. Price and Rind
(1994) (see their Fig. 1) developed a spatial calibration factor (c) to
adjust these expressions for varying model resolutions:
c=0.97241exp0.048203ΔxΔy,
where Δx is the longitudinal resolution and Δy 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
fL,O=cFL,OAAc,
where A is the model grid box area (which is a function of latitude), Ac
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. Any model grid cell that has a non-zero
land-surface fraction is considered land for the purposes of lightning NOx
calculation. Conversely, only grid cells with 100 % water surface coverage
are considered ocean.
We use Eq. (4) along with Eq. (3) to calculate the total flash rate fL,O
which is then apportioned into CG and IC
flash rates using an empirical parameterisation for the ratio zR=IC/CG developed by Price and Rind (1993) (PR93) based on thunderstorm
observations in the western United States. In this parameterisation,
zR increases as a function of the thickness (dH) of the cold-cloud region
in thunderstorms (from 0 ∘C to cloud top), and dH is parameterised
as a decreasing function of latitude. The PR93 parameterisation has been
used frequently, with further validation for case studies reported by
Pickering et al. (1998) and Fehr et al. (2004). Allen and Pickering (2002)
and Grewe et al. (2001) used it in global atmospheric chemistry models, with
the former evaluating it for cases in the US. The averaged values of
zR and the CG to total flash ratio obtained from the PR93
parameterisation in the present study are 3.14 and 0.24, respectively. These
values are comparable to zR∼4 and the CG to total flash ratio
∼0.2 obtained by Barthe and Barth (2008) using dH calculated directly
from modelled cloud temperature and total hydrometeor mixing ratio in the
PR93 parameterisation, and to zR=2.64–2.94 obtained by Boccippio et
al. (2001) using satellite- and ground-based lightning observations over the
continental US. Using IC / CG measurements, Bond et al. (2002) derived a
parameterisation for zR as a linearly decreasing function of latitude
and obtained zR=3.76 and a CG to total flash ratio of 0.21 over
the tropics (35∘ N–35∘ S).
Production of NO per flash
Both the moles of NO produced per flash, PNO, and the variation of this
parameter between CG and IC flashes are poorly constrained by atmospheric
observations. The overall rate, PNO, regulates the amount of nitrogen
oxides produced by lightning, whereas the variation of PNO between CG
and IC flashes regulates the level at which lightning nitrogen oxides are
introduced into the atmosphere, both are critical variables. In this study,
PNO is set at Sf×1026 molecules NO per flash, where
the scaling factor Sf=2 by default irrespective of whether a flash
is IC or CG, which is equivalent to 330 moles NO per flash. Assuming a mean
energy release of 0.67 GJ per IC flash and 6.7 GJ per CG flash (Price et
al., 1997), with 24 % of the total modelled flashes being CG, the
production of 330 moles NO per flash corresponds to 9.4×1016 molecules NO J-1.
If we use a mean energy release of 0.9 GJ per IC
flash and 3.0 GJ per CG flash based on Schumann and Huntrieser (2007), then
the NO production is calculated to be 14.2×1016 molecules NO J-1.
In bottom-up models, in addition to flash rate, PNO is a key source of
uncertainty, with a review by Schumann and Huntrieser (2007) suggesting a
range of ∼33–660 with an average of 250 moles NO per flash and
similarly 70–700 moles (Bucsela et al., 2019). This large range, in part,
reflects spatial variation in the frequency and uncertainty in the 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,
2016).
The value PNO=330 moles NO per flash used in our model lies close to
the middle of the range of current literature. Recent estimates include a
global average value of 310 moles NO per flash obtained by Miyazaki et al. (2014)
using an assimilation of multiple satellite measurements of
atmospheric composition and the LIS/OTD lightning flash data into a global
CTM; 665 moles NO per flash estimated by Nault et al. (2017) using airborne
observations of atmospheric composition, satellite-based Ozone Monitoring
Instrument (OMI) NO2 columns and the GEOS-Chem model; 280±80 moles
NO per flash by Marais et al. (2018) using the OMI NO2 columns
and satellite-based lightning data together with GEOS-Chem; 180±100 moles
NO per flash by Bucsela et al. (2019) for three northern midlatitude
regions that were primarily continental; and 170±100 moles NO per
flash by Allen et al. (2019) for the tropics. The last two stem from the
same OMI NO2 columns and ground-based lightning measurements. Values
used in calculating global estimates of LNOx include 360 moles NO per
flash by Ott et al. (2007), 500 moles NO per flash for selected
extratropical regions, and 260 moles NO per flash for the rest of the globe
by Murray et al. (2012).
We assume that both CG and IC flashes yield the same amount of NO, which
follows studies such as DeCaria et al. (2005), Ridley et al. (2005), Ott et
al. (2007, 2010), and Cummings et al. (2013). On the other hand, some studies
consider or find that the less frequent CG flashes yield a greater amount of
NO per flash than IC flashes (Price et al., 1997; Koshak et al., 2014; Luo
et al., 2017). A few studies suggest that PNO may not be constant over
the globe, with higher production rates in extratropics than tropics
(Huntrieser et al., 2008; Murray et al., 2012) and globally variable
production rates (Miyazaki et al., 2014). Differences in land and ocean
production rates have also been noted. Boersma et al. (2005) found that land
flashes were ∼1.6 times more productive than those over the
ocean, and conversely Allen et al. (2019) estimated marine flashes to be
twice as productive than those over land. Clearly, further measurements and
process understanding are needed to reconcile differences in LNOx
production.
Details about global LNOx reported in previous studies are given in
Sect. 3.7.1.
In our model, the calculated amount of LNOx at a grid point location at
a given time step (60 min) is distributed evenly in the vertical in
log-pressure coordinate from 500 hPa to the cloud top for IC
flashes, and from 500 hPa to surface for CG flashes (see
Sect. 3.7.2). The method is motivated by the data analysis of Price and
Rind (1993). Their observations from 139 thunderstorms cover cold-cloud
thickness (i.e. the cloud-top height minus the freezing level) values
ranging between 5.5–15 km and freezing level values between 2.7–5 km. The
ratio zR=IC/CG increases from 0 to 4.6 with cold-cloud thickness
from 5.5 to 15 km but remains relatively constant with freezing level. We
take the level below which the CG-generated LNOx is distributed as the
observed minimum freezing level plus half of the minimum cold-cloud
thickness, i.e. (2.7+5.5/2)≈5.5 km. The selected 500 hPa level
is closest to this 5.5 km value. Since the amount of NO produced per flash
is taken to be the same for both IC and CG flashes, the partitioning of the
total flash rate into the CG and IC flash rates only influences the shape of
the vertical distribution, with the total LNOx released remaining
independent of the partitioning.
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 (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 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
that convective velocity does. (However, as Williams (1985) writes, this does
not establish whether convective motion is directly
responsible for the charge separation.)
Boccippio's (2002) extension of Vonnegut's (1963) model and derivation of
scaling relationships for land and ocean
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 conceptualised 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 conceptualised 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 (the product of charge density multiplied by charge transport velocity). Scale
similarity between horizontal and vertical dimensions is invoked, and the
dipole separation (=2R) is assumed to vary linearly with cloud-top height,
a more readily observable parameter. This assumption is based on
observations that in many storms the lower negative charge region remains
relatively constant in height and that most upper positive charge is carried
on small ice crystals with negligible terminal velocity. 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
F∼k1wH4,
where the coefficient k1∼γε-1ρ2, H is cloud-top height (m), w is updraft velocity (m s-1), ρ
is charge density (coulomb m-3), ε is permittivity
constant (coulomb2 J-1 m-1), and the coefficient γ has
units of J-1. By assuming that each flash is responsible
for a constant electrostatic energy and that the variability in the charge
density of the dominant dipole regions is small, Boccippio (2002) treated
k1 as a single constant, irrespective of whether the flash is over land
or ocean.
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 current density
(which is taken to vary linearly with updraft velocity). In the case where
w(z) values for land and ocean are considered to be power-law fits of H,
wL,O=kL,OHaL,O.
The above approach based on Eq. (5) leads to the
following self-consistent scaling relationships, where aL,O
and kL,O are coefficients for land and ocean:
7FL,O=k1kL,OHaL,O+48FL,O=k1kL,O-4/aL,Ow1+(4/aL,O).
These self-consistent scaling relationships are central to this study.
