Chemical characterization of wet precipitation events and deposition of pollutants in coal mining region,India

The present study investigated the chemical composition of wet atmospheric precipitation in India’s richest coal mining belt. Total 418 samples were collected on event basis at six sites from July to October in 2003 and May to October in 2004 and analysed for pH, EC, F⁻, Cl⁻, , , Ca²⁺, Mg²⁺, Na⁺, K⁺ and . The average pH value (5.7) of the rainwater of the investigated area is alkaline in nature. However, the temporal pH variation showed the alkaline nature during the early phase of monsoonal rainfall but it trends towards acidic during the late and high rainfall periods. The rainwater chemistry of the region showed high contribution of Ca²⁺ (47%) and (21%) in cations and (55%) and Cl⁻ (23%) in anionic abundance. The high non seas salt fraction (nss) of Ca²⁺ (99%) and Mg²⁺ (96%) suggests crustal source of the ions, while the high nss (96%) and high ratio signifying the impact of anthropogenic sources and the source of the acidity. The ratio of varies from 0.03 to 3.23 with the average value of 0.84 suggesting that Ca²⁺ and play a major role in neutralization processes. The assessment of the wet ionic deposition rates shows no any specific trend, however Ca²⁺ deposition rate was highest followed by and _.     

Chemistry of Precipitation Events and Inter-Relationship with Ambient Aerosols over a Semi-Arid Region in Western India

The precipitation events (n = 91), collected for 3 years (2000–2002) during the period of SW-monsoon (Jun–Aug) from an urban site (Ahmedabad, 23.0°N, 72.6°E) of a semi-arid region in western India, are found to exhibit characteristic differences in terms of their solute contents. The low solute (<700 μeq L⁻¹) events are either marked by heavy precipitation amount or successive events collected during an extended rain spell; whereas light precipitation events occurring after antecedent dry period are characterized by high solutes (>700 μeq L⁻¹). The ionic composition of low solute events show large variability due to varying contribution of anthropogenic species (: 1%–74%; : 1%–25%; and : 8%–68%) to the respective ion balance. In high solute events, ionic abundances are dominated by mineral dust (Ca²⁺ and ) and sea-salts (Na⁺ and Cl⁻). These differences are also reflected in the pH of low solute events (range: 5.2–7.4, VWM: 6.4) and high solute events (range: 6.6–8.2, VWM: 7.3). The comparison of Ca²⁺/Na⁺ and nss- ratios (on equivalent basis) in rain and aerosols suggests that the ionic composition of high solute events is influenced by below-cloud scavenging; whereas evidence for in-cloud scavenging is significantly reflected in low solute events. The annual wet-deposition fluxes of and are 330 and 480 mg m⁻² y⁻¹, respectively, in contrast to their corresponding dry-deposition fluxes (14 and 160 mg m⁻² y⁻¹); whereas wet and dry removal of Ca²⁺, Mg²⁺ and are comparable.     

Simulation Chamber Studies of the Atmospheric Oxidation of 2-Methyl-3-Buten-2-ol: Reaction with Hydroxyl Radicals and Ozone Under a Variety of Conditions

This article presents a complete study of the diurnal chemical reactivity of the biogenic volatile organic compound (BVOC), 2-methyl-3-buten-2-ol (MBO) in the troposphere. Reactions of MBO with OH and with ozone were studied to analyse the respective parts of both processes in the global budget of MBO atmospheric reactivity. They were investigated under controlled conditions for pressure (atmospheric pressure) and temperature (298 ± 2 K) using three complementary European simulation chambers. Reaction with OH radicals was studied in the presence of and in the absence of NO _x . The kinetic study was carried out by relative rate study using isoprene as a reference. The rate constant found for this reaction was molecule⁻¹ cm³ s⁻¹. FTIR spectroscopy, DNPH- and PFBHA-derivatisation analyses were performed for reactions with both OH radicals and ozone. In both reactions, the hydroxycarbonyl compound, 2-hydroxy-2-methylpropanal (HMPr) was positively identified and quantified, with a yield of in the reaction with OH, and a yield of and 0.84 ± 0.08 in the reaction with ozone under dry (HR < 1%) and humid conditions (HR = 20%–30%). A primary production of two other carbonyl compounds, acetone , and formaldehyde was found in the case of the dry ozonolysis experiments. Under humid conditions, only formaldehyde was co-produced with HMPr as a primary carbonyl compound, with a yield of . For the reaction with OH, three other carbonyl compounds were detected, acetone , formaldehyde and glycolaldehyde . In addition some realistic photo-oxidation experiments were performed to understand in an overall way the transformations of MBO in the atmosphere. The realistic photo-oxidation experiments were conducted in the EUPHORE outdoor simulation chamber. It was found that this compound is a weak secondary aerosol producer (less than 1% of the carbon balance). But it was confirmed that it is a potentially significant source of acetone, Δ[Acetone]/Δ[MBO] = 0.45. With our experimental conditions ([MBO]₀ = 200 ppb, [NO]o = 50 ppb), an ozone yield of Δ[O₃]/Δ[MBO] = 1.05 was found.     

