Atmospheric information embedded in ice-core nitrate is disturbed by
post-depositional processing. Here we used a layered snow photochemical column
model to explicitly investigate the effects of post-depositional processing on
snow nitrate and its isotopes (δ15N and Δ17O)
at Summit, Greenland, where post-depositional processing was thought to be
minimal due to the high snow accumulation rate. We found significant
redistribution of nitrate in the upper snowpack through photolysis, and up to
21 % of nitrate was lost and/or redistributed after deposition. The model
indicates post-depositional processing can reproduce much of the observed
δ15N seasonality, while seasonal variations in
δ15N of primary nitrate are needed to reconcile the timing of
the lowest seasonal δ15N. In contrast, post-depositional
processing can only induce less than 2.1 ‰ seasonal
Δ17O change, much smaller than the observation
(9 ‰) that is ultimately determined by seasonal differences in
nitrate formation pathway. Despite significant redistribution of snow nitrate
in the photic zone and the associated effects on δ15N
seasonality, the net annual effect of post-depositional processing is
relatively small, suggesting preservation of atmospheric signals at the annual
scale under the present Summit conditions. But at longer timescales when large
changes in snow accumulation rate occur this post-depositional processing
could become a major driver of the δ15N variability in ice-core nitrate.
Introduction
Nitrate (NO3-) is one of the most abundant and commonly measured
species in ice cores. One of the major subjects of ice-core nitrate studies
involves its oxygen isotope mass-independent fractionation signal
(Δ17O=δ18O-0.52×δ17O), which is a proxy of atmospheric oxidation capacity
(Alexander and Mickley, 2015; Alexander et al., 2004; Geng et al.,
2017). Ice-core δ15N(NO3-) records have also been
studied, but the interpretation remains immature and sometimes conflicting
(Freyer et al., 1996; Geng et al., 2014a, 2015; Hasting et al., 2005,
2009). There are many factors, e.g., NOx sources, atmospheric chemistry
and transport, deposition, and post-depositional processing of nitrate,
affecting ice-core nitrate and its isotopes (Geng et al., 2014a, 2015; Hastings
et al., 2004, 2005; Morin et al., 2008; Wolff et al., 2008).
Deposition of atmospheric nitrate to snow is not irreversible. The ultimate
source of snow nitrate in the polar regions is from tropospheric long-range
transport and stratospheric denitrification (Goto-Azuma and Koerner, 2001;
Legrand and Delmas, 1986), which can be termed as primary nitrate
(Fpri) (Erbland et al., 2013). After deposition, nitrate undergoes
post-depositional processing which causes changes in its concentration and
isotopes (Blunier et al., 2005; Erbland et al., 2013; Frey et al., 2009).
Post-depositional processing of snow nitrate includes physical release (i.e.,
desorption and evaporation) and ultraviolet photolysis. Both processes result
in loss of snow nitrate and isotope fractionations of nitrogen and
oxygen. However, laboratory experiments and model calculations indicate a
minor influence of the physical processes, with photolysis dominating
post-depositional processing (Berhanu et al., 2014; Erbland et al., 2013; Frey
et al., 2009; Zatko et al., 2016).
Snow nitrate photolysis occurs when it is exposed to sunlight at wavelengths
less than 345 nm (Chu and Anastasio, 2003). The dominant photolysis
product is NO2, which is effectively transported to the overlying
atmosphere via diffusion or wind pumping (Zatko et al., 2013) and impacts the
local atmospheric oxidation environment (Thomas et al., 2012). The released
NO2 can reform HNO3 (i.e., the snow-sourced nitrate
hereafter) in the overlaying atmosphere, which is then redeposited to or
exported from the site of photolysis. The above-mentioned processes form a
cycle of nitrate between the air–snow interface, resulting in the redistribution
of nitrate in snowpack.
The photolysis also causes isotope fractionation. The isotope fractionation
factors (εp) associated with snow nitrate photolysis are
-47.9±6.8‰ and -34 ‰ for
δ15N and δ18O, respectively, for local
conditions at Dome C, East Antarctica (Berhanu et al., 2014; Blunier et al.,
2005; Frey et al., 2009). These large negative values indicate the photolysis
would enrich nitrate remaining in snow with heavier isotopes (i.e., 15N
and 18O). In comparison, Δ17O(NO3-) in snow will not
be directly disturbed by photolysis. However, part of the photoproduct can
undergo recombination reactions within snow grains to reform nitrate (i.e.,
the cage effect) (McCabe et al., 2005; Meusinger et al., 2014). This process
results in exchanges in oxygen atoms with snow and decreasing
Δ17O(NO3-) and δ18O(NO3-). In
addition, once the photoproduct NO2 is released to the overlying
atmosphere, it is rapidly converted to nitrate and carries different
Δ17O(NO3-) values from its precursors. These isotope
effects have been documented in multiple snowpack studies on the East
Antarctic Plateau, with increasing δ15N and decreasing
Δ17O(NO3-)/δ18O(NO3-) with depth
(Erbland et al., 2013; Frey et al., 2009; Shi et al., 2015).
The degree of post-depositional processing and the induced effects on snow
nitrate and isotopes vary site by site, depending on several factors including
actinic flux, snow properties (e.g., density, light-absorbing impurities,
specific surface area) and snow accumulation rate (Zatko et al.,
2013). Actinic flux describes the light intensity reaching the snow surface, while
snow properties determine the penetration of light in snow. Actinic flux
decreases exponentially from the snow surface, and the depth of the snow
photic zone is defined as 3 times the e-folding depth of the actinic flux
(Erbland et al., 2013). Snow accumulation rate determines the residence time
of nitrate in the photic zone where photolysis occurs, and thus at sites with
high snow accumulation rate the degree of post-depositional processing will be
limited (Erbland et al., 2013; Noro et al., 2018; Shi et al., 2015).