Using these scaling relationships, the data of Williams (1985), PR92, and LIS
satellite data, Boccippio (2002) derived
FL=2.13×10-5H5.09
(note there is a negative sign missing in the first exponent of this
equation in Boccippio, 2002), and
FO=4.09×10-5H4.38,
where k1=1.4314×10-5 was used in deriving the
relationships in Eqs. (9) and (10),
which are plotted in Fig. 1.
Various relationships, including those from this study (TS),
between lightning frequency F (flashes per minute) and convective cloud-top
height H (km). The land data points are from PR92, and the ocean data are
from Molinié and Pontikis (1995) (MP95) and Ushio et al. (2001) (Us01);
Bo02 – Boccippio (2002), Mi99 – Michalon et al. (1999), and PR92 – Price
and Rind (1992).
Price and Rind's (1992) (PR92) parameterisations
PR92, following Vonnegut (1963) and Williams (1985), present a simple
lightning parameterisation for calculating global lightning distributions.
Using continental storm observations used by Williams (1985) to establish
the fifth-power dependency, PR92 derived an empirical relationship between
continental lightning flash rate and H:
FL=3.44×10-5H4.9.
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 between maximum updraft velocity (w,
m s-1) and H (km) for continental and marine clouds:
12wL=1.49H1.0913wO=2.86H0.38.
Eliminating H from Eqs. (11) and
(12) yields
wL=14.66FL0.22.
Now, PR92 made the crucial assumption that Eq. (14)
is independent of location, so it is valid for the marine environment too.
Thus, by equating Eqs. (14) and (13), they obtained the following expression for
marine environment:
FO=6.4×10-4H1.73.
(Our calculation suggests that the coefficient 6.4 in the above equation
should actually be 5.94.) The relationships in Eqs. (11) and
(15) are plotted in Fig. 1,
which show that the oceanic flash frequencies that are roughly 2 to 3 orders
of magnitude smaller than those obtained for continental clouds.
According to Boccippio (2002), the derivation of Eq. (15) includes significant formal inconsistency and
yields non-physical cloud-height predictions upon inversion and other
non-physical behaviours, e.g. an inverse relationship between updrafts and
cloud heights.
PR92 parameterisations (11) and
(15) are widely used in global chemistry transport
models and coupled chemistry–climate models.
Michalon et al.'s (1999) ocean parameterisation
Michalon et al. (1999) identified that the PR92 parameterisation, when used
over water in global models, was producing lightning flash 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 F=AN2/3H5, where A is a
proportionality constant. They retained the continental PR92 expression (11) by considering that it has been directly
calibrated by using observed F and H values, and used it for the ocean by
multiplying it with a factor of (NO/NL)2/3 assuming that
cloud droplet concentrations for continental (NL) and marine (NO)
clouds are different:
FO=3.44×10-5NONL2/3H4.9=6.57×10-6H4.9,
where two “standard” continental and maritime cloud droplet concentrations
of NL=600 and NO=50 per mg of air, respectively, were used.
Equation (16) is plotted in Fig. 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).
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 empirical.
This study: alternative flash-rate parameterisations
This study includes (a) a reanalysis of the Williams (1985) and PR92 data
for lightning flashes vs. cloud-top height over land into the
self-consistent scaling relationships framework of Boccippio (2002) and
(b) the derivation of a new relationship for the oceanic environment using these
scaling relationships.
For land, considering initially the relationship of updraft velocity with
cloud-top height: equating the scaling relationship in Eq. (6) with the observed maximum updraft velocity from
PR92 given in Eq. (12) gives kL=1.49 and
aL=1.09. Substituting these values into Eq. (7) yields
FL=1.49k1H5.09.
At this stage, k1 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
Fig. 1 as solid blue circles). This gives
k1=1.612×10-5 and
FL=2.40×10-5H5.09.
The relationships of PR92 (Eq. 11), Boccippio (2002) (Eq. 9), and this study
(TS) (Eq. 18) are presented in Fig. 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) shows a slightly higher flash rate for higher
H than the other two. The almost-fifth-power dependence on H makes FL very
susceptible to even small changes in the FL–H relationship and in how
cloud-top height is calculated in the model. Note that variation of flash
rate at higher H is important for both global distributions of flash rate and
how it may change with changing convective activity, e.g. climate change.
Concerning the oceanic parameterisation, there are limited data on flash
rate vs. cloud-top height for marine environments.
Figure 1 presents Ushio et al.'s (2001) (Us01) data
(triangles) over the ocean in the tropics and extratropics (their Fig. 3b and d),
which they obtained by averaging flash rates every 1 km in cloud height.
Also shown
are the Molinié and Pontikis' (1995) (MP95) flash-rate data (solid black circles) over the 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
Fig. 1.
Applying Boccippio's (2002) scaling relationships to obtain an equivalent
relationship for marine clouds involves equating Eq. (6) with the observed oceanic convective updraft
velocity vs. cloud-top height from PR92 given in Eq. (13). This yields kO=2.86 and aO=0.38.
Substituting these into the scaling relationship (Eq. 7) gives
FO=k1×2.86×H4.38=AOH4.38.
For this study, fitting Eq. (19) to the ocean data in Fig. 1
leads to AO=2×10-5 (which gives k1=0.7×10-5)
and
FO=2.0×10-5H4.38.
This marine parameterisation yields flash rates that are approximately an
order of magnitude smaller than the PR92 continental formula and roughly 2
orders of magnitude larger than the PR92 marine parameterisation. In
Fig. 1, 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 TS Eq. (20) are shown. 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.
The values of k1 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
implies that one or both assumptions in the theory that each flash is
responsible for a constant electrostatic energy and that the variability in
ρ is small are not true, possibly due to differences in cloud
microphysics between land and ocean. If we use the same logic concerning
aerosol microphysics as Michalon et al. (1999) used in deriving Eq. (16),
then the different values of k1 in Eqs. (18) and (20) for land and
ocean can be interpreted in terms of NO and NL being different from
NO<NL.
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 five runs of the ACCESS-UKCA global chemistry–climate
model incorporating seven specified flash-rate parameterisations:
Run 1 (PR92): the default PR92 parameterisations: continental Eq. (11) and marine Eq. (15);
Run 2 (this study – TS1): the new parameterisations: continental Eq. (18) and marine Eq. (20);
Run 3 (this study – TS2): the PR92 continental Eq. (11) and new marine Eq. (20);
Run 4 (Mi99): the PR92 continental Eq. (11) and
Michalon et al.'s (1999) marine Eq. (16);
Run 5 (Bo02): Boccippio's (2002) Eqs. (9)
and (10).
Note that Runs 2 and 5 only differ in the values of the linear coefficients
used in the flash-rate parameterisations. We also did a model run with no
LNOx emissions for a broad comparison, where appropriate, with the
modelled changes in tropospheric composition resulting from the changes in
the flash-rate parameterisations.
ACCESS-UKCA was set up as a free-running simulation for 2 years (2005–2006)
for each of the above runs, and the simulation was started using model
initial conditions taken from a previously spun-up, nudged model run that
used a Newtonian relaxation nudging (Uhe and Thatcher, 2015) within model
levels 20–45 (between altitudes ∼3 to 14 km) and the default
lightning scheme. The variables nudged were the horizontal wind components
and potential temperature by using ECMWF's ERA-Interim reanalyses (Dee et
al., 2011) on pressure levels. The idea was to start the simulation with
meteorological/transport errors minimised in the free troposphere to the
extent possible. The first year of the free-running simulation was used as a
spin-up period and the model output for the year 2006 used for analysis
reported below. (We also did Runs 1 and 2 with meteorological nudging for the years
2005–2006 with the same initial conditions as for the free-running
simulations, and the results are summarised in Sect. 5.)
Comparison of the modelled lightning flash rates with satellite
observations
We analyse the global gridded lightning flash data from 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-climatology.html
(V2.3.2015, last access: 5 May 2021).
The high-resolution (0.5∘× 0.5∘) mean annual flash
climatology (HRFC), low-resolution (2.5∘× 2.5∘) mean annual flash
climatology (LRFC), and low-resolution (2.5∘× 2.5∘)
monthly time series (LRMTS) data products are useful for
our analysis. The climatology and time series data are flash density values
with the units of flashes km-2 yr-1 and
flashes km-2 d-1, respectively. The OTD data available from
July 1995 to January 2000 cover all latitudes, whereas the LIS data available
from February 2000 to February 2014 cover ±42.5∘. The
climatology data cover all latitudes. For comparison with the modelled flash
parameters, the satellite data were spatially regridded to the model N96
resolution (1.875∘ longitude × 1.25∘ latitude)
using the Climate Data Operators (CDO) software.
