scholarly journals A large and ubiquitous source of atmospheric formic acid

2015 ◽  
Vol 15 (11) ◽  
pp. 6283-6304 ◽  
Author(s):  
D. B. Millet ◽  
M. Baasandorj ◽  
D. K. Farmer ◽  
J. A. Thornton ◽  
K. Baumann ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Formic Acid ◽  
Transport Model ◽  
Model Simulation ◽  
Vertical Gradient ◽  
Precipitation Chemistry ◽  
Chemical Production ◽  
Chemical Transport Model ◽  
Criegee Intermediates ◽  
Isoprene Oxidation

Abstract. Formic acid (HCOOH) is one of the most abundant acids in the atmosphere, with an important influence on precipitation chemistry and acidity. Here we employ a chemical transport model (GEOS-Chem CTM) to interpret recent airborne and ground-based measurements over the US Southeast in terms of the constraints they provide on HCOOH sources and sinks. Summertime boundary layer concentrations average several parts-per-billion, 2–3× larger than can be explained based on known production and loss pathways. This indicates one or more large missing HCOOH sources, and suggests either a key gap in current understanding of hydrocarbon oxidation or a large, unidentified, direct flux of HCOOH. Model-measurement comparisons implicate biogenic sources (e.g., isoprene oxidation) as the predominant HCOOH source. Resolving the unexplained boundary layer concentrations based (i) solely on isoprene oxidation would require a 3× increase in the model HCOOH yield, or (ii) solely on direct HCOOH emissions would require approximately a 25× increase in its biogenic flux. However, neither of these can explain the high HCOOH amounts seen in anthropogenic air masses and in the free troposphere. The overall indication is of a large biogenic source combined with ubiquitous chemical production of HCOOH across a range of precursors. Laboratory work is needed to better quantify the rates and mechanisms of carboxylic acid production from isoprene and other prevalent organics. Stabilized Criegee intermediates (SCIs) provide a large model source of HCOOH, while acetaldehyde tautomerization accounts for ~ 15% of the simulated global burden. Because carboxylic acids also react with SCIs and catalyze the reverse tautomerization reaction, HCOOH buffers against its own production by both of these pathways. Based on recent laboratory results, reaction between CH3O2 and OH could provide a major source of atmospheric HCOOH; however, including this chemistry degrades the model simulation of CH3OOH and NOx : CH3OOH. Developing better constraints on SCI and RO2 + OH chemistry is a high priority for future work. The model neither captures the large diurnal amplitude in HCOOH seen in surface air, nor its inverted vertical gradient at night. This implies a substantial bias in our current representation of deposition as modulated by boundary layer dynamics, and may indicate an HCOOH sink underestimate and thus an even larger missing source. A more robust treatment of surface deposition is a key need for improving simulations of HCOOH and related trace gases, and our understanding of their budgets.

scholarly journals A large and ubiquitous source of atmospheric formic acid

2015 ◽  
Vol 15 (4) ◽  
pp. 4537-4599 ◽  
Author(s):  
D. B. Millet ◽  
M. Baasandorj ◽  
D. K. Farmer ◽  
J. A. Thornton ◽  
K. Baumann ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Formic Acid ◽  
Transport Model ◽  
Model Simulation ◽  
Vertical Gradient ◽  
Precipitation Chemistry ◽  
Chemical Production ◽  
Chemical Transport Model ◽  
Criegee Intermediates ◽  
Isoprene Oxidation