Summit, Greenland, is a typical high snow accumulation site
(250 kgm-2a-1; Dibb and Fahnestock, 2004), where snowpack and ice-core nitrate isotope records have been studied, but the interpretation of
δ15N remains conflicting (Geng et al., 2014a, 2015; Hastings
et al., 2005, 2009). Hastings et al. (2005) proposed the glacial–interglacial
δ15N difference observed in the GISP2 ice core was due to
changes in NOx source strengths despite the fact that there is no known NOx
source carrying high enough δ15N to explain the glacial
δ15N value (28.4±1.1 ‰). In contrast, Geng
et al. (2015) concluded that changes in the degree of post-depositional
processing between the glacial and interglacial climates can explain the more
enriched δ15N in the glacial period. On seasonal timescales,
there are also distinct variations in nitrate δ15N and
Δ17O at Summit (Geng et al., 2014b; Hastings et al., 2004;
Jarvis et al., 2009; Kunasek et al., 2008). The seasonality of
δ15N was originally attributed to variations in NOx
sources (Hastings et al., 2004), and the Δ17O was suggested to be
mainly caused by changes in atmospheric nitrate formation pathways (Kunasek
et al., 2008). However, the effect of post-depositional processing on seasonal
δ15N variation was not thoughtfully examined by Hastings
et al. (2004). Two later studies by Fibiger et al. (2013, 2016) examined
nitrate isotopes in the atmosphere and surface snow (<3cm depth)
at Summit to investigate the effects of post-depositional processing, and
they concluded that the effects of post-depositional processing on nitrate isotope
preservation is negligible. These studies, however, relied only on surface
snow samples and did not cover a full year of nitrate deposition. The snow
photic zone at Summit is 30 to 40 cm deep (Galbavy et al., 2007), and
thus surface snow samples cannot readily reflect the full degree of
post-depositional processing as the effects increase with time in the snow
photic zone and thus depth. In particular, Fibiger et al. (2013) used the
observed linear relationship between surface snow
Δ17O(NO3-) and δ18O(NO3-) to exclude
the effects of post-depositional processing on nitrate isotopes at Summit,
Greenland. This approach is flawed as neither δ18O(NO3-)
nor Δ17O(NO3-) is a good indicator of post-depositional
processing because the oxygen isotopes are mainly controlled by atmospheric
processes (Alexander et al., 2020; Kunasek et al., 2008). This is why a strong
linear relationship between Δ17O(NO3-) and
δ18O(NO3-) is observed in atmospheric and surface snow
samples at Dome C, Antarctica, where severe post-depositional processing of
nitrate occurs (Erbland et al., 2013; Frey et al., 2009). At sites with
extremely low snow accumulation rates (e.g., Dome C and Dome A in Antarctica)
the cage effect would cause apparent changes in δ18O(NO3-) and Δ17O(NO3-) in samples at
depth but not at the surface (Erbland et al., 2013; Shi et al., 2015).
Given the distinct seasonal differences in actinic flux in the polar regions
including Summit, Greenland, seasonal differences in the degree of
post-depositional processing and its effects on snow nitrate isotopes should
be examined. In fact, observations at Summit indicate that δ15N
in surface snow nitrate is negative during most of the year with an annual
mean of -6.2±1.1 ‰ (Jarvis et al., 2009), while in bulk
snowpack (0 to 1 m) the annual mean δ15N is 0±2.4 ‰ (Jarvis et al., 2009) and 0±6.3 ‰ (Geng
et al., 2014b). During spring and summer when snow photochemistry is most
active, δ15N in surface snow is -5.8±0.7 ‰,
while in snowpack (average of two springs at depths of 0.15 and 0.9 m) is 5.6±1.8 ‰. These differences between nitrate
at the surface and at depth suggest enrichment in nitrate δ15N
after deposition and recycling at the surface, and they are consistent with the
known isotope effects of post-depositional processing. In addition, Burkhart
et al. (2004) and Dibb et al. (2007) have observed <7 % to 25 %
loss of nitrate after deposition at Summit. This is close to the estimate of
16 %–23 % loss based on ice-core δ15N(NO3-)
(Geng et al., 2015). These results are also qualitatively consistent with the
observations of NO2 and HONO fluxes from snowpack at Summit which
were attributed to snow nitrate photolysis (Dibb et al., 2002; Honrath et al.,
2002). The spatial variations in the photo-driven nitrate recycling at the
air–snow interface and its impact on snow δ15N(NO3-) in
Greenland have been studied by Zatko et al. (2016) using a global 3-D chemical
transport model (GEOS-Chem). Their model captures the increasing trend in
snow δ15N(NO3-) from the coast to inland as snow
accumulation rate decreases, which enhances the degree of post-depositional
processing. This is consistent with field studies of snow nitrate δ15N(NO3-) in West Greenland (Curtis et al., 2018). But the model
treated snowpack as a whole and did not specify the behaviors of nitrate at
different depths in the photic zone, and it cannot distinguish seasonal
differences. In addition, it did not incorporate isotope fractionation
associated with photolysis but instead using a fixed fractionation constant
and a Rayleigh fractionation model to calculate the changes in isotope with
mass loss.
In order to investigate the impacts of snow nitrate photolysis on the
preservation of nitrate and its isotopes on the seasonal timescale at Summit,
Greenland, we used a snow photochemical column model to simulate the recycling
of nitrate at the air–snow interface. We use the model to quantify to what
degree the magnitude of the observed seasonality of nitrate isotopes at Summit
can be explained by post-depositional processing. The model was built to
explicitly investigate the loss of snow nitrate due to photolysis and quantify
the induced isotope effects with layer specific calculations (i.e., changes in
δ15N and Δ17O after deposition). A comparison of
the model results with observations should add insight into the preservation
of nitrate at high snow accumulation sites and shed light on the
interpretation of ice-core nitrate and its isotopes.
Model description
TRANSITS (TRansfer of Atmospheric Nitrate Stable Isotopes To the Snow) is a
multi-layer, 1-D model that simulates nitrate recycling at the air–snow
interface and its preservation in snow including its isotopes (Erbland
et al., 2015). The model divides a year into 52 time steps (i.e., weekly
resolution), and at each step the snowpack is divided into 1 mm layers
in which photolysis of nitrate is calculated according to the depth-dependent
actinic flux and nitrate concentration. The produced NO2 is
transported to the overlying atmosphere where it is re-oxidized to nitrate. At
the next time step, a portion of the reformed nitrate together with primary
nitrate originating from long-range transport is deposited onto the snow surface. When
snowfall occurs, the snowpack moves down, and the newly deposited snow is
immediately re-divided into 1 mm layers. Nitrate is considered as
archived once it is buried below the photic zone.