Observed vs. modelled flash rates from the five model runs
(corresponding to PR92, TS1 and TS2, Mi99, and Bo02) conducted for
the year 2006. The vertical clusters of points are the values over the
globe, ocean, land, Southern Hemisphere (SH), Northern Hemisphere (NH).
(a) The observations are the LIS/OTD climatological data, and (b) the
observations are the LIS data for the year 2006 that are available for the
latitude range ±42.5∘ (with the modelled values also
corresponding to this range).
Observed and simulated lightning flash frequencies for the various
model runs. The values in the parentheses are for the latitudinal range
±42.5∘ (which correspond to the latitudinal coverage of
the LIS data).
Table 1 gives the observed and modelled lightning
flash frequencies (flashes s-1) averaged over the globe, Northern
Hemisphere (NH), Southern Hemisphere (SH), land, and ocean for the five
model runs, and these are plotted in Fig. 2. In
Fig. 2a, the observations are the combined LIS and
OTD climatological data, whereas in Fig. 2b, the
observations are the LIS data for the year 2006 which are only available for
the latitudinal range ±42.5∘ with the modelled values
also given for this range. The observations for the year 2006 are very well
correlated to the climatology, and the two are very similar in magnitude as
well since most lightning activity would fall within ±42.5∘. The data show that ∼80 % of the global
lightning flashes are over land, and ∼55 % are in the Northern
Hemisphere. On average, the default PR92 parameterisations (Run 1)
underestimate the flash frequency data by 28 % for the globe, by ∼13 % for land, and by ∼96 % for the ocean. Clearly, the oceanic
PR92 flash-rate parameterisation Eq. (15) does not
work well at all over the ocean, yielding an almost-zero flash 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 Hemisphere and Southern Hemisphere, compared to ∼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. Over the ocean, Run 5 predicts
flash rate nearly twice as large as that observed and that from Run 2, which
leads to an overestimation of the observed global total. Over land, the Run 5
estimate is about 10 % lower than that from Run 2.
Monthly variation of the observed and modelled flash rates from
the five model runs for the year 2006: (a) NH,
(b) SH, (c) globe, (d) land, and (e) ocean.
The observations are the LIS/OTD climatological data
(with 1 standard deviation variability) and the LIS data for the year 2006.
The monthly variation of the observed and modelled flash rates is shown in
Fig. 3. The observed variation for the year 2006
is very similar to the climatological variation, mostly within the
1 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
(Fig. 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 (Fig. 3b), again the model is able to
simulate the observed variation well qualitatively, but a significant
overprediction for January–April and an underprediction for August–October is apparent. The underprediction in spring in the Northern
Hemisphere and overprediction in autumn in the Southern Hemisphere could be
due to a displacement of lightning activity across the Equator. The
underprediction in spring in the Southern Hemisphere appears to be due to
model deficiency over land (Fig. 3d). In the
global plot (Fig. 3c), while Run 1 always
underestimates the observed flash rate, which is mostly because of its underprediction of the flash
rate over the ocean (Fig. 3e), the other runs
underestimate it in the first 3 months of the year and overestimate it during
September–November, and these differences can be explained in terms of
the hemispheric differences shown above. The nature of monthly variation in
Fig. 3d for land-based flash rates is very similar
to that in Fig. 3c, 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
Fig. 3e; there are also differences in the monthly
variation. Run 5 overestimates the observed oceanic variation the most out
of all runs, and this leads to an overprediction of the observed global
variation except for September and October.
Normalised mean square error (NMSE), fractional bias (FB), and
correlation coefficient (r) for the monthly varying observed climatology and
modelled flash rates shown in Fig. 3.
Normalised mean square errors (NMSEs) ((M-O)2‾/(M¯O¯)) calculated from the monthly varying
observed climatology (O) and modelled (M) flash-rate time series shown in
Fig. 3 are given in Table 2 for the globe, land, and ocean. Also given are the values of fractional
bias (FB) 2(O¯-M¯)/(O¯+M¯) which varies between -2
(overestimation) and +2 (underestimation), and the (Pearson) correlation
coefficient (r). Considering these performance statistics together suggests
that the Run 2 flash-rate parameterisations from this study yield the best
comparison with the data.
Observed and modelled zonal mean flash densities (flashes km-2 yr-1)
from the five 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.
Figure 4 presents the observed and modelled zonal
mean flash density (flashes km-2 yr-1) over the globe, land, and
ocean. All modelled global distributions and the data agree that the flash
density is largely concentrated in the tropics. The observed peak for the
year 2006 in Fig. 4a is better simulated by Runs 2–4 than by Run 1 (underestimation) or Run 5 (overestimation). The results
over land (Fig. 4b) are very similar for all runs.
Over the ocean (Fig. 4c), while the default
oceanic parameterisation (Run 1) yields a near-zero flash density
distribution and Run 5 overestimates the data considerably, the new flash
parameterisation (in Runs 2 and 3) performs much better. There are
significant distributional differences compared to the data. It is clear in
these plots that the observed latitudinal distributions of flash density are
wider than the modelled ones, with larger observed flash densities in the
subtropics stretching into the midlatitudes (roughly 20–40∘ in
both hemispheres) than modelled. The reason for this may be the inherent
limitation of the simple flash parameterisation approach based on convective
cloud-top height or uncertainty and/or biases in the modelled convection (e.g. Allen and Pickering, 2002; Tost et al., 2007). Another potential factor
could be greater vertical wind shear 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. The LIS/OTD
observations have some limitations too, such as a short sampling duration
(just minutes) for a particular global location and lightning detection
efficiencies not being perfect (Clark et al., 2017).
Hereafter, we only present plots from Run 1 (default) and Run 2 (new), but
the results from Runs 3–5 are included in all comparison tables except
Table 5.
Global distribution of the mean annual lightning flash density
(flashes km-2 yr-1): (a) LIS/OTD satellite climatology, (b) LIS
satellite data for the year 2006 (available only for ±42.5∘
latitudes), (c) model simulation with the default PR92 flash-rate
parameterisations (Run 1), and (d) model simulation with the new flash-rate
parameterisations from this study (Run 2).
Figure 5 compares the various global distributions
of the mean annual lightning flash density at N96 resolution. The LIS data
for the year 2006 in Fig. 5b are only available
for the latitudinal range ±42.5∘ and have no sampling for
some regions within this range. Where there are data, there is a good
agreement between the observed distribution in Fig. 5b and the LIS/OTD climatology in Fig. 5b,
showing high flash density over land in the tropics and subtropics, and also in the
lower midlatitudes. 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 Fig. 5c is very similar to
other global modelling studies that use the same PR92 scheme, e.g. Allen and
Pickering (2002) using the Goddard Earth Observing System – Stratospheric
Tracers of Atmospheric Transport Data Assimilation System (GEOS-STRAT DAS), Tost et al. (2007) using
ECHAM5/MESSy, Murray et al. (2012) using GEOS-Chem, Finney et al. (2014)
using ERA-Interim reanalyses, Finney et al. (2016) using UM-UKCA, and
Clark et al. (2017) using CAM5. It is remarkable that the simple PR92 scheme
based on the convective cloud-top height is able to simulate the broad
observed global distribution of flash density over land at low latitudes
(except parts of India) but it does not properly reproduce the extension of
lightning flash density into the temperate latitudes, particularly in the
Northern Hemisphere. Over the ocean, in contrast to the observations, the
PR92 scheme predicts almost zero flash density. However, as shown in
Fig. 5d, ACCESS-UKCA with the new flash-rate
parameterisations (Run 2) simulates the oceanic distribution of flash
density much better than the PR92 scheme, although it is clear that there
are some significant spatial differences (e.g. low bias over western Indian
Ocean near southern Africa and high bias over equatorial Indian Ocean and
the Pacific) compared to the corresponding observations and climatology. The
modelled flash-density distributions over land in
Fig. 5c and d are
nearly the same.
NMSE, FB, and r for the spatially varying annual-mean modelled flash rates
and observed climatology shown in Fig. 5a.
The area-weighted NMSE, FB, and r comparing the
spatial patterns of the observed climatology presented in
Fig. 5a with the annually averaged modelled
patterns of flash rate are given in Table 3 for the
five model runs. The NMSE and FB values clearly show that Run 1 performs the
worst, a result dominated by the oceanic component. While the NMSE values
are nearly the same for Runs 2–4, Run 2 has the best FB values for both
land and ocean. While Run 5 has the best FB value for the globe, this is
fortuitous because the model underestimation and overestimation for land and
ocean, respectively, counteract in the calculation of global FB. Thus, these
statistics should be considered separately for land and ocean in examining
the model performance. 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 is 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.
