Investigation of the Ultraviolet Photolysis Method for the Determination of Organic Nitrogen in Aerosol Samples

Abstract

The research objective was to adapt the ultraviolet (UV)photolysis method to determine dissolved organic nitrogen (DON) in aqueous extracts of aerosol samples. DON was assumed to be the difference in total concentration of inorganic nitrogen forms before and after sample irradiation. Using a 2² factorial design the authors found that the optimal conversion of urea, amino acids (alanine, aspartic acid, glycine, and serine), and methylamine for a reactor temperature of 44 °C occurred at pH 2.0 with a 24-hr irradiance period at concentrations < µM of organic nitrogen. Different decomposition mechanisms were evident: the photolysis of amino acids and methylamine released mainly ammonium (NH₄ ⁺), but urea released a near equimolar ratio of NH₄ ⁺ and nitrate (NO₃ ^?). The method was applied to measure DON in the extracts of aerosol samples from Tampa, FL, over a 32-day sampling period. Average dissolved inorganic (DIN) and DON concentrations in the particulate matter fraction PM₁₀ were 78.1 ± 29.2 nmol-Nm^?3and 8.3 ± 4.9 nmol-Nm^?3, respectively. The ratio between DON and total dissolved nitrogen ([TDN] = DIN + DON) was 10.1 ± 5.7%, and the majority of the DON (79.1 ± 18.2%) was found in the fine particulate matter (PM_2.5) fraction. The average concentrations of DIN and DON in the PM_2.5 fraction were 54.4 ± 25.6 nmol-Nm^?3 and 6.5 ± 4.4 nmol-Nm^?3, respectively.     

Detrital control on the release of dissolved organic nitrogen (DON) and dissolved inorganic nitrogen (DIN) from the forest floor under chronic N deposition

The role of detrital quantity and quality in forest floor N leaching was investigated in a litter manipulation experiment at a deciduous forest under chronic N deposition. Dissolved inorganic nitrogen (DIN) comprised the bulk of nitrogen leaching from the control except a short period following autumn litterfall. The dominance of DIN was strengthened by litter exclusion, whereas the addition of glucose or fresh litter led to a small increase in dissolved organic nitrogen (DON) and either a temporary or gradual reduction in NO(3)(-) release, respectively. Changes in soluble organic C and microbial C in the forest floor implied that increased availability of C sources might have enhanced microbial immobilization of DIN, either temporarily following glucose application or over the longer term following litter addition. The results suggest that detrital quantity and quality can play a crucial role in determining the balance between DIN and DON in N-enriched forest soils.     

Inorganic PM2.5 at a U.S. agricultural site

In this study, we present approximately two years (January 1999-December 2000) of atmospheric NH3, NH4+, HCl, Cl-, HNO3, NO3-, SO2, and SO4= concentrations measured by the annular denuder/filter pack method at an agricultural site in eastern North Carolina. This site is influenced by high NH3 emissions from animal production and fertilizer use in the surrounding area and neighboring counties. The two-year mean NH3 concentration is 5.6 (+/-5.13) microg m(-3). The mean concentration of total inorganic PM2.5, which includes SO4=, NO3-, NH4+, and Cl-, is 8.0 (+/-5.84) microg m(-3). SO4=, NO3-, NH4+, and Cl- represent, respectively, 53, 24, 22, and 1% of measured inorganic PM2.5. NH3 contributes 72% of total NH3 + NH4+, on an average. Equilibrium modeling of the gas+aerosol NH3/H2SO4/HNO3 system shows that inorganic PM2.5 is more sensitive to reductions in gas + aerosol concentrations of sulfate and nitrate relative to NH3.     