Role of atmospheric ammonia in the formation of inorganic secondary particulate matter: A study at Kanpur,India

Levels of fine Particulate Matter (PM_fine), SO₂ and NO_x are interlinked through atmospheric reactions to a large extent. NO_x, NH₃, SO₂, temperature and humidity are the important atmospheric constituents/conditions governing formation of fine particulate sulfates and nitrates. To understand the formation of inorganic secondary particles (nitrates and sulfates) in the atmosphere, a study was undertaken in Kanpur, India. Specifically, the study was designed to measure the atmospheric levels of covering winter and summer seasons and day and night samplings to capture the diurnal variations. Results showed are found to be significantly high in winter season compared to the summer season. In winter, the molar ratio of to was found to be greater than 2:1. This higher molar ratio suggests that in addition to (NH₄)₂SO₄, NH₄NO₃ will be formed because of excess quantity of present. In summer, the molar ratio was less than 2:1 indicating deficit of to produce NH₄NO₃. The nitrogen conversion ratio (NO₂ to NO₃) was found to be nearly 50% in the study area that suggested quick conversion of NO₂ into nitric acid. As an overall conclusion, this study finds that NH₃ plays a vital role in the formation of fine inorganic secondary particles particularly so in winter months and there is a need to identify and assess sources of ammonia emissions in India.     

Kinetics of the reactions of Cl atoms with 2-buten-1-ol, 2-methyl-2-propen-1-ol, and 3-methyl-2-buten-1-ol as a function of temperature

The reactions of three structurally similar unsaturated alcohols, 2-buten-1-ol (crotyl alcohol), 2-methyl-2-propen-1-ol (MPO221) and 3-methyl-2-buten-1-ol (MBO321) with Cl atoms, have been investigated for the first time, using a 400 l Teflon reaction chamber coupled with gas chromatograph-coupled with flame-ionization detection (GC-FID). The experiments were performed at atmospheric pressure and at temperatures between 255 and 298 K, in air or nitrogen as the bath gas. The obtained kinetic data were used to derive the Arrhenius expressions , , (in units of cm³ molecule⁻¹ s⁻¹). Finally, atmospheric lifetimes of those unsaturated alcohols with respect to OH, NO₃, O₃ and Cl have been calculated.     

A dual site study of the rainwater chemistry within the Western Pacific region

The two-year (1999–2000) rainwater chemistry at two monitoring sites in nearby coastal areas [Taiwan (TW) and Hong Kong (HK)] within the Western Pacific region has been studied. The volume weighted average pH values for the entire sampling period in TW and HK were 4.6 and 4.2, respectively. Sea salt Na⁺ and Cl⁻ were the most abundant species in the TW samples but and H⁺ were the most abundant in the HK samples. The sea salt and concentrations at TW were higher than those at HK both in the cold and warm seasons. Chloride depletion was minimal in the rainwater samples at both sites. Non seasalt- was associated with . Under the influence of the East Asian Winter Monsoon, the back-trajectory studies revealed that elevated anthropogenic species concentrations were associated with trajectories (1) very near to the continental boundary layer of Mainland China; or (2) along the coastline of Eastern China where large cities/industrial areas are located or (3) passing through the region of stagnant air over Northern/Eastern China. The lowest anthropogenic and crustal species concentrations measured in HK are associated with the summer monsoon and are attributed not only to the clean marine air masses but also to the relatively low SO₂, NO _x and NH₃ emissions from the South/ South East Asian countries, as well as infrequent biomass burning activities and wet scavenging at sources during the summer months. Approaching tropical cyclones led to the lowest pH values (4.2 in TW and 3.8 in HK) amongst the other weather categories. The findings here have been compared with other studies within East Asia and elsewhere.     