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 climatology
(∼46 flashes s-1), by applying a constant scaling factor to the
modelled global flash-rate spatial distribution (e.g. Tost et al., 2007;
Finney et al., 2016; Clark et al., 2017; Gordillo-Vázquez et al., 2019),
where the scaling factor is the ratio of the observed global average flash
rate to the modelled global average flash rate and is calculated by doing a
model pre-run. However, such a scaling would be misleading when there are
large differences in the spatial representativeness of the flash rate
computed by the parameterisation used in a model. For example, scaling the
PR92-derived global flash-rate distribution would overadjust the flash rate
(and hence LNOx) over land to compensate for the deficiency in the
oceanic parameterisation. (Scaling can also be applied to tune the
amount of NO produced per flash to get a desired total global LNOx
amount, as per Eq. 1.). In the present study, no
scaling factor was applied to the modelled flash rate, nor was it necessary.
Modelled LNOx and comparisonGlobal LNOx
The modelled global lightning-generated NOx using the various lightning
flash-rate schemes is 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 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, whereas the
Run 5 value is 14 % greater than that for Run 2 due to the higher value of
the oceanic component. Given the same value of NO emitted per flash used for
both IC and CG flashes, the partitioning of the global LNOx into the NH,
SH, 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.
Modelled global lightning-generated NOx using various
lightning flash-rate schemes (Tg N yr-1).
The amount of global LNOx produced, LG (Tg N yr-1), is a
function of the global average flash rate, fs (flash s-1), and the
moles of NO produced per flash, PNO:
LG=441.5×10-6fsPNO.
If the climatological average fs=46.5 flash s-1 based on the
LIS/OTD satellite data is used, then
LG=20.5×10-3PNO.
If the NO production per flash differs for IC and CG flashes, then PNO
can be taken as a weighted average over mean IC and CG flash fractions. The
values in Table 4 are consistent with Eq. (21) when PNO=330 moles NO per flash as used in
ACCESS-UKCA and the modelled fs from Table 1
are substituted. These values can be compared with a global estimate of
LG=5±3 Tg N yr-1 based on Schumann and Huntrieser's
(2007) review. More recently, there have been estimates of LNOx
incorporating top-down approaches, which we divide into (a) verification
studies using other constraints and (b) model experiments.
Verification studies include the following. Using a CTM representing the LIS/OTD flash
data, Martin et al. (2007) obtained an estimate of 6±2 Tg N yr-1
that best reproduced satellite observations of tropospheric
NO2, O3 and HNO3. Miyazaki et al. (2014) obtained LG=6.3±1.4 Tg N yr-1 and a global average production of 310 moles NO
per flash using an assimilation of multiple satellite measurements of
NO2, O3, HNO3 and CO, and the LIS/OTD flash data into a
global CTM. The global values for Runs 2–4 in Table 4 compare very well with
the above constrained estimates, considering their
differences in NO per flash used (the ratio LG/PNO≈0.02
in these estimates as per Eq. 22). Using upper-tropospheric airborne observations of LNOx and global
satellite-retrieved tropospheric NO2 column densities along with
GEOS-Chem, Nault et al. (2017) estimated 665 moles NO per flash with global
LNOx at ∼9 Tg N yr-1. Using global satellite data
of NO2 columns and lightning flashes together with the GEOS-Chem model,
Marais et al. (2018) derived a global production rate of 280±80 moles NO
per flash, with a global LNOx emission of 5.9±1.7 Tg N yr-1.
Boersma et al. (2005) analysed above-cloud tropospheric NO2 column
retrievals from the Global Ozone Monitoring Experiment (GOME) satellite observations for the year 1997 for cloudy
scenes over tropical oceans and continents, and found that the above-cloud
annual-mean NO2 column increases sharply with convective cloud-top
height (H) – as H5.1 for continents and H4.6 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 very good agreement between
these power-law exponents and those in the flash-rate relationships of Eqs. (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) is unrealistic.
Model experiments include the following. Using a 3-D cloud-resolving model coupled with
observations from a thunderstorm and assuming PNO=360 moles NO per
flash, Ott et al. (2007) estimated a global LNOx of 7 Tg N yr-1.
Using a CTM constrained by the LIS/OTD flash together with a production of
500 moles NO per flash for all extratropical lightning north of
23∘ N in America and 35∘ N in Eurasia, and 260 moles NO
per flash for the rest of the globe, Murray et al. (2012)
In
Murray et al. (2012), these production values are given as N per flash, but
a cross-referencing suggests that these should be in NO per flash.
determined a global LNOx of 6±0.5 Tg N yr-1.
Global distribution of the annual-averaged LNOx
(10-13 kg N m-2 s-1) for the year 2006: (a) model simulation with the
default PR92 flash-rate parameterisations (Run 1), (b) model simulation with
the new flash-rate parameterisations from this study (Run 2), and (c) the
distribution obtained by Miyazaki et al. (2014, plot redrawn) using
assimilation of multiple satellite datasets into a global CTM for the
year 2007. The respective global LNOx totals are 4.8, 6.6, and 6.3 Tg N yr-1.
The modelled mean global distributions of LNOx from the two runs
presented in Fig. 6a and b are essentially in
proportion to the flash density distributions given in
Fig. 5c and d,
respectively. The new flash-rate scheme (Run 2) leads to a larger and
broader distribution of LNOx over the ocean compared to the PR92
scheme, while over land they are very similar.
In the absence of any direct measurements of global spatial distribution of
LNOx for comparison, we present in Fig. 6c the
annual LNOx distribution obtained by Miyazaki et al. (2014) using an
assimilation of satellite measurements of atmospheric composition and the
LIS/OTD lightning flash data into a global CTM for the year 2007. This plot
is a reproduction of their Fig. 6 (middle-left plot) based the
data
The units in Miyazaki et al.'s (2014) plot are incorrect –
they should be 10-13 kg N m-2 s-1 instead of
10-12 kg N m-2 s-1 (Kazuyuki Miyazaki, personal communication, 2020). The
reproduced Fig. 6c has the correct units.
supplied by Kazuyuki Miyazaki (personal communication, 2020) at a horizontal
resolution of 2.8∘× 2.8∘. Over the ocean, the
new flash-rate scheme (Fig. 6b) agrees much better
with the assimilated field than does the PR92 scheme, but it is clear that the
oceanic LNOx distribution in the plot with assimilation is broader,
more diluted in the tropics, and even extends to high latitudes, which is not
seen in Fig. 6b nor indicated by the observed
flash-rate distributions in Fig. 5a and
b (this could be due to limitations of the
data assimilation used). Over land, the LNOx distributions predicted by
both PR92 and the new scheme are similar and broadly agree with
Fig. 6c at low latitudes (except parts of India)
but do not properly describe the extension of LNOx into the temperate
latitudes, particularly in the Northern Hemisphere.
Figure 6c yields a total LNOx of 6.36, 3.67,
2.69, 5.58, and 0.78 Tg N yr-1 for the globe, NH, SH, land, and ocean,
respectively, which except for SH are closer to the Run 2 values than to the
Run 1 values in Table 4. Direct and more extensive
measurements would be necessary for a better evaluation of the predicted
LNOx distribution.
Average vertical distribution of percentage of LNOx mass per
kilometre for (a) tropical continental, (b) tropical marine, (c) midlatitude
continental, and (d) subtropical regimes. The total LNOx for these
regimes calculated using model Run 1 (PR92) is 3.69, 0.035, 1.09, and
0.74 Tg N yr-1, respectively, whereas that calculated using Run 2 (TS1)
is 4.10, 1.09, 1.16, and 0.92 Tg N yr-1, respectively. The vertical
profiles from Pickering et al. (1998) and Ott et al. (2010) are also shown
(where available).