Aerosol ion characteristics during the Big Bend Regional Aerosol and Visibility Observational study

The ionic compositions of particulate matter with aerodynamic diameter < or = 2.5 microm (PM2.5) and size-resolved aerosol particles were measured in Big Bend National Park, Texas, during the 1999 Big Bend Regional Aerosol and Visibility Observational study. The ionic composition of PM2.5 aerosol was dominated by sulfate (SO4(2-)) and ammonium (NH4+). Daily average SO4(2-) and NH4+ concentrations were strongly correlated (R2 = 0.94). The molar ratio of NH4+ to SO4(2-) averaged 1.54, consistent with concurrent measurements of aerosol acidity. The aerosol was observed to be comprised of a submicron fine mode consisting primarily of ammoniated SO4(2-) and a coarse particle mode containing nitrate (NO3-). The NO3- appears to be primarily associated with sea salt particles where chloride has been replaced by NO3-, although formation of calcium nitrate (Ca(NO3)2) is important, too, on several days. Size-resolved aerosol composition results reveal that a size cut in particulate matter with aerodynamic diameter < or = 1 microm would have provided a much better separation of fine and coarse aerosol modes than the standard PM2.5 size cut utilized for the study. Although considerable nitric acid exists in the gas phase at Big Bend, the aerosol is sufficiently acidic and temperatures sufficiently high that even significant future reductions in PM2.5 SO4(2-) are unlikely to be offset by formation of particulate ammonium nitrate in summer or fall.     

The use of ambient measurements to identify which precursor species limit aerosol nitrate formation

A thermodynamic equilibrium model was used to investigate the response of aerosol NO3 to changes in concentrations of HNO3, NH3, and H2SO4. Over a range of temperatures and relative humidities (RHs), two parameters provided sufficient information for indicating the qualitative response of aerosol NO3. The first was the excess of aerosol NH4+ plus gas-phase NH3 over the sum of HNO3, particulate NO3, and particulate SO4(2-) concentrations. The second was the ratio of particulate to total NO3 concentrations. Computation of these quantities from ambient measurements provides a means to rapidly analyze large numbers of samples and identify cases in which inorganic aerosol NO3 formation is limited by the availability of NH3. Example calculations are presented using data from three field studies. The predictions of the indicator variables and the equilibrium model are compared.     

Water-soluble organic nitrogen in atmospheric aerosol: a comparison of UV and persulfate oxidation methods

Two well established methods that are widely applied in the determination of marine dissolved organic nitrogen (DON) have been investigated in their application to the determination of rainwater DON and the water-soluble organic nitrogen component of atmospheric aerosol. Empirical observation highlighted some difficulties in the analysis of DON in these non-marine matrices, so some practical suggestions for the extension of the oxidative methods to atmospheric samples are proposed.Ten rain samples, 20 aqueous aerosol extracts, and a suite of commercially obtained organic nitrogen compounds were both chemically oxidised by persulfate and oxidised by exposure to high-intensity ultraviolet light. The total dissolved nitrogen concentration of the rains in this study ranged from 4 to 35 μM nitrogen. The aerosol extracts were diluted to a pre-oxidation concentration range of 12–65 μM N for oxidation and analysis. Both UV and persulfate methods require the aqueous extract of the aerosol organic nitrogen to be diluted approximately to rainwater concentrations for optimal oxidation efficiency, since sub-optimal recoveries and high analytical variability arise at high concentration. Some potential causes of analytical interference at higher concentration are discussed.This study shows that total dissolved nitrogen results obtained by the two methods are linearly correlated (with an R² of 0.87 for 30 samples) over the full range of natural rainwater concentrations, but results obtained using the persulfate oxidation are about 30% lower than those obtained by photo-oxidation.     