At each step, the model also calculates the isotope effects. In the model,
nitrogen isotope fractionation mainly occurs during the photolysis with a
wavelength-sensitive fractionation constant εp, and another
fractionation occurs during nitrate deposition with a fractionation constant
εd. The oxygen isotope effect is only calculated for
Δ17O, which is caused by (1) exchange of oxygen atoms with
water during the photolysis (i.e., the cage effect) and (2) local atmospheric
NO–NO2 cycling and the subsequent conversion of NO2 to
HNO3.
To run the model, actinic flux and its e-folding depth in snowpack, snow
accumulation rate, and other atmospheric properties including the
boundary layer height, surface ozone and HOx concentrations are needed.
Additional model inputs are the flux of primary nitrate from long-range
transport and its isotopic composition (i.e., δ15N and
Δ17O). In this study we focus on the seasonal changes in
isotopes caused by post-depositional processing, making the results
independent of δ15N and Δ17O of primary nitrate.
In this study, we run the model from the year 2004 to 2007 constrained by
local observations at Summit. The modeled snow nitrate concentration and
isotope profiles were compared with observations in Geng et al. (2014b).
Model inputsAtmospheric characterizations
The overlying atmosphere at Summit was assumed to be a 1-D box
with a constant boundary layer height of 156 m (Cohen et al., 2007),
where primary and the snow-sourced nitrate are assumed to be well
mixed. Weekly air temperature, pressure, surface ozone concentration and total
column ozone (TCO) at Summit were obtained from the NOAA ozonesonde dataset
(https://gml.noaa.gov/aftp/ozwv/Ozonesonde/, last access: 1 September 2021). Concentrations of local atmospheric oxidants including
O3, OH, peroxyl radicals and BrO are needed to calculate the cycling
of NO–NO2 and the conversion of NO2 to HNO3. At
Summit, there are no long-term observations of OH and peroxyl radicals
(RO2, HO2) which are necessary to calculate the
atmospheric transformation of NOx to HNO3, so we estimated
their mixing ratio by assuming a linear relationship with local
J(NO2). More specifically, the photolysis rate constants of NO2
were first calculated using local actinic flux, and the concentrations of OH
and peroxyl radicals were calculated by assuming their linear relationships
with J(NO2) (Kukui et al., 2014). Diurnal observations of
OH and peroxyl radicals exist at Summit with noon values of 6.3×106
and 2.4×108molec.cm-3 (Sjostedt et al., 2007),
respectively. We used these values to justify the calculated OH and peroxyl
radical values by applying scaling factors to match them with the
observations. We set a constant BrO concentration of 2 pptv (parts per trillion volume) in summer
and zero in other seasons, given the observed summer BrO concentration
(1–3 pptv) at Summit (Fibiger et al., 2016).
The mass balance of nitrate in snowpack and the overlying atmosphere is
controlled by nitrate flux in and out of the snow. We denote the nitrate
fluxes as “FY” following Erbland et al. (2015), with Fpri, FP,
FD and FA representing the primary nitrate flux from long-range transport, the
nitrate flux that originates from photolysis of snow nitrate, the deposition
flux (FD) of atmospheric nitrate and the archived snow nitrate flux that is buried
under the photic zone, respectively. These fluxes determine the variations in
snow and atmospheric nitrate and their isotope compositions.
Radiative transfer and nitrate photolysis rate in snow
Downward/upward actinic flux spectrum at the snow surface was calculated using
the Troposphere Ultraviolet and Visible (TUV) radiation model (Madronich
et al., 1998) constrained by TCO. Radiative transfer inside the snowpack was
then computed using the Two-stream Analytical Radiative TransfEr in Snow
(TARTES) model (Libois et al., 2013). The attenuation of light in snow is
characterized by its e-folding depth, which represents the depth where
radiation decreases to 1/e of the surface intensity. Snow e-folding depth
depends on its optical properties (e.g., bulk density, snow grain size) and on
the concentrations of light-absorbing impurities (Zatko et al., 2013). In this
study, for simplification, we set constant snowpack concentrations of the
three main snow light-absorbing impurities – soot, dust and organic humic-like
substance (HULIS) – at 1.4, 138 and 31 ngg-1, respectively (Zatko
et al., 2013; Carmagnola et al., 2013). Snow density and grain size also impact
the e-folding depth. The snow radiation equivalent mean grain radius
(re) is linked to the specific surface area (SSA) of snow grains
by re=3/(SSA×ρice). Since direct
observations of SSA of the reported snowpack in Geng et al. (2004b) are lacking
and only density profile data exist, we used the regression relationship
between SSA and ρsnow (SSA=-174.13×ln(ρsnow)+306.4, in units of cm2g-1 for SSA and
gcm-3 for density) from Domine et al. (2007) to
calculate SSA. Using the observed snow density, fixed light-absorbing impurity
concentrations and the calculated SSA profile, we obtained an e-folding depth
of 12.3 cm (at a wavelength of 305 nm, which is the peak
wavelength of nitrate photolysis) that is similar to the measured average
summer midday value (11.6 cm) at Summit (Galbavy et al., 2007) but
lower than the modeled result (15–17 cm) by Zatko
et al. (2013). Note Zatko et al. (2013) applied the measured snow
re profile at Dome C to Summit conditions with SSA ranging from 7
to 38 m2kg-1, which was lower than our calculated SSA of 44 to
51 m2kg-1. This likely explains why our calculated e-folding
depth was smaller than Zatko et al. (2013) despite using the same impurity
content. We also note that the regression relationship between SSA and ρ snow from Domine et al. (2007) was for fresh snow, which may not be suitable
for SSA prediction for the whole snowpack. However, using this equation
yielded an e-folding depth that is similar to the observations by Galbavy
et al. (2007) despite the yielded SSA appearing to be larger than the observed
values (20 to 40 m2kg-1) by Carmagnola et al. (2013) for a
Summit snowpack which has a much lower snow density (averaged
330 kgm-3 in the top 50 cm) than ours (averaged
395 kgm-3). Nevertheless, given the uncertainties related to the
calculation of snow radiative transfer that are currently not well
constrained, the regression relationship between SSA and ρ snow used here
yielded a reasonable e-folding depth similar to the observations. Improvements
can be made if snow physicochemical properties (e.g., SSA, density and
impurity concentrations) can be precisely well constrained by future
observations.