Abstract. Formic acid (HCOOH) is one of the most abundant acids in the atmosphere, with an important influence on precipitation chemistry and acidity. Here we employ a chemical transport model (GEOS-Chem) to interpret recent airborne and ground-based measurements over the US Southeast in terms of the constraints they provide on HCOOH sources and sinks. Summertime boundary layer concentrations average several parts-per-billion, 2–3× larger than can be explained based on known production and loss pathways. This indicates one or more large missing HCOOH sources, and suggests either a key gap in current understanding of hydrocarbon oxidation or a large, unidentified, direct flux of HCOOH. Model-measurement comparisons implicate biogenic sources (e.g., isoprene oxidation) as the predominant HCOOH source. Resolving the unexplained boundary layer concentrations based: (i) solely on isoprene oxidation would require a 3× increase in the model HCOOH yield, or (ii) solely on direct HCOOH emissions would require approximately a 25× increase in its biogenic flux. However, neither of these can explain the high HCOOH amounts seen in anthropogenic air masses and in the free troposphere. The overall indication is of a large biogenic source combined with ubiquitous chemical production of HCOOH across a range of precursors. Laboratory work is needed to better quantify the rates and mechanisms of carboxylic acid production from isoprene and other prevalent organics. Stabilized Criegee intermediates (SCIs) provide a large model source of HCOOH, while acetaldehyde tautomerization accounts for ~ 15% of the simulated global burden. Because carboxylic acids also react with SCIs and catalyze the reverse tautomerization reaction, HCOOH buffers against its own production by both of these pathways. Based on recent laboratory results, reaction between CH3O2 and OH could provide a major source of atmospheric HCOOH; however, including this chemistry degrades the model simulation of CH3OOH and NOx:CH3OOH. Developing better constraints on SCI and RO2 + OH chemistry is a high priority for future work. The model does not capture the large diurnal amplitude in HCOOH seen in surface air, nor its inverted vertical gradient at night. This implies a substantial bias in our current representation of deposition as modulated by boundary layer dynamics, and may indicate an HCOOH sink underestimate and thus an even larger missing source. A more robust treatment of surface deposition is a key need for improving simulations of HCOOH and related trace gases, and our understanding of their budgets.

scholarly journals Formaldehyde production from isoprene oxidation across NO<sub><i>x</i></sub> regimes

2016 ◽  
Vol 16 (4) ◽  
pp. 2597-2610 ◽  
Author(s):  
G. M. Wolfe ◽  
J. Kaiser ◽  
T. F. Hanisco ◽  
F. N. Keutsch ◽  
J. A. de Gouw ◽  
...  
Keyword(s):  
Transport Model ◽  
Model Simulation ◽  
Nonlinear Function ◽  
Peroxy Radical ◽  
Fold Increase ◽  
Oxidation Products ◽  
Box Model ◽  
Chemical Transport Model ◽  
Mixing Ratios ◽  
Isoprene Oxidation

Abstract. The chemical link between isoprene and formaldehyde (HCHO) is a strong, nonlinear function of NOx (i.e., NO + NO2). This relationship is a linchpin for top-down isoprene emission inventory verification from orbital HCHO column observations. It is also a benchmark for overall photochemical mechanism performance with regard to VOC oxidation. Using a comprehensive suite of airborne in situ observations over the southeast US, we quantify HCHO production across the urban–rural spectrum. Analysis of isoprene and its major first-generation oxidation products allows us to define both a "prompt" yield of HCHO (molecules of HCHO produced per molecule of freshly emitted isoprene) and the background HCHO mixing ratio (from oxidation of longer-lived hydrocarbons). Over the range of observed NOx values (roughly 0.1–2 ppbv), the prompt yield increases by a factor of 3 (from 0.3 to 0.9 ppbv ppbv−1), while background HCHO increases by a factor of 2 (from 1.6 to 3.3 ppbv). We apply the same method to evaluate the performance of both a global chemical transport model (AM3) and a measurement-constrained 0-D steady-state box model. Both models reproduce the NOx dependence of the prompt HCHO yield, illustrating that models with updated isoprene oxidation mechanisms can adequately capture the link between HCHO and recent isoprene emissions. On the other hand, both models underestimate background HCHO mixing ratios, suggesting missing HCHO precursors, inadequate representation of later-generation isoprene degradation and/or underestimated hydroxyl radical concentrations. Detailed process rates from the box model simulation demonstrate a 3-fold increase in HCHO production across the range of observed NOx values, driven by a 100 % increase in OH and a 40 % increase in branching of organic peroxy radical reactions to produce HCHO.

scholarly journals Seasonal features and origins of carbonaceous aerosols at Syowa Station, coastal Antarctica

2019 ◽  
Vol 19 (11) ◽  
pp. 7817-7837 ◽  
Author(s):  
Keiichiro Hara ◽  
Kengo Sudo ◽  
Takato Ohnishi ◽  
Kazuo Osada ◽  
Masanori Yabuki ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Marine Boundary Layer ◽  
Transport Model ◽  
Model Simulation ◽  
Chemical Transport ◽  
Chemical Transport Model ◽  
Backward Trajectory ◽  
Syowa Station ◽  
The Antarctic ◽  
Measurement Period