Vertical distribution
The vertical distribution of LNOx in the model at a grid point location
is a parameter (see Sect. 2.2) that is essentially unconstrained by
observations. Figure 7 presents the modelled average
vertical distribution of percentage of LNOx mass in each 1 km layer for
(a) tropical continental, (b) tropical marine, (c) midlatitude continental,
and (d) subtropical regimes. The non-uniform shape of the averaged modelled
vertical distributions is largely caused by the averaging of the LNOx
profile from every time step over spatial and temporal variations in the
cloud-top height. Also shown for comparison are the average profiles based
on thunderstorm cases simulated by Pickering et al. (1998) using a 2-D
convective cloud-resolving tracer transport model and those by Ott et
al. (2010) using a 3-D convective cloud-resolving chemical transport model, with
both studies using parameterised lightning. The profiles of Pickering et
al. (1998) show peaks near the surface, as significant mass is transported to
the boundary layer by downdrafts, and in the upper troposphere (the
so-called “C-shaped” profile), whereas those by Ott et al. (2010) show very
little LNOx mass in the boundary layer with the majority of LNOx
remaining in the middle and upper troposphere (the so-called “backward
C-shaped” profile) where it is originally produced. Our model profiles match
better with the Ott et al. (2010) profiles, but the model gives an almost uniform
distribution of LNOx mass below 5 km, whereas the latter decrease to
almost zero. There is not a large difference between the modelled profiles
for the various regimes, except that the tropical ones are almost uniformly
distributed between 5 and 12 km, whereas the midlatitude and subtropical
ones show a peak at 6.5 km. There are no direct measurements to verify any
of the LNOx profiles, and we believe further work is needed to constrain
them.
Zonal-averaged tropospheric total NO2 column
(Nv,trop) (in units 1015 molecules cm-2) obtained from Run 1 (with the default PR92 flash-rate
parameterisations) and Run 2 (with the new flash-rate parameterisations from
this study), and the OMI satellite data (green diamonds), for the year 2006.
The orange data points are the OMI satellite data
(Nv,trop,180) over the longitude 180∘ W.
Modelled tropospheric total column NO2 and validation
As lightning impacts atmospheric NOx directly, any changes in the
modelled total tropospheric NOx can be examined and compared with
available observations. The modelled variations of the zonal-averaged
tropospheric total NO2 column (Nv,trop) for the globe presented in
Fig. 8 show a broad peak in the industrialised
Northern Hemisphere dominated by surface NO2 emissions. Within the
latitudes ±30∘, the new lightning flash-rate
parameterisations yield 12 % larger values of tropospheric total NO2
column compared to the default PR92 scheme and the difference between the
two is ≈0.1×1015 molecules cm-2.
Figure 8 also presents tropospheric NO2 column
retrievals from the Ozone Monitoring Instrument (OMI) satellite overpasses
at ∼13:30 local time (LT) for the year 2006. These zonal averages
were derived from the OMI monthly mean tropospheric NO2 columns
(QA4ECV, version 1.1) given at a horizontal resolution of
0.125∘× 0.125∘ (https://www.temis.nl/airpollution/no2.php,
last access: 6 May 2021; Boersma et al., 2018). While
the model simulations qualitatively agree with the satellite observations in
Fig. 8, it is apparent that except for the
latitudes 30∘ S–60∘ S the modelled values are generally
higher than the observations. Notwithstanding any model shortcomings in
predicting the global NO2 distribution, there are limitations of the
OMI satellite data used. Firstly, there is limited sensitivity of the OMI
sensor to NO2 below the cloud level, where most NO2 is situated,
and thus cloudy tropospheric NO2 retrievals (with cloud radiance
fraction >0.5 or cloud fraction >0.2) cannot be
interpreted as valid down to the Earth's surface (Boersma et al., 2017).
Secondly, given that the OMI satellite data are representative of overpass
time, comparing them with the mean model fields averaged over full
diurnal periods introduces uncertainty.
As an alternate to the OMI data, we use data from the global reanalysis of
atmospheric composition produced by the Copernicus Atmosphere Monitoring
Service (CAMS) (Inness et al., 2019;
https://ads.atmosphere.copernicus.eu/cdsapp#!/dataset/cams-global-reanalysis-eac4-monthly,
last access: 6 May 2021)
for comparison with the 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, 13:30, and 09:30 LT,
respectively (for the year 2006, only SCIAMACHY and OMI data were available
for assimilation). Monthly averaged total vertical column NO2
reanalysis data (version – ECMWF Atmospheric Composition Reanalysis 4) are
available and used here.
We obtain the tropospheric NO2 column (Nv,trop) from the CAMS
total NO2 column (Nv) as follows:
Nv,trop=Nv-Nv,180+Nv,trop,180,
where Nv,180 is the CAMS total NO2 column over the Pacific
(180∘ W) and Nv,trop,180 is the tropospheric NO2 column
over 180∘ W. This is one approach used with satellite data to
separate the tropospheric and stratospheric amounts (Inness et al., 2019),
which assumes a longitudinal homogeneity of the stratospheric NO2
column amounts and a constant and negligibly small Nv,trop,180 (Lauer
et al., 2002). Nv,trop,180 is not available from the CAMS data, but
that obtained from the OMI data discussed above is shown in
Fig. 8 (orange data points) for the year 2006.
While these Nv,trop,180 values are small, they are neither constant nor
negligibly small compared to the modelled or OMI Nv,trop plotted in
Fig. 8 and would reflect contributions from
sources such as lightning, aviation, shipping, and possibly regional
transport over the ocean. The Nv,trop,180 values are also greater and
possibly more uncertain than the differences between the two model
simulations.
Zonal-averaged total tropospheric NO2 column
(Nv,trop) (in units 1015 molecules cm-2) modelled using the default PR92 parameterisations (Run 1), the
new lightning flash-rate parameterisations from this study (Run 2), and the
CAMS reanalysis data for the year 2006 over (a) globe,
(b) ocean, and (c) land. The model variation without LNOx is also shown.
Since Nv,trop,180 is not available from the CAMS data, we take
the OMI-derived Nv,trop,180 shown in Fig. 8 and use
it in Eq. (23) to determine Nv,trop from the
CAMS data. (While these OMI NO2 column data at 180∘ W have
the same limitations as the global OMI data mentioned earlier, we expect
that the impact of these limitations would be much smaller at 180∘ W
with almost no surface source contributions compared to terrestrial
locations.) The resulting CAMS zonal annual-mean Nv,trop as a function
of latitude for the globe is presented in Fig. 9a,
together with the corresponding modelled variations. The modelled variations
agree well with the CAMS data, better than with the direct OMI data in
Fig. 8. A comparison with the model variation
without LNOx in Fig. 9a suggests that the
modelled increase in NOx due to lightning is largely confined to
±35∘.
In Fig. 9b for the ocean, the agreement with the
data is again good, except for considerable model underestimation for
latitudes greater than 35∘ which, presumably not related to
LNOx, may be due to factors such as possible underestimation of the
calculated Nv,trop,180 and overestimation of shipping emissions of
NOx for these latitudes. Within ±35∘, the new
parameterisation yields 22 % larger NO2 column values compared to the
default model setup, whereas, as expected, the two model curves are virtually
the same for the other latitudes. The CAMS NO2 columns are somewhat
better simulated by the model with the new oceanic flash rate than with the
PR92 parameterisation, particularly in the northern tropics.
For land (Fig. 9c), the two model curves are
nearly identical and overall compare very well with the CAMS reanalysis
data. An overestimation of the reanalysis data in the southern tropical
region is evident.
Mean (1015 molecules cm-2), NMSE, FB, and r for the modelled and CAMS
reanalysis NO2 columns shown in Fig. 9 for
latitudes between ±30∘.
Flash-rate schemeGlobe Ocean Land MeanNMSEFBrMeanNMSEFBrMeanNMSEFBrRun 1 (PR92)0.740.0330.0580.900.450.0320.1400.921.350.058-0.0230.72Run 2 (TS1)0.830.040-0.0590.860.550.025-0.0610.821.420.067-0.0730.68CAMS data0.78–––0.52–––1.32–––
The statistics in Table 5 show that PR92 and TS1
have similar agreement with CAMS, except for a noticeably better FB over the
ocean with TS1. We expect no significant changes over land because the
LNOx is almost unchanged in the two runs.
Clearly, the comparison also depends on the selected value of NO produced
per flash. We have used the model default value of 330 moles NO per flash.
However, if we were to match the average CAMS column value in
Table 5, the new parameterisation with 310 moles NO
per flash, the value suggested by Miyazaki et al. (2014), would probably
yield a somewhat better prediction. Obviously, there are other sources of
uncertainties in the NO2 comparison, such as those associated with the
CAMS reanalysis and the assimilated satellite columns, which are documented
in the appropriate references cited above, as well as those to do with model
inputs (e.g. emissions) and processes.
Impact on tropospheric composition
We present the impact of LNOx determined from the flash-rate
parameterisations from Runs 1 and 2 on tropospheric composition, namely
total NOx, O3, OH, methane lifetime, and CO.