The photolysis rate constant of snow NO3- was calculated by the following:
J(z)=∫280nm350nmΦ(λ)×σNO3-(λ)×I(z,λ)dλ,
where I is actinic flux, and Φ and σ are the quantum yield and
absorption cross section of nitrate photolysis, respectively. The absorption
cross sections of 14NO3- and 15NO3- were
from Berhanu et al. (2014). In this study, we used the measured surface snow
nitrate photolysis rate constant j0(NO3-) (Galbavy et al.,
2007) to constrain the quantum yield at Summit. Galbavy et al. (2007) reported
that j0(NO3-) in surface snow at summer noon generally falls
in the range of 1–2×10-7s-1 with a mean value of
1.1×10-7s-1. This value corresponds to a quantum yield
of 0.002 given typical Summit summer column ozone density (350 DU) and
noon solar zenith angle (50∘). We adopted this value of quantum yield
in our model, and, according to summer actinic flux, its penetration in
snowpack and snow nitrate concentration at Summit, we calculated a summer mean
NOx flux from the snowpack of 2.96±0.3×1012molec.m-2s-1 that is close to the observation of
2.52×1012molec.m-2s-1 by Honrath
et al. (2002).
Flux of primary nitrate (<inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mtext>pri</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) and the export fraction
Primary nitrate from long-range transport was assumed to be the only external
nitrate source for Summit. Given the mean snow accumulation rate
(250 kgm-2a-1) and the mean snowpack nitrate concentration
(117 ngg-1) at Summit, a minimum annual Fpri of
6.6×10-6kgNm2a-1 was estimated and used in the
model. This value is at the same order of magnitude (≈2×10-6kgNm2a-1) as that modeled by Zatko et al. (2016). The
seasonal variability in Fpri was adjusted to 1.6×10-6,
2.1×10-6, 1.6×10-6 and 1.2×10-6kgNm-2 per season for spring, summer, autumn and
winter, respectively, according to back-trajectory analyses and a regional
emission inventory (Iizuka et al., 2018). The values and seasonal variations
in δ15N and Δ17O of Fpri are
currently unknown. We set δ15N and Δ17O of
Fpri at 0 and 30 ‰ (close to their average values in
snowpack), respectively, throughout the year. This has the advantage of the
model explicitly assessing the effects of the photolysis while excluding other
influencing factors. In addition, previous studies proposed δ15N of snow nitrate at Summit should reflect δ15N of
NOx sources (Hasting el al., 2004, 2005); thus, in order to investigate
the sensitivity of snowpack δ15N(NO3-) to
δ15N of Fpri, we also used the measured
δ15N in surface snow nitrate at Summit that varies seasonally
(Jarvis et al., 2009) as a first-order estimation of δ15N of
Fpri. Note this may underestimate δ15N of
Fpri as surface snow nitrate could be influenced by snow-sourced
nitrate that is in general depleted of δ15N. Nevertheless, we
note that δ15N and Δ17O of Fpri are
just starting points to run the model, and the predicted changes caused by
post-depositional processing are independent of these values.
Another parameter influencing the preservation of nitrate is the export
fraction, fexp, which represents the fraction of the snow-sourced
NOx and nitrate transported away from the site of photolysis. At the site
of photolysis, part of the reformed nitrate in the atmosphere will be exported,
and this represents the net loss of nitrate through the post-depositional
processing. We estimated the export fraction (fexp) following the
method used by Erbland et al. (2015):
fexp=1τ21τ1+1τ2×1+1τ11τ3+1τ1,
where τ1, τ2 and τ3 denote the lifetimes of horizontal
transport, oxidation of NO2 by OH radicals and vertical deposition,
respectively. τ1, τ2 and τ3 were calculated as
follows:
3τ1=Lvh,4τ2=1kOH,5τ3=Hvd,
where Hand L represent the vertical and horizontal characteristic
dimensions of 156 m (average summer boundary layer height at Summit)
and 350 km (characteristic length of summit of the Greenland ice cap;
Honrath et al., 2002), respectively, vh is the mean horizontal
wind speed at Summit (5 ms-1), vd is the dry
deposition velocity of HNO3 (0.63 cms-1) (Björkman
et al., 2013), and k is the kinetic rate constant as a function of temperature
and pressure for NO2+OH→HNO3 (3×10-12cm3molec.-1s-1 on
average in summer; Atkinson et al., 2004). From Eq. (2) we obtained a value of
0.35 for fexp in summer conditions and kept it constant in the
model simulations. Note this value is irrelevant in winter when photolysis
stops; therefore, there is no need to consider the seasonal difference of
fexp. In addition, we note the fexp calculated from
the above equations is just a rough estimate as it may oversimplify the
processes governing nitrate deposition and chemical loss pathways of
NOx. The sensitivity of model results to fexp is discussed in
Sect. 3.3.
Calculation of the isotope effects
The nitrogen isotope fractionation constant (15εp) during
photolysis was calculated from the ratio of 14NO3- and
15NO3- photolysis rates in each snow layer
(15εp=J15/J14-1). The deposition of atmosphere
nitrate can induce isotope fractionation (εd) in
δ15N based on simultaneous measurements of atmospheric and
surface δ15N(NO3-) (Erbland et al., 2013; Fibiger et al.,
2016). Fibiger et al. (2016) suggested that at Summit the fresh snow
NO3- is enriched in δ15N by +13 ‰
compared to atmospheric NO3-, similar to the observation at Dome
C, Antarctica (+10 ‰, Erbland et al., 2013). In contrast,
Jarvis et al. (2009) found no difference in δ15N of gas-phase
HNO3 and surface snow NO3- at Summit. Here we followed
Erbland et al. (2013) to set εd at
+10 ‰. We did not use the results from Fibiger et al. (2013)
whose study was conducted in spring when photolysis of snow nitrate had already
started and disturbed the connection between atmospheric nitrate and that in
surface snow. For oxygen isotopes, the Δ17O of the reformed
nitrate in the air was assumed to be 2/3 of Δ17O(NO2),
which assumes that NO2+OH is the dominant nitrate production mechanism
under sunlight. Δ17O(NO2) was estimated according to
the relative importance of O3 and BrO versus HO2 and
RO2 oxidation of NO to NO2. The Δ17O value
of bulk O3 is taken at 26 ‰ (Vicars and Savarino,
2014), that of BrO is 39 ‰, and other oxidants are
0 ‰. We assumed a cage effect of 15 % following Erbland
et al. (2015).