Abstract. We have measured black carbon (BC) concentrations at Syowa Station, Antarctica, since February 2005. The measured BC concentrations in 2005–2016 were corrected to equivalent BC (EBC) concentrations using Weingartner's method. Seasonal features of EBC concentrations, long-range transport from mid-latitudes to the Antarctic coast, and their origins were characterized. Results show that daily median EBC concentrations were below the detection limit (0.2 ng m−3) to 63.8 ng m−3 at Syowa Station (median, 1.8 ng m−3; mean, 2.7 ng m−3 during the measurement period of February 2005–December 2016). Although seasonal features and year-to-year variations in EBC concentrations were observed, no long-term trend of EBC concentrations was clear during our measurement period. Seasonal features of EBC concentrations showed a spring maximum during September–October at Syowa Station. To elucidate EBC transport processes, origins, and the potential source area (PSA), we compared EBC data to backward trajectory analysis and chemical transport model simulation. From comparison with backward trajectory, high EBC concentrations were found in air masses from the marine boundary layer. This finding implies that transport via the marine boundary layer was the most important transport pathway to EBC concentrations at Antarctic coasts. Some EBC was supplied to the Antarctic region by transport via the upper free troposphere. Chemical transport model simulation demonstrated that the most important origins and PSA of EBC at Syowa Station were biomass burning in South America and southern Africa. Fossil fuel combustion in South America and southern Africa also have important contributions. The absorption Ångström exponent (AAE) showed clear seasonal features with 0.5–1.0 during April–October and maximum (1.0–1.5) in December–February. The AAE features might be associated with organic aerosols and mixing states of EBC.

scholarly journals A global off-line model of size-resolved aerosol microphysics: I. Model development and prediction of aerosol properties

2005 ◽  
Vol 5 (8) ◽  
pp. 2227-2252 ◽  
Author(s):  
D. V. Spracklen ◽  
K. J. Pringle ◽  
K. S. Carslaw ◽  
M. P. Chipperfield ◽  
G. W. Mann
Keyword(s):  
Boundary Layer ◽  
Sulfuric Acid ◽  
Size Distribution ◽  
Marine Boundary Layer ◽  
Transport Model ◽  
Model Development ◽  
Aerosol Size Distribution ◽  
Chemical Transport Model ◽  
Cloud Processing ◽  
Nucleation Mechanisms

Abstract. A GLObal Model of Aerosol Processes (GLOMAP) has been developed as an extension to the TOMCAT 3-D Eulerian off-line chemical transport model. GLOMAP simulates the evolution of the global aerosol size distribution using a sectional two-moment scheme and includes the processes of aerosol nucleation, condensation, growth, coagulation, wet and dry deposition and cloud processing. We describe the results of a global simulation of sulfuric acid and sea spray aerosol. The model captures features of the aerosol size distribution that are well established from observations in the marine boundary layer and free troposphere. Modelled condensation nuclei (CN>3nm) vary between about 250–500 cm-3 in remote marine boundary layer regions and are generally in good agreement with observations. Modelled continental CN concentrations are lower than observed, which may be due to lack of some primary aerosol sources or the neglect of nucleation mechanisms other than binary homogeneous nucleation of sulfuric acid-water particles. Remote marine CN concentrations increase to around 2000–10 000 cm

scholarly journals Secondary organic aerosol in the global aerosol – chemistry transport model Oslo CTM2

2007 ◽  
Vol 7 (3) ◽  
pp. 9053-9092 ◽  
Author(s):  
C. R. Hoyle ◽  
T. Berntsen ◽  
G. Myhre ◽  
I. S. A. Isaksen
Keyword(s):  
Ammonium Sulphate ◽  
Secondary Organic Aerosol ◽  
Transport Model ◽  
Model Simulation ◽  
Anthropogenic Activities ◽  
Organic Aerosol ◽  
Oxidation Products ◽  
Total Production ◽  
Chemical Transport Model ◽  
Sulphate Aerosol