Chemical composition of wet deposition in a Mediterranean site Athens,Greece related to the origin of air masses

The goal of this study is to determine the chemical composition of rain, in the wider region of Athens, Greece for the time period 1st September 2001 to 31st August 2002. Two model automatic rain samplers were installed in the Meteorological Station of Laboratory of Climatology (latitude: 37° 58′ N, longitude: 23° 47′ E) inside the Athens University Campus and in a site at Heraklio Attica, a northern suburb of Athens (latitude: 38° 03′ N, longitude: 23° 45′ E). The concentrations (μeq l⁻¹) of the major cations (H⁺, Na⁺, K⁺, Ca²⁺ and Mg²⁺) and anions (Cl⁻, , και ), as well as pH and conductivity of rain in 39 total samples were determined. The figures of pH range from 6.4 to 8.4 and conductivity from 8 to 207 μS cm⁻¹. The analysis showed that Ca²⁺ ions are abundant within all examined samples, while and present the highest concentrations from the anions. In order to find out the origin of the air masses, the air mass back trajectories were calculated. Five sectors of the origin of air masses were revealed: the North, the South, the Local, the West and the East sector. Multivariate methods included Factor Analysis and Discriminant Analysis were applied to the examined ion concentrations and three main factors were extracted, which discriminated the ions according to their origin. The first group of ions is interpreted as the result of the anthropogenic activity, the second group represents the acidity–alkalinity independently of their source and the third one the marine influence.     

Kinetics of ammonia and ammonium ion inhibition of the atmospheric oxidation of aqueous sulfur dioxide by oxygen

This is the first study, which shows both NH₃ and NH₄⁺ to inhibit the autoxidation of aqueous SO₂ in the pH range 7.0–8.5. The rate of the autoxidation, R _aut , in both buffered and unbuffered media at a fixed pH is in conformity with the rate law:

Aqueous Oxidation of Sulfur(IV) Catalyzed by Manganese(II): A Generalized Simple Kinetic Model

The reaction kinetics of S(IV) autoxidation catalyzed by Mn(II) in the pH range 3–5 typical for atmospheric liquid water, was investigated. For reactions with pH maintained constant during the reaction course, the predictions obtained by a simple integral approach cover kinetic results only for concentrations of HSO ₃ ⁻ up to 0.2 mM at pH 4.5. Thus, a generalized simple kinetic model, which can be used for predicting the reaction kinetics in wider concentration, pH and temperature ranges, was derived. This model is based on the assumption that the reaction rate is proportional to the concentration of a transient manganese-sulfito complex formed in the initial step of a radical chain mechanism. In the proposed power law rate equation

An Investigation on Temperature Variance Scaling in the Atmospheric Surface Layer

We present surface-layer measurements of temperature fluctuation variance from a site characterized by small-scale inhomogeneities. Periods of marked radiative forcing are selected. The data characterized by diabatic conditions and vertical heat flux larger than some threshold (here, chosen to be 0.01 K ms⁻¹) agree quite well with the convective scaling in unstable cases, and with the z-less parameterisation (with a large scatter) in stable cases. For near-neutral cases, the similarity function diverges because of the loss of significance of the temperature scale. Departures from similarity are highlighted in cases with smaller thermal fluxes, because horizontal heterogeneity and unsteadiness become important as production terms.     

Mass closure of total suspended particles over the coal burning power production area of western Macedonia, Greece

Ambient suspended particles (TSP) were collected from January to June 2001 at seven sampling sites in western Macedonia, Greece, where four thermal power stations are located. TSP samples were chemically characterized for minerals (Fe, Al, Mg, Ca, K, Ti and Si), trace elements (P, Cd, Cr, Cu, Mn, Pb, V, Zn, Te, Co, Ni, Se, Sr, As, and Sb), water-soluble ions , carbonaceous compounds (OC/EC) and polycyclic aromatic hydrocarbons (PAHs). These classes of compounds were consequently compared with PM mass concentrations of TSP in order to perform mass closure. PM chemical compositions exhibited differences at the seven sites. Minerals were found to be more abundant at four sites, electrolytes dominated the composition at two of the sites while carbonaceous material was most abundant only at one site. The fraction unaccounted for ranged between 22 and 34%. Spatial variations of atmospheric concentrations showed significantly higher levels of minerals, some trace metals and TC at the site that was closest to the power plants. At the same site ions exhibited high correlations with minerals and the majority of trace elements.     