Model initiation
The model was initiated by deposition of primary nitrate mixed with
snow-sourced nitrate. A real snowpack with a depth of 2.1 m and known
nitrate concentration and isotope profiles (Geng et al., 2014b) was set at time
(t)=0. Weekly snow accumulation rate was obtained by averaging the
observed snow accumulation of the same week (week 1 to week 52) of a year
over 2003 to 2007 at Summit. Average instead of real accumulation data were
used to avoid negative values in some weeks due to wind blowing which causes
net loss instead of gain of snow. After a 3-year simulation, the snow
nitrate concentration and isotope profiles above the pre-existing snowpack
were sampled from the model to compare with the observations from Geng
et al. (2014b). All parameters needed to run the model are listed in Table S1.
Results and discussionThe simulated snowpack nitrate depth profiles at Summit, Greenland
The observed and modeled snowpack nitrate concentration and its isotopes
(i.e., δ15N and Δ17O) from July 2004 to 2007 are
plotted in Fig. 1. The observations were from a snow pit collected in July
2007 so that the top of the observed profiles represents a summer, and we used
the observed Δ17O minimum and concentration maximum to identify
other summers to match the modeled profiles with the observations. In
addition, the depth of the modeled snowpack was adjusted according to the
difference in fresh snow density and the measured snow density profile in the
upper 2 m at Summit (Geng et al., 2014b).
Snowpack nitrate concentration and isotope profiles at
Summit, Greenland (red: observations; blue: modeled). The gray curve in (a)
is the modeled weekly data, while the blue curve is the monthly average. The dashed green line in (b) represents measured δ15N in surface snow
throughout a year (Jarvis et al., 2009). The measured minimum Δ17O(NO3-) was used as the indicator of June–July when local
photochemistry is the most active.
As shown in Fig. 1, nitrate concentrations and isotopes in the modeled
snowpack in general display similar seasonal patterns to the observations
except for Δ17O whose magnitude of seasonal change is much
smaller than the observations. The modeled average NO3-
concentration was 115±65ngg-1, similar to the observation
of 117±62ngg-1. The modeled concentration profile displays
high variability which is mainly caused by variations in weekly snow
accumulation. The modeled results indicate clear summer peaks and winter
valleys similar to the observations. In addition, we found with or without
seasonal variations in Fpri that the modeled concentration and isotope
profiles were almost identical.
The modeled Δ17O(NO3-) deviated by about
2.1 ‰ from primary nitrate (Δ17O(NO3-)=30‰) in summer. This is consistent with expectations as
post-depositional processing will not cause mass-independent fractionation, so it has no direct effects on Δ17O. The model deviation is
mainly caused by the reformation of nitrate in the local atmosphere which
leads to nitrate with different Δ17O from primary nitrate. In
summer, nitrate reformed in the overlying atmosphere occurs mainly through OH
oxidation of NO2. In the model, nitrate formed through this process
possessed Δ17O of 19.6±0.3 ‰ on average. This
value is close to the modeled results (18.9 ‰) for summer at
Summit by Kunasek et al. (2008) who used a box model and assumed local
NOx chemistry is the only nitrate source. Δ17O of nitrate
formed from local chemistry is lower than that in summer snow (∼25‰), and this could be related to transport of external nitrate
as suggested by Kunasek et al. (2008). Indeed, unlike in summer
conditions at Summit, nitrate transported from outside of the Arctic would be formed by
both night- and daytime reactions and should possess higher
Δ17O than locally formed nitrate which is mainly from OH
oxidation (Kunasek et al., 2008). In our model, the Δ17O(NO3-) of Fpri was assumed to be
30 ‰. Although this is unlikely to be the true value of long-range-transported nitrate, it can be viewed as the starting value from
which we can assess the effects of post-depositional processing (i.e., the
changes caused by post-depositional processing) which is the focus of this
study. In the model, the summer-deposited nitrate possesses Δ17O
that is 1.9 ‰ lower than that of Fpri due to the
mixing of Fpri with snow-sourced nitrate. In wintertime, local
nitrate formation in the overlying atmosphere is muted in the model as there
is no sunlight, and thus the deposited Δ17O(NO3-) is
completely controlled by Δ17O(NO3-) of Fpri.
In addition, the cage effect during photolysis further reduces Δ17O
in snow nitrate by ∼0.2‰. This is different from what
occurs on the East Antarctic Plateau where the cage effect dominates the
post-depositional Δ17O(NO3-) decrease (Erbland et al.,
2013). This is because on the East Antarctic Plateau, the snow accumulation
rate is very low, and nitrate remains in the photic zone for 5 years or longer
(compared to less than a year at Summit, Greenland). Taking into account the
cage effect in Summit snow, a 2.1 ‰Δ17O
seasonality was simulated by the model, which is much smaller compared to the
observed 9 ‰ seasonality (Fig. 1c). Note that as our model does not
consider nitrate formation via BrONO2 hydrolysis, which tends to
produce nitrate with higher Δ17O than OH oxidation, the modeled
2.1 ‰ seasonality is an upper limit. In all, the results suggest
that post-depositional processing does not play a significant role in regulating
the observed seasonality of Δ17O(NO3-) at Summit, which
is probably mainly caused by seasonal differences in Δ17O(NO3-) of Fpri in addition to seasonal
differences in local nitrate formations as suggested by Kunasek et al. (2008).
The observed surface snow δ15N(NO3-) (green curve in
Fig. 1b) varies from -13.0 ‰ to -2.8 ‰ in a
year (Jarvis et al., 2009). In comparison, observed snowpack
δ15N(NO3-) varies from -9.8±3.1 ‰ of
the annual valleys to 6.3±1.8 ‰ of the annual peaks (average
of 3 years of observations) and displays apparent enrichments in spring
and early summer. This difference suggests substantial changes in
δ15N(NO3-) after deposition. The model with constant
δ15N of Fpri (i.e., 0 ‰ throughout
the year) predicted a δ15N(NO3-) seasonality with a
spring peak (dashed black curve in Fig. 2b), and the modeled magnitude of
seasonal difference is ∼17.5‰, which is similar to the
observations (16.1±3.6 ‰ seasonality). But there is a constant
model–observation discrepancy that the lowest δ15N(NO3-)
value in a year appears earlier in the model than in the observations. When
including seasonal variations in δ15N of Fpri
(i.e., using year-round surface δ15N(NO3-)), the
modeled seasonal δ15N(NO3-) pattern, as well as the
magnitude (∼18.3‰) (blue curve in Fig. 1b), became almost
identical to the observations except that the absolute values of the modeled
δ15N(NO3-) are on average 5.2 ‰ lower than
the observations. This modeled underestimate could be due to the use of
observed δ15N of surface snow nitrate (-6.2±1.1 ‰ on average) which may underestimate δ15N of
Fpri. The δ15N of surface snow nitrate is affected
by the input of snow-sourced nitrate depleted of δ15N in the
summer. Therefore, the modeled snowpack δ15N should be lower
than the observation given that the starting values in the model are biased
low. In comparison, the simulation with constant δ15N of
Fpri (i.e., 0 ‰) predicted absolute values generally
higher than the observations, which may be because the value of
0 ‰ might be an overestimate.