Abstract. The global chemical transport model Oslo CTM2 has been extended to include the formation, transport and deposition of secondary organic aerosol (SOA). Precursor hydrocarbons which are oxidised to form condensible species include both biogenic species such as terpenes and isoprene, as well as species emitted predominantly by anthropogenic activities (toluene, m-xylene, methylbenzene and other aromatics). A model simulation for 2004 gives an annual global SOA production of approximately 55 Tg. Of this total, 2.5 Tg is found to consist of the oxidation products of anthropogenically emitted hydrocarbons, and about 15 Tg is formed by the oxidation products of isoprene. The global production of SOA is increased to about 76 Tg yr−1 by allowing semi-volatile species to condense on ammonium sulphate aerosol. This brings modelled organic aerosol values closer to those observed, however observations in Europe remain significantly underestimated, raising the possibility of an unaccounted for SOA source. Allowing SOA to form on ammonium sulphate aerosol increases the contribution of anthropogenic SOA from about 4.5% to almost 9% of the total production. The importance of NO3 as an oxidant of SOA precursors is found to vary regionally, causing up to 50%–60% of the total amount of SOA near the surface in polluted regions and less than 25% in more remote areas. This study underscores the need for SOA to be represented in a more realistic way in global aerosol models in order to better reproduce observations of organic aerosol burdens in industrialised and biomass burning regions.

scholarly journals Importance of secondary sources in the atmospheric budgets of formic and acetic acids

2010 ◽  
Vol 10 (10) ◽  
pp. 24435-24497 ◽  
Author(s):  
F. Paulot ◽  
D. Wunch ◽  
J. D. Crounse ◽  
G. C. Toon ◽  
D. B. Millet ◽  
...  
Keyword(s):  
Formic Acid ◽  
Carboxylic Acids ◽  
Transport Model ◽  
Negative Temperature ◽  
Photochemical Oxidation ◽  
Secondary Source ◽  
Chemical Transport Model ◽  
Wet And Dry Deposition ◽  
Secondary Sources ◽  
Acetic Acids

Abstract. We present a detailed budget of formic and acetic acids, two of the most abundant trace gases in the atmosphere. Our bottom-up estimate of the global source of formic and acetic acids are ~1200 and ~1400 Gmol/yr, dominated by photochemical oxidation of biogenic volatile organic compounds, in particular isoprene. Their sinks are dominated by wet and dry deposition. We use the GEOS-Chem chemical transport model to evaluate this budget against an extensive suite of measurements from ground, ship and satellite-based Fourier transform spectrometers, as well as from several aircraft campaigns over North America. The model captures the seasonality of formic and acetic acids well but generally underestimates their concentration, particularly in the Northern midlatitudes. We infer that the source of both carboxylic acids may be up to 50% greater than our estimate and report evidence for a long-lived missing secondary source of carboxylic acids that may be associated with the aging of organic aerosols. Vertical profiles of formic acid in the upper troposphere support a negative temperature dependence of the reaction between formic acid and the hydroxyl radical as suggested by several theoretical studies.

scholarly journals Sensitivity to grid resolution in the ability of a chemical transport model to simulate observed oxidant chemistry under high-isoprene conditions

2016 ◽  
Author(s):  
Karen Yu ◽  
Daniel J. Jacob ◽  
Jenny A. Fisher ◽  
Patrick S. Kim ◽  
Eloise A. Marais ◽  
...  
Keyword(s):  
Negative Correlation ◽  
Transport Model ◽  
Chemical Transport ◽  
Grid Resolution ◽  
Cumulative Probability ◽  
Peroxy Radicals ◽  
Chemical Transport Model ◽  
Coarse Resolution ◽  
Isoprene Oxidation ◽  
Southeast Us