Alkyl nitrate formation from the reaction of a series of branched RO2 radicals with NO as a function of temperature and pressure

Alkyl nitrate yields from the NO _x photooxidations of neopentane, 2-methylbutane and 3-methylpentane have been determined over the temperature and pressure ranges 281–323 K and 54–740 torr, respectively. The formation of the alkyl nitrates is attributed to the reaction pathway (1b) $${\text{RO}}_{\text{2}} + {\text{NO}}^{{\text{ }}\underrightarrow {\text{M}}} {\text{ RONO}}_{\text{2}}$$ and rate constant ratios k _1b/(k _1a+k _1b) are estimated, where (1a) is the reaction pathway (1a) $${\text{RO}}_{\text{2}} + {\text{NO}} \to {\text{RONO}}_{\text{2}} .$$ A method for estimating this rate constant ratio for primary, secondary and tertiary alkyl peroxy radicals is presented.     

Oligomerization of levoglucosan by Fenton chemistry in proxies of biomass burning aerosols

Reactions of levoglucosan with produced from Fenton chemistry were studied in solution serving as a proxy for biomass burning aerosols. Two modes of oligomerization (≤2000 u) were observed for reaction times between 1 and 7 days using matrix-assisted laser desorption time-of-flight mass spectrometry (MALDI-TOF-MS) and laser desorption ionization time-of-flight mass spectrometry (LDI-TOF-MS). Single-mass unit continuum mass distributions with dominant −2 u patterns were measured and superimposed by a +176/+162 u oligomer series. This latter oligomer pattern was attributed to a Criegee rearrangement (+14 u) of levoglucosan, initiated by , forming a lactone (176 u). The acid-catalyzed reaction of any ROH from levoglucosan (+162 u) forms an ester through transesterification of the lactone functionality, whereupon propagation forms polyesters. Proposed products and chemical mechanisms are suggested as sources and precursors of humic-like substances (HULIS), which are known to possess a large saccharic component and are possibly formed from biomass burning aerosols (Andreae, Global Biomass Burning, MIT Press, Cambridge, Massachusetts, 3–21, 1991).     

Probabilistic Model for Concentration Fluctuations in Compact-Source Plumes in an Urban Environment

A comprehensive model for the prediction of concentration fluctuations in plumes dispersing in the complex and highly disturbed wind flows in an urban environment is formulated. The mean flow and turbulence fields in the urban area are obtained using a Reynolds-averaged Navier-Stokes (RANS) flow model, while the standard k-ϵ turbulence model (k is the turbulence kinetic energy and ϵ is the viscous dissipation rate) is used to close the model. The RANS model provides a specification of the velocity statistics of the highly disturbed wind flow in the urban area, required for the solution of the transport equations for the mean concentration and concentration variance (both of which are formulated in the Eulerian framework). A physically-based formulation for the scalar dissipation time scale t _d , required for the closure of the transport equation for , is presented. This formulation relates t _d to an inner time scale corresponding to “internal” concentration fluctuation associated with relative dispersion, rather than an outer time scale associated with the entire portion of the fluctuation spectrum. The two lowest-order moments of concentration ( and ) are used to determine the parameters of a pre-chosen functional form for the concentration probability density function (clipped-gamma distribution). Results of detailed comparisons between a water-channel experiment of flow and dispersion in an idealized obstacle array and the model predictions for mean flow, turbulence kinetic energy, mean concentration, concentration variance, and concentration probability density function are presented.     