Zonal annual-mean total tropospheric NOx (as NO2,
pptv) modelled using (a) the default PR92 parameterisations (Run 1) and
(b) the new lightning flash-rate parameterisations from this study (Run 2).
The difference between Run 2 and Run 1 is shown in panel (c).
Oxides of nitrogen
The modelled tropospheric NO2 columns and their comparison with
observations have already been presented in Sect. 3.7.3.
Figure 10 presents the zonal distribution of total
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 identical, with
highest levels predicted within latitudes 20–60∘ N. These
levels are governed by surface emissions of NOx which are the same in
both simulations. The secondary concentration maximum at ∼15 km is due
to the lightning-generated NOx. The new lightning parameterisations
cause an increase in the mid- to upper-tropospheric NOx
(Fig. 10c), particularly within the tropics and
subtropics, and this increase is by as much as 40 pptv in the
northern tropics. There are some localised decreases in concentration in the
lower troposphere over the Northern Hemisphere.
The volume-weighted global tropospheric NOx obtained from the PR92
scheme is 55.1 pptv, and it is 35.2 pptv over the ocean and 94.0 pptv over
land. With the new flash-rate scheme, these values increase by 8.7 pptv
(15.7 %), 9.9 pptv (28.0 %), and 6.3 pptv (6.7 %), respectively, and can
be compared with the values 36.9, 20.7, and 68.5 pptv, respectively, obtained
from the model simulation with no LNOx emissions. To some extent, the
modelled tropospheric averages also depend on how the tropopause is defined.
Ozone
Tropospheric ozone is a byproduct of the oxidation of CO,
CH4, and other volatile organic compounds in the presence of NOx
and is thus impacted by LNOx.
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) (cf. 219 Tg O3 with no LNOx
emissions in the model). The new burden is closer to 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.
Mean relative difference (%) between the global annual-mean
ozone mixing ratios predicted by Run 2 using the new lightning flash-rate
parameterisations from this study and the default PR92 parameterisations
(Run 1): (a) at 20 m (the lowest model level) and (b) at 6400 m (∼450 hPa).
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 Fig. 11. Near the surface (Fig. 11a), there are
significant increases in ozone over the tropical oceans, especially in the
Pacific and western Indian Ocean, and in most of the Southern Hemisphere
(roughly by 8 % on average). Over land, there are regions (e.g. southeastern US and northern Australia) where ozone has increased, and
there are a few regions in the midlatitudes to high latitudes in the Northern
Hemisphere where ozone has decreased very slightly. Tropospheric ozone
chemistry is complex, but broadly speaking the O3 increases in the
Southern Hemisphere are influenced by low ambient NOx concentrations
where the O3 production increases with NO concentration. O3 is
produced through photodissociation of NO2, which is produced through
oxidation of NO by HO2 and RO2 radicals (e.g. NO + HO2→ NO2+ OH).
In the Northern Hemisphere, the increase in O3
is lower beyond the tropics, partly because the smaller oceanic area results
in a smaller increase in LNOx through the use of the new oceanic
flash-rate parameterisation. Carpenter et al. (1997) suggest that the
tropospheric production potential of the Southern Hemisphere is more
responsive to the availability of NO than that of the (more polluted)
Northern Hemisphere.
At an altitude of 6400 m (∼450 hPa) (Fig. 11b), there are even bigger increases in global ozone using the new
flash-rate parameterisations, particularly in the tropics, by as much as
25 %, and in the Southern Hemisphere. This is because most LNOx
emissions occur in the middle to upper tropical troposphere where the
photochemical production of ozone is most efficient.
Comparison of the modelled monthly averaged ozone concentrations
with observations at five oceanic/coastal ground stations for the year 2006.
The two model runs are with the default PR92 parameterisations (Run 1)
and new lightning flash-rate parameterisations (Run 2, this study). The
values of r and NMSE
are also shown.
In Fig. 12, we compare the modelled monthly averaged ozone with
ground-based in situ observations from the Global Atmosphere Watch – World Data
Centre for Reactive Gases (GAW-WDCRG, http://ebas.nilu.no, last access: 6 May 2021;
https://www.gaw-wdcrg.org, last access: 6 May 2021) for the year 2006 at five stations: Ushuaia
(54.85∘ S, 68.31∘ W), Cape Grim
(40.68∘ S, 144.69∘ E), Mauna Loa
(19.54∘ N, 155.58∘ W), Minamitorishima
(24.29∘ N, 153.98∘ E), and Mace Head
(53.33∘ N, 9.90∘ W). Apart from data
availability and covering a range of latitudes, the site selection was based
on these sites being either oceanic or coastal so that the relatively large
difference between the PR92 oceanic flash rate parameterisation and the new
one could be examined against the observations. 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.
Mauna Loa is located at an elevation of 3397 m on an island which is smaller
in size than the grid resolution of the model, and therefore it is difficult
to correspond the sampling height to a particular vertical model level. We
used the modelled concentrations from the bottom model level for all sites.
The two model simulations describe the observed monthly variations
reasonably well, except at Mauna Loa and Mace Head (the relatively large
disagreement at Mauna Loa is likely due to the model resolution issues).
There are small, but noticeable, differences in the modelled ozone from the
two simulations. The relative change in the modelled yearly averaged O3
at these ground-based sites with the use of the new lightning
parameterisation is small, at 5.9 %, 1.3 %, -1.9 %, 5.9 %, and 0 %,
respectively. There is some improvement in the modelled seasonal variation
at Ushuaia, Cape Grim, and Minamitorishima with the new LNOx scheme,
but for the other two sites the model–data differences are much larger than
those due to the LNOx changes. Generally, factors such as model's
transport and chemical mechanisms, and input precursor emissions and their
distributions are probably more influential in governing ozone model–data
differences than LNOx near the Earth's surface. There is no clear
indication if the differences in ozone between the two models are larger in
the winter or summer, except at Ushuaia, where the differences are larger
during winter to spring.
Profiles of annual-mean ozone constructed using the SHADOZ
ozonesonde measurements at eight sites for the year 2006, and the
corresponding modelled profiles obtained using the default PR92
parameterisations (Run 1) and the new lightning flash-rate parameterisations
from this study (Run 2). The modelled profiles without LNOx are also
shown as a reference.
In Fig. 13, we compare the modelled profiles of
annual-mean ozone with those obtained from the Southern Hemisphere
ADditional OZonesondes (SHADOZ) ozonesonde measurements at eight
tropical/subtropical sites (Witte et al., 2017; https://tropo.gsfc.nasa.gov/shadoz,
last access: 6 May 2021) for the year 2006. These sites are
Hilo (19.40∘ N, 155.0∘ W), Paramaribo (5.81∘ N,
55.21∘ W), Costa Rica (9.94∘ N, 84.04∘ W),
Natal (Brazil) (5.42∘ S, 35.38∘ E), Ascension Island
(7.98∘ S, 14.42∘ W), Irene (25.9∘ S,
28.22∘ E), Nairobi (1.27∘ S, 36.80∘ E),
Réunion Island (21.1∘ S, 55.48∘ E). The above eight
sites were selected based on data availability and to have a mix of Northern Hemisphere
and Southern Hemisphere locations where O3 could be more impacted by
LNOx. The profile data are given at a greater resolution in height than
the vertical model resolution and were binned in the model vertical levels
and averaged. The number of observed profiles at a location typically varied
between one and five per month. At Irene, Nairobi, and Réunion Island, there
were no data for 3–4 months. The observed profiles were averaged over the
year. The modelled monthly averaged profiles were averaged over the months
for which profile observations were available. Clearly, the number of
observed profiles is not sufficient for averaging over the year, and
therefore the model–data comparison is essentially qualitative.
The observed O3 profiles are simulated better by the new lightning
flash-rate parameterisations (Run 2) than by the default PR92
parameterisations (Run 1) at Costa Rica (Fig. 13c)
and for all the southern hemispheric sites (Fig. 13d–h). At northern latitudes beyond
Costa Rica, the PR92 scheme performs better at Hilo and Paramaribo
(Fig. 13a and b). The model with the PR92 scheme
has a general tendency to overestimate ozone at most levels within
15–50∘ N, which is probably due to reasons not
related to LNOx, and the use of the new lightning flash-rate
parameterisations worsens it (see Fig. 15). The
model describes the general shape of the observed profiles reasonably well.
The model profiles with no LNOx included highlight the importance of
LNOx on tropospheric ozone, particularly in the middle to upper
troposphere.