Abstract. Formation of ozone and organic aerosol in continental atmospheres depends on whether isoprene emitted by vegetation is oxidized by the high-NOx pathway (where peroxy radicals react with NO) or by low-NOx pathways (where peroxy radicals react by alternate channels, mostly with HO2). We used mixed layer observations from the SEAC4RS aircraft campaign over the Southeast US to test the ability of the GEOS-Chem chemical transport model at different grid resolutions (0.25° × 0.3125°, 2° × 2.5°, 4° × 5°) to simulate this chemistry under high-isoprene, variable-NOx conditions. Observations of isoprene and NOx over the Southeast US show a negative correlation, reflecting in part the spatial segregation of emissions; this negative correlation is captured in the model at 0.25° × 0.3125° resolution but not at coarser resolutions. As a result, less isoprene oxidation takes place by the high-NOx pathway in the model at 0.25° × 0.3125° resolution (54 %) than at coarser resolution (59 %). The cumulative probability distribution functions (CDFs) of NOx, isoprene, and ozone concentrations show little difference across model resolutions and good agreement with observations, while formaldehyde is overestimated at coarse resolution because excessive isoprene oxidation takes place by the high-NOx pathway (which has high formaldehyde yield). Correlations of simulated vs. observed concentrations do not improve with grid resolution because finer modes of variability are intrinsically more difficult to capture. Higher model resolution leads to decreased conversion of NOx to organic nitrates and increased conversion to nitric acid, with total reactive nitrogen oxides (NOy) changing little across model resolutions. In the lower free troposphere, model output is similarly insensitive to grid resolution, indicating that the effect on export of ozone and NOx is small. The overall low sensitivity of modeled concentrations to grid resolution implies that coarse resolution is adequate when modeling regional boundary layer chemistry for global applications.

scholarly journals New constraints on biogenic emissions using satellite-based estimates of carbon monoxide fluxes

2019 ◽  
Vol 19 (21) ◽  
pp. 13569-13579 ◽  
Author(s):  
Helen M. Worden ◽  
A. Anthony Bloom ◽  
John R. Worden ◽  
Zhe Jiang ◽  
Eloise A. Marais ◽  
...  
Keyword(s):  
Carbon Monoxide ◽  
Transport Model ◽  
A Priori ◽  
Primary Source ◽  
Biogenic Emissions ◽  
Chemical Production ◽  
Chemical Transport Model ◽  
Ozone Monitoring Instrument ◽  
Top Down ◽  
Decadal Scale

Abstract. Biogenic non-methane volatile organic compounds (NMVOCs) emitted from vegetation are a primary source for the chemical production of carbon monoxide (CO) in the atmosphere, and these biogenic emissions account for about 18 % of the global CO burden. Partitioning CO fluxes to different source types in top-down inversion methods is challenging; typically a simple scaling of the posterior flux to prior flux values for fossil fuel, biogenic and biomass burning sources is used. Here we show top-down estimates of biogenic CO fluxes using a Bayesian inference approach, which explicitly accounts for both posterior and a priori CO flux uncertainties. This approach re-partitions CO fluxes following inversion of Measurements Of Pollution In The Troposphere (MOPITT) CO observations with the GEOS-Chem model, a global chemical transport model driven by assimilated meteorology from the NASA Goddard Earth Observing System (GEOS). We compare these results to the prior information for CO used to represent biogenic NMVOCs from GEOS-Chem, which uses the Model of Emissions of Gases and Aerosols from Nature (MEGAN) for biogenic emissions. We evaluate the a posteriori biogenic CO fluxes against top-down estimates of isoprene fluxes using Ozone Monitoring Instrument (OMI) formaldehyde observations. We find similar seasonality and spatial consistency in the posterior CO and top-down isoprene estimates globally. For the African savanna region, both top-down CO and isoprene seasonality vary significantly from the MEGAN a priori inventory. This method for estimating biogenic sources of CO will provide an independent constraint on modeled biogenic emissions and has the potential for diagnosing decadal-scale changes in emissions due to land-use change and climate variability.

scholarly journals Formaldehyde over the eastern Mediterranean during MINOS: Comparison of airborne in-situ measurements with 3D-model results

2003 ◽  
Vol 3 (3) ◽  
pp. 851-861 ◽  
Author(s):  
R. Kormann ◽  
H. Fischer ◽  
M. de Reus ◽  
M. Lawrence ◽  
Ch. Brühl ◽  
...  
Keyword(s):  
Boundary Layer ◽  
3D Model ◽  
Transport Model ◽  
Eastern Mediterranean ◽  
Lower Atmosphere ◽  
Photochemical Degradation ◽  
Chemical Transport Model ◽  
Acetone Concentration ◽  
Volatile Organic ◽  
The Mediterranean