Characterization of nutrients in the atmospheric wet and dry deposition observed at the two monitoring sites over Yellow Sea and East China Sea

To investigate the atmospheric deposition of nutrients into the coastal and shelf regions of the northwest Pacific Ocean, observation sites were established upon Qianliyan Island (within the Yellow Sea) and the Shengsi Archipelago (within the East China Sea), respectively. Nutrient concentrations, including , were determined in both aerosols and rainwater samples. The analytical results contain clear seasonal signatures, with high values during the dry season and low values during the rainy season. Similar trends are observed for deposition fluxes. The amount of wet deposition is greater than that of dry deposition for the studied nutrient species. The influence of meteorological factors such as rainfall means that samples from Qianliyan Island record higher nutrient values than those from Shengsi. Along with riverine inputs, atmospheric deposition plays an important role in determining the biogeochemistry of nutrient species in coastal and shelf oceans. An erratum to this article can be found at     

Oxidized Nitrogen in the Remote Pacific: The Role of Electrical Discharges over the Oceans

Simulations of oxidized nitrogen performed withglobal transport tracer models systematicallyunderestimate the concentrations of total nitrate atremote marine locations in the Mid-Pacific. Higheremission rates in the models of nitrogen oxides( ) from continental sources or alarger influx from the stratosphere do not seem tobe able to account for the shortfall. We are led toconclude that there has to be a substantial sourcelocated in oceanic areas. We speculate that -emission from electrical discharges overthe oceans could be the source we are looking for.Airborne observations of atmospheric concentrationsof oxidized nitrogen and ozone in the remoteatmosphere and observations of nitrate wetdeposition in remote sites are used as additionalconstraints to check the plausibility of thishypothesis. We find that a larger emission of due to lightning activity over the oceansindeed results in a much improved simulation oftotal nitrate in the remote Pacific, particularly inthe Equatorial and Tropical South Pacific and thatsuch a scenario is generally consistent withavailable observations of nitrate wet deposition andatmospheric concentrations of oxidized nitrogen andozone. An alternative hypothesis is that there is ahitherto unknown in situ source of over thePacific Ocean.     

The gas-phase reaction of ClONO2 with hydrogen chloride

The gas-phase reaction of ClONO₂ with HCl was investigated using two large-volume environmental chambers with analysis by in situ long pathlength Fourier transform infrared absorption spectroscopy. In these chambers the reaction was observed to proceed, at least in part, by heterogenous routes, and an upper limit to the rate constant for the homogeneous gas-phase reaction of geneous routes, and an upper limit to the rate constant for the homogeneous gas-phase reaction of $$k\left( {{\text{ClONO}}_{\text{2}} + {\text{HCl}}} \right) < 1.5 \times 10^{ - 19} {\text{ cm}}^{\text{3}} {\text{ molecule}}^{{\text{ - 1}}} {\text{ s}}^{{\text{ - 1}}}$$ Was derived at 298±2K. Assuming that this room-temperature upper limit to the rate constant is applicable to stratospheric temperatures, this homogeneous gas-phase reaction can be estimated to be of negligible importance as a ClONO₂ loss process in the stratosphere.     

Particle composition and size distributions in and around a deep-pit swine operation,Ames, IA

The contribution of emissions from agricultural facilities is rapidly becoming a major concern for local and regional air quality. Characterization of particle properties such as physical size distribution and chemical composition can be valuable in understanding the processes contributing to emissions and ultimate fate of particulate matter from agricultural facilities. A measurement campaign was conducted at an Iowa, deep-pit, three-barn swine finishing facility to characterize near-source ambient particulate matter. Size-specific mass concentrations were determined using minivol samplers, with additional size distribution information obtain using optical particle counters. Particulate composition was determined via ion chromatographic analysis of the collected filters. A thermal-CO₂ elemental/organic carbon analyzer measured particulate carbon. The chemical composition and size distribution of sub-micron particles were determined via real-time aerosol mass spectrometry. Primary particulate was not found to be a major emission from the examined facility, with filter-based impactor samples showing average near-source increases (~15–50 m) in ambient PM₁₀ of 5.8 ± 2.9 μg m⁻³ above background levels. PM_2.5 also showed contribution attributable to the facility (1.7 ± 1.1 μg m⁻³). Optical particle counter analysis of the numerical size distributions showed bimodal distributions for both the upwind and downwind conditions, with maximums around 2.5 μm and below the minimum quantified diameter of 0.3 μm. The distributions showed increased numbers of coarse particles (PM₁₀) during periods when wind transport came from the barns, but the differences were not statistically significant at the 95% confidence level. The PM₁₀ aerosols showed statistically increased concentrations of sulfate, nitrate, ammonium, calcium, organic carbon, and elemental carbon when the samplers were downwind from the pig barns. Organic carbon was the major constituent of the barn-impacted particulate matter in both sub-micron (54%) and coarse size (20%) ranges. The AMS PM₁ chemical speciation showed similar species increases, with the exception of and Ca⁺², the latter not quantified by the AMS.     