The occurrence of the spring δ15N peak should be also driven by
post-depositional processing. Post-depositional processing starts after polar
sunrise and continues to operate until the beginning of polar winter. During
this time, the effect of post-depositional processing accumulates, and the
spring snow layer has experienced the largest degree of post-depositional loss
and thus exhibits the most enriched δ15N. The annual snow
thickness at Summit is ∼65±10cma-1, which is twice
the depth of the photic zone, and therefore there should be no additional
post-depositional processing after a year, and the spring high
δ15N(NO3-) caused by post-depositional processing is
preserved as seen in the model and observations.
Seasonality of photolysis flux (FP) and deposition flux (FD)
To discern the processes leading to the seasonal isotope patterns, we further
investigated the weekly nitrate deposition flux (FD) and isotopes, as well as
the weekly flux of snow-sourced nitrate (FP) and isotopes, using the model. As
shown in Fig. 2a, during mid-summer when actinic flux reaches its maximum, FP
reaches the maximum (and is zero in winter). Our simulated average daily
NO2 flux from snowpack in summer was 2.96×1012molec.m-2s-1, in good agreement with summer
observations at Summit (2.52×1012molec.m-2s-1; Honrath et al., 2002). FD is a
mixture of Fpri and FP, so it also reaches the maximum in summer
due to the contribution of FP, in addition to the summer high
Fpri. This at least in part explains the modeled summer nitrate
concentration maximum. But even in summer, FP was only about 25 % of FD,
demonstrating the importance of Fpri in determining the budget of
snow nitrate at Summit.
Weekly distribution of photolysis flux (FP) and
deposition flux (FD) and their nitrate isotopic compositions. Gaps in FP
(red line) are during the winter when there is no sunlight and thus no
photolysis. The results shown are those simulated with seasonal variations
in the flux and δ15N of primary nitrate (Fpri).
The δ15N of FP in the half year of summer (-77 ‰ to
-65 ‰) was severely depleted compared toFpri
(-6.7 ‰ to -2.8 ‰). As shown in Fig. 2b,
δ15N of FP gradually increased from the onset of photolysis
and reached the highest in mid-summer and decreased after that. This is
mainly caused by the wavelength-dependent εp (Berhanu et al.,
2014) which varies from -57 ‰ to -87 ‰ and
peaks in mid-summer at Summit (Fig. 3a), corresponding to the smallest isotope
effect in mid-summer. The δ15N(NO3-) of FD was a
combination of FP and Fpri. Therefore, a clear decrease in
δ15N(NO3-) of FD can be expected in summer (Fig. 2b) when
the contribution of FP was the largest. The isotope effect in
δ15N during the deposition of nitrate was also included in the
model but turns out to have no apparent impact on the modeled snowpack
δ15N(NO3-) profile. This is because essentially all
nitrate in the atmosphere except the fraction being exported was deposited
(i.e., FD) over the period of each simulation step (i.e., 1 week), and thus
the isotope effects were negligible due to mass balance.
(a) The fraction of nitrate loss after deposition and the
photolysis fractionation factor (εp) at different weeks.
(b) PIE: the photo-induced isotope effect. The solid star represents the
estimated PIE from surface and snowpack nitrate data reported by Jarvis et al. (2009). The green, red, blue and white background colors represent
spring, summer, autumn and winter, respectively.
The modeled Δ17O(NO3-) of FP is mainly determined by
local atmospheric chemistry, e.g., the NO–NO2 cycling and the
subsequent formation of HNO3. Under the prescribed Summit
atmospheric conditions, we calculated the Δ17O(NO3-) of
FP with a mean of 19.7±0.3 ‰ during summer. This
Δ17O(NO3-) of FP combined with Fpri (Δ17O=30‰), leading to a summer minimum
Δ17O of FD that was 1.9 ‰ lower than that of
Fpri. An additional ∼0.2‰ difference was
induced upon archiving from the cage effect, suggesting the cage effect plays a
negligible role in snow Δ17O (NO3-) at
Summit. This reinforces why oxygen isotopes should not be used to investigate
the degree of post-depositional processing, especially at high snow
accumulation sites, because it is dominated by regionally and/or local
atmospheric processes.
In addition, our model results indicate apparent recycling of nitrate at the
air–snow interface leading to changes in snow nitrate isotopes. This is
opposite to Fibiger et al. (2016) who concluded there is little to no local
recycling of nitrate at Summit based on the fact that surface snow nitrate
Δ17O was not elevated when atmospheric BrO concentration
increased. However, high BrO concentration does not necessarily lead to high
atmospheric and/or snow nitrate Δ17O for several reasons.
First, the production of BrO will consume O3, and this is a tradeoff
in terms of influencing Δ17O(NO3-). Second, BrO
concentration always covaries with HOx (HOx= OH, RO2 and
HO2) (Liao et al., 2011), and increases in HOx tend to lower Δ17O(NO3-), which offsets the effect of increased BrO
concentration on Δ17O(NO3-). Third, the BrO
increase observed by Fibiger et al. (2016) only lasted for a few hours, and whether
this is long enough to significantly perturb the local atmospheric nitrate
budget over longer time periods and nitrate in snow is questionable.
Nevertheless, BrONO2 hydrolysis is only one of the many pathways of
atmospheric nitrate formation, and for atmospheric nitrate to perturb the
surface snow nitrate budget (in the top 2 cm, the observations of
Fibiger et al., 2016) through dry deposition, it will need days to weeks of
nitrate deposition given its dry deposition flux (7.16×1011molec.m-2s-1) at Summit (Honrath et al.,
2002). A chemical transport model with the post-depositional processing
incorporated would be best to investigate this further but is out of the scope
of this study.