Abstract. Formaldehyde (HCHO) is an important intermediate product in the photochemical degradation of methane and non-methane volatile organic compounds. In August 2001, airborne formaldehyde measurements based on the Hantzsch reaction technique were performed during the Mediterranean INtensive Oxidant Study, MINOS. The detection limit of the instrument was 42 pptv (1s) at a time resolution of 180 s (10-90%). The overall uncertainty of the HCHO measurements was 30% at a mixing ratio of 300 pptv. In the marine boundary layer over the eastern Mediterranean Sea average HCHO concentrations were of the order of 1500 pptv, in reasonable agreement with results from a three-dimensional global chemical transport model of the lower atmosphere including non-methane volatile organic compound (NMVOC) chemistry. Above the boundary layer HCHO mixing ratios decreased with increasing altitude to a minimum level of 250 pptv at about 7 km. At higher altitudes (above 7 km) HCHO levels showed a strong dependency on the airmass origin. In airmasses from the North Atlantic/North American area HCHO levels were of the order of 300 pptv, a factor of 6 higher than values predicted by the model. Even higher HCHO levels, increasing to values of the order of 600 pptv at 11 km altitude, were observed in easterlies transporting air affected by the Indian monsoon outflow towards the Mediterranean basin. Only a small part (~30 pptv) of the large discrepancy between the model results and the measurements of HCHO in the free troposphere could be explained by a strong underestimation of the upper tropospheric acetone concentration by up to a factor of ten by the 3D-model. Therefore, the measurement-model difference in the upper troposphere remains unresolved, while the observed dependency of HCHO on airmass origin might indicate that unknown, relatively long-lived NMVOCs - or their reaction intermediates - associated with biomass burning are at least partially responsible for the observed discrepancies.

scholarly journals Ammonia in the summertime Arctic marine boundary layer: sources, sinks, and implications

2016 ◽  
Vol 16 (4) ◽  
pp. 1937-1953 ◽  
Author(s):  
Gregory R. Wentworth ◽  
Jennifer G. Murphy ◽  
Betty Croft ◽  
Randall V. Martin ◽  
Jeffrey R. Pierce ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Transport Model ◽  
Canadian Arctic ◽  
Atmospheric Composition ◽  
Chemical Transport Model ◽  
Data Set ◽  
Baffin Bay ◽  
Melt Ponds ◽  
Ambient Nh3 ◽  
The Impact

Abstract. Continuous hourly measurements of gas-phase ammonia (NH3(g)) were taken from 13 July to 7 August 2014 on a research cruise throughout Baffin Bay and the eastern Canadian Arctic Archipelago. Concentrations ranged from 30 to 650 ng m−3 (40–870 pptv) with the highest values recorded in Lancaster Sound (74°13′ N, 84°00′ W). Simultaneous measurements of total ammonium ([NHx]), pH and temperature in the ocean and in melt ponds were used to compute the compensation point (χ), which is the ambient NH3(g) concentration at which surface–air fluxes change direction. Ambient NH3(g) was usually several orders of magnitude larger than both χocean and χMP (< 0.4–10 ng m3) indicating these surface pools are net sinks of NH3. Flux calculations estimate average net downward fluxes of 1.4 and 1.1 ng m−2 s−1 for the open ocean and melt ponds, respectively. Sufficient NH3(g) was present to neutralize non-sea-salt sulfate (nss-SO42−) in the boundary layer during most of the study. This finding was corroborated with a historical data set of PM2.5 composition from Alert, Nunavut (82°30′ N, 62°20′ W) wherein the median ratio of NH4+/nss-SO42− equivalents was greater than 0.75 in June, July and August. The GEOS-Chem chemical transport model was employed to examine the impact of NH3(g) emissions from seabird guano on boundary-layer composition and nss-SO42− neutralization. A GEOS-Chem simulation without seabird emissions underestimated boundary layer NH3(g) by several orders of magnitude and yielded highly acidic aerosol. A simulation that included seabird NH3 emissions was in better agreement with observations for both NH3(g) concentrations and nss-SO42− neutralization. This is strong evidence that seabird colonies are significant sources of NH3 in the summertime Arctic, and are ubiquitous enough to impact atmospheric composition across the entire Baffin Bay region. Large wildfires in the Northwest Territories were likely an important source of NH3, but their influence was probably limited to the Central Canadian Arctic. Implications of seabird-derived N-deposition to terrestrial and aquatic ecosystems are also discussed.

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