Methoxy formation in the reaction of CH3O2 radicals with NO

Formation of methoxy (CH₃O) radicals in the reaction (1) CH₃O₂+NOCH₃O+NO₂ at 298 K has been observed directly using time resolved LIF. The branching ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdyMaae% 4qaiaabIeadaWgaaWcbaGaae4maaqabaGccaqGpbGaaeiiaiaabIca% ieqacaWF9aGaa8hiaiaa-nbicaWFGaGaeuiLdqKaai4waiaaboeaca% qGibWaaSbaaSqaaiaabodaaeqaaOGaae4taiaac2facaWFVaGaeuiL% dqKaai4waiaaboeacaqGibWaaSbaaSqaaiaabodaaeqaaOGaae4tam% aaBaaaleaacaqGYaaabeaakiaac2facaqGPaaaaa!4E31!\[\phi {\rm{CH}}_{\rm{3}} {\rm{O (}} = -- \Delta [{\rm{CH}}_{\rm{3}} {\rm{O}}]/\Delta [{\rm{CH}}_{\rm{3}} {\rm{O}}_{\rm{2}} ]{\rm{)}}\] has been determined by quantitative cw-UV-laser absorption at 257 nm of CH₃O₂ and CH₃ONO, the product of the consecutive methoxy trapping reaction (2) % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4qaiaabI% eadaWgaaWcbaGaae4maaqabaGccaqGpbacbeGaa83kaiaa-bcaieaa% caGFobGaa43taiaa+bcacaGFOaGaa83kaiaa+1eacaGFPaGaa4hiai% abgkziUkaabccacaqGdbGaaeisamaaBaaaleaacaqGZaaabeaakiaa% b+eacaqGGaGaaeOtaiaab+eacaqGGaGaa4hkaiaa-TcacaGFnbGaa4% xkaiaa+5cacaGFGaGaa4hiaiabeA8aMnaaBaaajqwaacqaaiaaboea% caqGibWaaSbaaKazcaiabaGaae4maaqabaqcKfaGaiaab+eaaSqaba% aaaa!55AC!\[{\rm{CH}}_{\rm{3}} {\rm{O}} + NO ( + M) \to {\rm{ CH}}_{\rm{3}} {\rm{O NO }}( + M). \phi _{{\rm{CH}}_{\rm{3}} {\rm{O}}} \] is found to be (1.0±0.2). The rate constant k ₁ is (7±2) 10^-12 cm³/molecule · s in good agreement with previous results.     

Optimal estimation of atmospheric 14C production over the Holocene: paleoclimate implications

A tree-ring ¹⁴C record and a simple box model of the global ¹⁴C cycle are combined using a method of optimal estimation theory (Rauch-Tung-Striebel smoother). The combination is used to infer information about the time evolution of ¹⁴C production in the atmosphere for the period 9400 year BC to AD 1900 year. Unlike previous attempts to infer changes from the tree-ring record, the errors in both the ¹⁴C data and the model, which are assumed to be purely random (not systematic), are formally considered. The optimal time evolution of is compared to independent evidence of changes in cosmogenic nuclide production over the Holocene from a variety of records on their original chronology, e.g., a record of the virtual axial dipole moment (VADM) based on a compilation of archeomagnetic data, the record of ¹⁰Be concentration from the GISP2 ice core (Central Greenland), and the record of ¹⁰Be concentration from the PS1 ice core (South Pole). The rank correlations between and are highly significant (p < 0.01), indicating that geomagnetic field intensity and ¹⁰Be concentration in GISP2 and PS1 changed monotonically with ¹⁴C production. The linear correlation coefficients between are also highly significant (p<0.01) but relatively small (–0.76, 0.48, and 0.60, respectively). Thus, an important fraction (42–77%) of the variance in the geomagnetic and ¹⁰Be data is not accounted for by linear regression on the ¹⁴C productions implied by the tree-ring record. The variance near the 1500 yr period, which previous authors interpreted as solar variability, represents a small fraction of the total variance in the time series (<15% for the band 1200–1800 yr) and does not correspond to a spectral peak. Hence, the hypothesis of a direct solar forcing mechanism for the postulated millennial climate variability during the Holocene is not supported.