Loss of snow nitrate due to photolysis at Summit
The lost fraction (floss) of snow nitrate upon archiving is plotted
in Fig. 3a, calculated as the difference in nitrate concentration of an
archived layer to the concentration when it was at the surface. As shown in
Fig. 3a, throughout a year, floss varied from 1.9 % to
21.1 %, similar to the <7 % to 25 % loss estimated by Burkhart
et al. (2004) and Dibb et al. (2007). In particular, Dibb et al. (2007)
calculated the average NO3- concentrations in fresh and buried
snow layers and found a mean of ∼9 % loss which is in good
agreement with our calculated mean floss of 10.4±6.6 %. The loss of nitrate in a snow layer corresponds to the enrichment of
δ15N(NO3-) in that layer. Here we defined the enrichment
in snow δ15N(NO3-) due to photolysis as PIE (the
photo-induced isotope effect), i.e., the difference between δ15N(NO3-) of a newly deposited snow layer and the same layer that
was finally buried below the photic zone. As shown in Fig. 3b, PIE is the
highest in the 18th week of the year, corresponding to the time of the highest
floss. In addition, PIE displays a maximum in spring and minimum
in autumn, in good agreement with the observed seasonal δ15N(NO3-) pattern in snowpack. We also estimated PIE based on the
observed δ15N(NO3-) in surface snow and snowpack at
Summit as reported by Jarvis et al. (2009). As shown in Fig. 3b, PIE estimated
based on observations (PIE_ob) agrees well with the modeled PIE. These
further confirm the dominant role of the photo-driven post-depositional
processing in the seasonal snowpack δ15N(NO3-)
pattern. Note in the model neither floss nor PIE varied with
seasonal differences in the flux and δ15N of Fpri,
respectively. The agreement between the modeled and observed PIE further
demonstrates the dominant role of photo-driven post-depositional processing in
seasonal δ15N(NO3-) variations at Summit. Physical loss
of snow nitrate through adsorption/evaporation is associated with very small
εp (e.g., 3.6 ‰ by Erbland et al., 2013), and
given the mean summertime temperature at Summit (261±3K) and a
maximum lost fraction of 25 % (Dibb et al., 2007), only a ∼1‰ change in δ15N(NO3-) can be caused by
physical loss.
The floss calculated above referred to a specific archived
layer relative to when it was at the surface, and part of the loss was
recycled to layers above that specific layer. Therefore, the net loss
integrated over a certain period should be less than floss. Here
we calculated an annual net loss floss as follows:
f¯lossannual=1-FaFpri,
where Fa represents the archival flux of nitrate (6.33×10-6kgNm2a-1), and
f¯lossannual was calculated as 4.1 %. This is
consistent with the annual mean δ15N(NO3-) which was
2.6 ‰ enriched compared to δ15N of
Fpri. For Δ17O(NO3-), upon archiving, the
annual mean is 0.9 ‰ lower than Δ17O of
Fpri. These values represent the integrated effects of the
post-depositional processing on isotopes of the archived nitrate under present
Summit conditions. In addition, these results suggest that although
photochemistry was active and resulted in significant redistribution of snow
nitrate in the photic zone at Summit, the annual net loss is small, consistent
with the results of previous studies at Summit based on cumulative inventory
assessments of nitrate mass in snow pits (Burkhart et al., 2004; Dibb et al.,
2007), as well as the result from a southeastern Greenland ice core where
negligible annual nitrate loss was suggested due to the even higher snow
accumulation rate (≈300cm snow per year) than Summit
(≈65cm snow per year) (Iizuka el al., 2018). It is also
interesting to note that despite having a similar source region (Geng et al.,
2015, Iizuka el al., 2018), δ15N(NO3-) in this
southeastern Greenland ice core is lower than in Summit ice cores
(Shohei Hattori, personal communication, 2021). This is
qualitatively consistent with the difference in the snow accumulation rate at
the two sites since the lower snow accumulation rate at Summit will result in a
higher degree of post-depositional processing.
The annual net loss in the model is mainly determined by fexp
which represents the fraction of exported nitrate from the site of photolysis.
Although fexp does not influence the loss fraction of a specific
snow layer and subsequently the predicted seasonal δ15N(NO3-) pattern as modeled (Fig. S3 in the Supplement), it
determines how much of the reformed nitrate was recycled back to snow. In
Fig. 4, we investigated the sensitivity of the annual net loss, as well as the annual
mean archived Δ17O(NO3-) and δ15N(NO3-) to fexp. We found the archived Δ17O(NO3-) decreases with increasing fexp, while
δ15N(NO3-) is the opposite because larger
fexp corresponds to less of a contribution of FP to FD. Under the
extreme circumstance with fexp=1, i.e., all snow-sourced nitrate
was exported, δ15N(NO3-) in snow was on average
6.8 ‰ enriched compared to primary Fpri under
present Summit conditions, while Δ17O(NO3-) was only
0.2 ‰ lower than Δ17O ofFpri caused
entirely by the cage effect. In this study, fexp was determined to
be 0.35 following the method used by Erbland et al. (2015), but this could be
an underestimate. At Summit, observations by Honrath et al. (2002) indicate
that NOx and/or HNO3 emitted from sunlit snow are largely
exported from the local boundary layer if no wet deposition occurs.
Sensitivity of annual mean δ15N(NO3-)/Δ17O(NO3) upon archiving
to fexp. Positive/negative values indicate the deviations of
Fpri. Note when fexp is set to 1, the small non-zero value (-0.19 ‰) of Δ17O(NO3-) represents the
effects of the cage effect.
Implications for interpretation of ice-core nitrate isotope records
Due to the fast cycling of nitrate at the air–snow interface, the annual net
loss (4.1 %) and the associated annual mean changes in δ15N(NO3-) (2.6 ‰) and Δ17O(NO3-) (0.9 ‰) caused by post-depositional
processing are small under present Summit conditions. Despite this, at
seasonal scale, given the strong variations in actinic flux, post-depositional
processing plays an important role in the seasonal δ15N
fluctuation. The degree of post-depositional processing is also strongly
depending on snow accumulation rate which is usually very different in
different climates. As such, the net loss and the associated isotope effects
could be increased in periods with a reduced snow accumulation rate. For
example, over the last glacial–interglacial period, considering only the
changes in snow accumulation rate at Summit (Geng et al., 2015), the model
calculated a 11 % annual nitrate loss in the glacial period and a
glacial–interglacial δ15N difference of 9.2 ‰.