Zonal annual-mean tropospheric ozone (ppbv) modelled
using (a) the default PR92 parameterisations (Run 1) and (b) the new
lightning flash-rate parameterisations from this study (Run 2). The
difference between Run 2 and Run 1 is shown in panel (c).
Zonal distribution of tropospheric ozone concentration (ppbv) for
the year 2006: (a) observed distribution based on the global monthly mean
vertical ozone profile database available from Bodeker Scientific; (b) the
relative difference (%) between the concentration modelled using the
default PR92 lightning parameterisations (Run 1) and the observations;
(c) the relative difference (%) between the concentration modelled using the
new lightning parameterisations (Run 2) and the observations; and (d) the
relative difference (%) between the concentration modelled without any
LNOx and the observations.
The modelled zonal annual-mean tropospheric O3 from the two runs and
the difference between the two are presented in
Fig. 14. In the lower troposphere, the modelled
ozone is smaller over the Southern Hemisphere than over the Northern
Hemisphere (Fig. 14a and
b). The new flash-rate parameterisations
result in O3 increases everywhere (Fig. 14c).
Closer to the surface, the increase is approximately 2 ppbv in
the Southern Hemisphere and 0.5–2 ppbv in the Northern Hemisphere. The
largest increases are nearly 8 ppbv in the tropics at altitudes ∼9 km.
The modelled zonal ozone distribution can be compared with observations. We
use the monthly mean vertical ozone profile data for the year 2006, given as
zonal means, from the Bodeker Scientific database
(Hassler et al., 2009; http://www.bodekerscientific.com/data/monthly-mean-global-vertically-resolved-ozone,
last access: 6 May 2021)
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 5∘ latitude resolution
and 70 altitude levels (1 to 70 km). Different “tiers” of data are provided,
and we used the highest tier (Tier 1.4 vn1.0) data. For comparison with the model
predictions, these monthly profile data were regridded to the model
resolution. The modelled monthly tropospheric mask was averaged zonally and
then applied to the monthly regridded data.
There is an agreement, both in magnitude and distribution, between the
modelled zonal ozone in Fig. 14a–b and the
data plotted in Fig. 15a. The model reproduces the
observed lower levels of tropospheric ozone in the Southern Hemisphere. The
observed high levels just below the tropopause within
10–40∘ N are somewhat better reproduced by the new
flash-rate parameterisations. Figure 15b and c
represent the relative differences (=[M¯-O¯)/O¯]×100 %) between the annual-averaged modelled and observed ozone for the
PR92 scheme and the new parameterisations, respectively. On average, the
model underestimation in the Southern Hemisphere has been reduced with the new
parameterisations, but there are areas such as that within 10–20∘ S
below 5 km where there is some overprediction. There is
a clear improvement in the predicted ozone between
10∘ S–10∘ N throughout the troposphere using the new scheme, while
that in the northern high latitudes below 6 km remains unaffected. In the
Northern Hemisphere, the new scheme tends to overestimate ozone within
10–50∘ N below ∼9 km; this is where there was
already some overprediction by the PR92 scheme. In this region, even when
LNOx is not included in the model (Fig. 15d),
the model–data differences are either small or there is some overestimation
(near the surface) of the observed ozone. This suggests that there are
likely to be factors other than LNOx responsible for the predicted
overestimation within 10–50∘ N. Additional factors that
influence tropospheric ozone distribution in the model include dynamics,
including interhemispheric mixing and stratosphere-to-troposphere exchange,
precursor emissions, and how chemical mechanisms are represented.
Considering the above, we can say that the new flash-rate scheme leads the
modelled tropospheric ozone in the right direction, which is also supported
by the fact that it causes the tropospheric ozone burden to improve, as
stated above. 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).
The volume-weighted tropospheric O3 obtained from the PR92 scheme is
51.5 ppbv over the globe, 48.8 ppbv over the ocean, and 56.6 ppbv over land.
With the new flash-rate scheme, these values increase by 4.1 ppbv (8.0 %),
4.4 ppbv (9.1 %), and 3.6 ppbv (6.3 %), respectively, and can be compared
with the values 38.7, 36.2, and 43.4 ppbv, respectively, obtained from the
model simulation with no LNOx emissions.
Hydroxyl radical
OH is the dominant oxidising (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, 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.
Zonal annual-mean tropospheric OH (×105 molecules cm-3)
modelled using (a) the default PR92 parameterisations (Run 1) and
(b) the new lightning flash-rate parameterisations from this study (Run 2).
The difference between Run 2 and Run 1 is shown in panel (c).
The modelled zonal total annual-mean tropospheric OH in
Fig. 16 shows highest OH concentrations near the
surface in the tropics, with values as high as (25–30) × 105 molecules cm-3 at ∼20∘ 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
(Fig. 16c), particularly in the upper troposphere
in the tropics, by as much as 5×105 molecules cm-3.
Mean relative difference (%) between the hydroxyl radical (OH)
predicted using the new lightning flash-rate parameterisations (Run 2) and
the default PR92 parameterisations (Run 1): (a) at 20 m (the lowest model
level) and (b) at 6400 m (∼450 hPa).
The annual-mean relative OH difference (%) between Run 2 and Run 1 near
the surface (Fig. 17a) shows an increase in OH
over the Southern Hemisphere oceans and Antarctica, and pockets of increase
and slight decrease in the Northern Hemisphere. In the mid-troposphere, at a
model height of 6.4 km (∼450 hPa) (Fig. 17b), there are large areas showing an increase in OH by up to 20 %–25 %
with the new flash-rate parameterisations, particularly in the tropics and
Southern Hemisphere. The broad hemispheric differences in OH are
qualitatively similar to those for O3. With an increase in NO due to
the new flash-rate parameterisation, OH increases (e.g. via the recycling of
HO2 by reaction with NO). In highly polluted air, NO2 can be an OH
sink (Lelieveld et al., 2016). Of course, transport would also influence
these patterns, both horizontally and vertically.
Overall, we find that, with the new flash-rate parameterisations, there is a
13 % increase in the annual-average volume-weighted global tropospheric
OH, from 10.6×105 to 12.0×105 molecules cm-3.
The increase over the ocean is by 1.6×105
(16.3 %) and that over land by 0.9×105 molecules cm-3
(7.6 %). For comparison, the respective annual-average values obtained for the globe, ocean, and land from the model
simulation with zero LNOx emissions are 7.6×105, 7.3×105,
and 8.1×105 molecules cm-3.
The global amount can be compared with the ACCMIP multi-model mean of 11.1±1.6×105 molecules cm-3 derived by Naik et al. (2013)
for the year 2000. Recent observationally based values reported by
Wolfe et al. (2019) for August 2016 are 12.6±2.9×105
for the Northern Hemisphere and 8.1±1.9×105 molecules cm-3
for the Southern Hemisphere, and these for February 2017
are 8.8±2.1×105 and 11.4±2.8×105 molecules cm-3, respectively. These can be compared with the
corresponding modelled values 16.9×105, 7.3×105, 8.0×105, and 11.6×105 using the PR92 scheme, and 18.7×105, 8.5×105, 9.2×105, and 13.5×105 molecules cm-3
using the new scheme. The LNOx-induced increase in
OH due to the new scheme adds to the model high bias in the OH burden in
summer, whereas it reduces the magnitude of the bias in winter with the bias
shifting from low to high. 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 (Archibald et al.,
2020).
The surface methane concentrations were prescribed in the model and methane
was allowed to undergo loss processes in the rest of the atmosphere. 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 (τCH4_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. This value without the LNO emissions in the model is
9.2 years. The modelled methane lifetime is lower than the multi-model mean
9.7±1.5 years reported by Naik et al. (2013), which could be due to
a higher tropospheric burden of non-lightening-related NOx in
ACCESS-UKCA and/or a more intense photolysis.
The difference between the zonal total annual-mean tropospheric
CO (ppbv) modelled using the new lightning flash-rate
parameterisations (Run 2) and the default PR92 parameterisations (Run 1).
Carbon monoxide
There is a decrease in the modelled total tropospheric CO
with the use of the new lightning parameterisations, as evident from the
zonal annual-mean difference plot in Fig. 18 (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 ppbv (∼7 %) in the Southern Hemisphere and
2–4 ppbv (∼3 %) in the Northern Hemisphere. This reduction gets a little
larger in the middle to upper troposphere in the tropics. Overall, the
reduction in the volume-weighted global CO is 4.5 ppbv (5.6 %). Over the
ocean, it is 4.7 ppbv (6.2 %) and over land it is 4.0 ppbv (4.5 %). The
volume-weighted tropospheric CO obtained from the PR92 scheme is 80.3 ppbv
over the globe, 75.4 ppbv over the ocean, and 89.9 ppbv over land. With the new
flash-rate scheme, these values decrease by 4.5 ppbv (5.6 %), 4.7 ppbv
(6.2 %), and 4.0 ppbv (4.5 %), respectively, and can be compared with the
values 96.4, 91.8, and 105.4 ppbv, respectively, obtained from the model
simulation with no LNOx emissions.