In comparison, the observed glacial–interglacial δ15N
difference is 16.7±4.8 ‰ (Geng et al., 2015). This suggests
changes in the degree of post-depositional processing caused by the
glacial–interglacial snow accumulation rate difference alone can explain more
than half of the observed δ15N(NO3-) difference. Note the
modeled 11 % net loss in the glacial climate according to Eq. (2) is
not in conflict with the 45–54 % loss estimated by Geng et al. (2015),
who calculated the loss fraction from Fa and FD instead of
Fpri. If Fpri in Eq. (2) is replaced with FD, the
loss fraction is then 31 %. With the effects of changes in snow
accumulation rate alone, the model predicted the glacial
Δ17O(NO3-) would be 2 ‰ lower than in the
present. This amount is significant compared to the observed
glacial–interglacial Δ17O(NO3-) difference of
6.2 ‰ (Geng et al., 2017). Note that many other factors can
influence the degree of post-depositional processing in the glacial climate,
e.g., local wind speed, actinic flux, quantum yield of snow nitrate
photolysis, etc., which are out of the scope of this study. But our
results here reinforce the effects of post-depositional processing on ice-core
nitrate concentrations and isotopes even at high snow accumulation rate sites,
and such effects must be quantified and corrected in order to use ice-core
nitrate records to retrieve past information on NOx emissions and
abundance and atmospheric oxidation capacity especially when the records cover
different climates.
Conclusions
In this study we applied the TRANSITS model to explicitly investigate the
impact of the photo-driven post-depositional processing on the preservation of
nitrate and its isotopes at Summit, Greenland, with the focus on changes in
nitrate isotopes after deposition. The results suggest that the photo-driven
post-depositional processing is active at Summit, causing strong
redistribution of snow nitrate accompanied by isotope effects in the photic
zone. Despite the high snow accumulation rate at Summit, up to 21 %
loss/redistribution of nitrate can be induced by the photolysis, resulting in
a spring δ15N(NO3-) peak consistent with the
observations. Despite uncertainties in the model, e.g., specific surface area,
quantum yield of snow nitrate photolysis and the export fraction, the modeled
loss/redistribution of nitrate after deposition is consistent with previous
studies and explains the observed difference between δ15N(NO3-) in surface snow and snow at depth. The latter is evidence
of changes in δ15N(NO3-) after deposition. The model
also reproduced the observed seasonal patterns of snow nitrate concentration
and δ15N(NO3-) reasonably well, and the model–observation
discrepancy in the timing of the lowest seasonal δ15N(NO3-) was addressed when seasonal variations in
δ15N(NO3-) of Fpri were included. But the
effects of δ15N of Fpri on snow
δ15N(NO3-) seasonality appear to be mainly pronounced in
autumn and winter, i.e., the period with the lowest seasonal
δ15N(NO3-) when photolysis is negligible. This makes
sense as when photolysis is muted snow nitrate δ15N(NO3-)
should be the same as that of Fpri. When photolysis is active, the
δ15N(NO3-) signal of Fpri is not
preserved. In contrast, the post-depositional processing only led to
2.1 ‰ seasonal change in Δ17O. These results are
consistent with the expectation that photo-driven post-depositional processing
modifies δ15N but has only moderate impacts on
Δ17O.
Overall, the model results suggest an important, perhaps even dominant role of
post-depositional processing in regulating the snowpack δ15N(NO3-) seasonality at Summit. Although the impact of photolysis
of snow nitrate on δ15N(NO3-) must be carefully evaluated
when interpreting snowpack and ice-core nitrate isotope records even at sites
with high snow accumulation rates such as Summit, Greenland, we note that this
study does not address to what extent seasonal variations in
δ15N(NO3-) of Fpri affect the snowpack
δ15N(NO3-). Observations on the concentration and
isotopic composition of Fpri and its seasonal variations would be
best to answer this question. However, it would be difficult to distinguish
primary from recycled nitrate during sunlit time periods due to the local
influence of snow-sourced nitrate. Additional observations including a full
year or multiple years of atmospheric nitrate isotopes along with surface snow
and snowpack data at a single site should be pursued in the future to fully
investigate the evolution of nitrate isotopes before and after deposition, as well as
to thoughtfully evaluate the effects of post-depositional processing. On the
other hand, precise measurements of snowpack properties, e.g., specific
surface area, impurity concentrations and observational constraints on the
quantum yield of snow nitrate photolysis, and better constraints on the export
fraction are also needed in order to improve the model's performance.
Code availability
The codes for the numerical simulations and their analysis will be provided
upon direct request to the corresponding author.
Data availability
The model output data are available through OSF, the Open Science Framework: 10.17605/OSF.IO/A4B7D (Jiang et al., 2020).
The supplement related to this article is available online at: https://doi.org/10.5194/tc-15-4207-2021-supplement.
Author contributions
LG conceived this study. ZJ performed the model simulations, analyzed the
data and wrote the manuscript with LG. JE, JS and BA providing the
model and helping with the model setup. All authors contributed to data
interpretation and writing.
Competing interests
The authors declare that they have no conflict of interest.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
Zhuang Jiang thanks John Robinson for his assistance in starting the TRANSITS model, and we would like to thank the reviewers and the editors of the Cryosphere for their suggestions and comments to improve the manuscript. The French Polar institute (Institut Polaire Français – program SUNITEDC 1011) is thanked for field and funding support (Joel Savarino, Joseph Erbland).
Financial support
This research is funded by the National Natural Science Foundation of China (Awards: 41822605, 41871051 and 41727901), the Fundamental Research Funds for Central Universities, the Strategic Priority Research Program of Chinese Academy of Sciences (grant no. XDB 41000000), and the National Key R&D Program of China (grant nos. 2019YFC1509100 and 2016YFA0302200). Support for Joel Savarino and Joseph Erbland was provided by the French national programme LEFE/INSU and the ANR grants ANR-15-IDEX-02 (project IDEX Université Grenoble Alpes) and ANR-16-CE01-0011-01 (EAIIST project) of the French Agence Nationale de la Recherche. Becky Alexander was supported by the NSF (grant no. PLR 1542723).
Review statement
This paper was edited by Florent Dominé and reviewed by two anonymous referees.
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