Comparison of the modelled monthly averaged CO concentrations
(ppbv) with observations at four oceanic/coastal ground stations
for the year 2006. The two model runs are with the default PR92
parameterisations (Run 1) and new lightning flash-rate parameterisations
(Run 2). The values of r and NMSE are also shown.
In Fig. 19, we compare the modelled
monthly averaged CO with surface flask observations from the same GAW-WDCRG
sites as in Fig. 12 (data from Minamitorishima
were missing for 4 months, so they are not presented). With the use of the new
lightning parameterisation, the relative change in the modelled
yearly averaged CO at Ushuaia, Cape Grim, Mauna Loa, and Mace Head is -8.1 %,
-9.8 %, -3.8 %, and -0.3 %, respectively. The modelled ground-level CO
is affected only very marginally by the flash-rate modification compared to
the magnitude of the model–data differences, except at Ushuaia and at Cape
Grim during the austral summer. Clearly, as in the case of ground-level
O3, the lightning changes alone do not reconcile the differences
between the modelled CO and observations.
Model simulations with meteorological nudging
As mentioned in Sect. 3.5, we also did Run 1 (PR92) and Run 2 (TS1) with
meteorological nudging (which could impact convection indirectly in the
model) with the same initial conditions as for the free-running simulations.
Broadly speaking, the results were not too different from the respective
free-running simulation results for the year 2006 reported above. The
averaged global, land, and ocean flash rates obtained from Run 1 with nudging
were 32.87, 32.50, and 0.37 flashes s-1, respectively, which are very
similar to 32.92, 32.56, and 0.36 flashes s-1, respectively, obtained
from the free-running Run 1 in Table 1. These
obtained from Run 2 with nudging were 46.88, 36.80, and 10.08 flashes s-1,
respectively, which are on average 5 % higher than 44.96, 35.88,
and 9.08 flashes s-1, respectively, obtained from the free-running Run 2 in Table 1 (so a scaling factor of 0.95 would make
the nudged model flash rates approximately match the free-running model
flash rates). The total LNOx produced over the globe, land, and ocean
changed in the same proportions since the NO produced per flash was the
same.
The annual-averaged global spatial distributions of the modelled flash rate
with nudging for both runs were very similar to the respective free-running
model plots shown in Fig. 5c and
d, with the overall spatial correlation with
the LIS/OTD satellite climatology (Fig. 5a)
slightly improved from 0.72 to 0.75, and some improvement in the model
performance over the Indian subcontinent but a slight deterioration over the
southern US. Nudging would have an impact on tropospheric composition, which
we have not presently investigated, but we estimate that with flash rate
constrained the modelled tropospheric composition with and without nudging
would, on average, be within ∼5 %.
Conclusions
We have critically examined parameterisations of lightning flash rate that
are based on the cloud-top-height approach. Testing of the widely used Price
and Rind (1992) (PR92) parameterisations within the ACCESS-UKCA global
chemistry–climate 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 proportionally over the ocean and thus influencing
tropospheric composition. Any interannual variability in lightning was not
investigated.
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 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. There is a large uncertainty
in the amount of NO produced per flash in the scientific literature. The
model's use of 330 moles NO produced per flash is relatively close to the average value
310 moles NO per flash determined by Miyazaki et al. (2014) using data
assimilation but requires better constraining.
The use of the new flash-rate parameterisations in ACCESS-UKCA demonstrated
a considerable impact on the modelled tropospheric composition compared to
the default PR92 parameterisations, mainly due to the change in the oceanic
flash-rate component. In particular, the following impacts were observed.
There was an increase in the mid- to upper-tropospheric NOx by as much as 40 pptv
(as NO2) in the northern tropics. There was an overall increase in the
global NOx by 8.7 pptv (15.7 %) and by 9.9 pptv (28.0 %) over the
ocean. A better agreement was yielded of the modelled tropospheric NO2 columns with
the CAMS reanalysis data over the ocean.
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
somewhat compared to global observations in the Southern Hemisphere.
There
are considerable ozone biases in the model in the Northern Hemisphere that
are not related to LNOx.
There was a 13 % increase in the annual-average volume-weighted global tropospheric
OH, from 10.6×105 to 12.0×105 molecules cm-3, and
a decrease in the global annual-mean methane lifetime against loss by
tropospheric OH by 6.7 %.
There was an overall reduction in the global CO by 4.5 ppbv (5.6 %).
The approach of parameterising lightning flash rate in terms of convective
cloud-top height works well given its simplicity 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-fifth-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.
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
CAPE and precipitation-rate-based parameterisations (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 decrease in future lightning flash density
(under the RCP8.5 scenario). The study of Finney et al. (2018) argues that
the ice flux method performs better than the PR92 cloud-top-height method,
and this should be reanalysed using the scheme proposed here which
drastically alters the flash rate over the ocean. In addition, there is an
existing uncertainty as to which physical parameterisation approach best
represents the reality and the feedbacks that are important for lightning
under climate change. This will be difficult, as parameters such as cloud ice
content and/or updraught mass flux used in flux-based lightning schemes are
poorly constrained by available observations.
Code availability
The model used for this study is a licensed product of the UK Met Office and is available to specific users under a license agreement.
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 the corresponding author (Ashok Luhar: ashok.luhar@csiro.au). The observational datasets used in the present
study were available from the following sources: the LIS/OTD lightning flash
data (Cecil et al., 2014) from https://lightning.nsstc.nasa.gov/data/data_lis-otd-climatology.html (last access:
6 May 2021), monthly mean vertical ozone profile data (Hassler et al., 2009) from
http://www.bodekerscientific.com/data/monthly-mean-global-vertically-resolved-ozone (last
access: 6 May 2021),
surface ozone and CO data from https://www.gaw-wdcrg.org (last access: 6 May 2021),
ERA-Interim global reanalysis data (Dee et al., 2011) from https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim
(last access: 6 May 2021),
SHADOZ ozonesonde measurements (Witte et al., 2017) from https://tropo.gsfc.nasa.gov/shadoz (last access:
6 May 2021), OMI NO2 column data (Boersma et al., 2018) from
https://www.temis.nl/airpollution/no2.php (last access: 6 May 2021), and CAMS global
reanalysis data (Inness et al., 2019) from https://ads.atmosphere.copernicus.eu/cdsapp#!/dataset/cams-global-reanalysis-eac4-monthly
(last access: 6 May 2021).
Author contributions
AKL designed the study, performed the flash-rate parameterisation formulation
and model runs, analysed model output and data, and wrote the paper with
contributions and comments from all co-authors. IEG assisted with the
flash-rate parameterisations and advised on various components of the paper,
MTW performed some of the early model–data comparison for atmospheric
composition and advised on the model setup, and NLA advised on the model
configuration and provided relevant technical details on UM-UKCA.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This research was undertaken with the assistance of resources and services
from the National Computational Infrastructure (NCI), which is supported by
the Australian government. Martin Dix of CSIRO is acknowledged for his help
with model configuration issues. Fiona O'Connor and Mohit Dalvi of the UK
Met Office are thanked for their assistance with the UKCA emission
methodology and for answering questions about UM-UKCA in the early stages of
model implementation. We would like to thank Bodeker Scientific, funded by
the New Zealand Deep South National Science Challenge, for providing the
Bodeker Scientific vertically resolved ozone database. Surface ozone and CO
data from the World Data Centre for Reactive Gases, tropospheric NO2
column data from the OMI sensor from the Tropospheric Emission Monitoring
Internet Service (TEMIS), ERA-Interim data from the European Centre for
Medium-Range Weather Forecasts (ECMWF), Copernicus' CAMS global
reanalysis (EAC4) data, and ozonesonde data from the SHADOZ networks were used in this research. Useful comments by the
three anonymous referees and Fraser Dennison, and a short comment by
Declan Finney, are much appreciated. We thank Kazuyuki Miyazaki for supplying the
data corresponding to a diagram in Miyazaki et al. (2014).
Review statement
This paper was edited by Ronald Cohen and reviewed by three anonymous referees.
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