The Aerosol Research and Inhalation Epidemiology Study (ARIES): PM2.5 mass and aerosol component concentrations and sampler intercomparisons

The Aerosol Research and Inhalation Epidemiology Study (ARIES) was designed to provide high-quality measurements of PM2.5, its components, and co-varying pollutants for an air pollution epidemiology study in Atlanta, GA. Air pollution epidemiology studies have typically relied on available data on particle mass often collected using filter-based methods. Filter-based PM2.5 sampling is susceptible to both positive and negative errors in the measurement of aerosol mass and particle-phase component concentrations in the undisturbed atmosphere. These biases are introduced by collection of gas-phase aerosol components on the filter media or by volatilization of particle phase components from collected particles. As part of the ARIES, we collected daily 24-hr PM2.5 mass and speciation samples and continuous PM2.5 data at a mixed residential-light industrial site in Atlanta. These data facilitate analysis of the effects of a wide variety of factors on sampler performance. We assess the relative importance of PM2.5 components and consider associations and potential mechanistic linkages of PM2.5 mass concentrations with several PM2.5 components. For the 12 months of validated data collected to date (August 1, 1998-July 31, 1999), the monthly average Federal Reference Method (FRM) PM2.5 mass always exceeded the proposed annual average standard (12-month average = 20.3 +/- 9.5 micrograms/m3). The particulate SO4(2-) fraction (as (NH4)2SO4) was largest in the summer and exceeded 50% of the FRM mass. The contribution of (NH4)2SO4 to FRM PM2.5 mass dropped to less than 30% in winter. Particulate NO3- collected on a denuded nylon filter averaged 1.1 +/- 0.9 micrograms/m3. Particle-phase organic compounds (as organic carbon x 1.4) measured on a denuded quartz filter sampler averaged 6.4 +/- 3.1 micrograms/m3 (32% of FRM PM2.5 mass) with less seasonal variability than SO4(2-).     

Mass-size distributions of particulate sulfate, nitrate, and ammonium in a particulate matter nonattainment region in southern Taiwan

Concentrations and distributions of three major water-soluble ion species (sulfate, nitrate, and ammonium) contained in ambient particles were measured at three sampling sites in the Kao-ping ambient air quality basin, Taiwan. Ambient particulate matter (PM) samples were collected in a Micro-orifice Uniform Deposit Impactor from February to July 2003 and were analyzed for water-soluble ion species with an ion chromatograph. The PM1/ PM2.5 and PM1/PM10 concentration ratios at the emission source site were 0.73 and 0.53 and were higher than those (0.68 and 0.48) at the background site because there are more combustion sources (i.e., industrial boilers and traffic) around the emission source site. Mass-size distributions of PM NO3- were found in both the fine and coarse modes. SO4(2-)and NH4+ were found in the fine particle mode (PM2.5), with significant fractions of submicron particles (PM1). The source site had higher PM1/PM10(79, 42, and 90%) and PM1/PM2.5 concentration ratios (90, 58, and 93%) for the three major inorganic secondary aerosol components (SO4(2-), NO3-, and NH4+) than the receptor site (65, 27, and 65% for PM1/PM10, 69, 51, and 70% for PM1/PM2.5. Results obtained in this study indicate that the PM1 (submicron aerosol particles) fraction plays an important role in the ambient atmosphere at both emission source and receptor sites. Further studies regarding the origin and formation of ambient secondary aerosols are planned.     

Chemical coupling between ammonia, acid gases, and fine particles

The concentrations of inorganic aerosol components in the fine particulate matter (PM(fine)< or =2.5 microm) consisted of primarily ammonium, sodium, sulfate, nitrate, and chloride are related to the transfer time scale between gas to particle phase, which is a function of the ambient temperature, relative humidity, and their gas phase constituent concentrations in the atmosphere. This study involved understanding the magnitude of major ammonia sources; and an up-wind and down-wind (receptor) ammonia, acid gases, and fine particulate measurements; with a view to accretion gas-to-particle conversion (GTPS) process in an agricultural/rural environment. The observational based analysis of ammonia, acid gases, and fine particles by annular denuder system (ADS) coupled with a Gaussian dispersion model provided the mean pseudo-first-order k(S-1) between NH(3) and H(2)SO(4) aerosol approximately 5.00 (+/-3.77)x10(-3) s(-1). The rate constant was found to increase as ambient temperature, wind speed, and solar radiation increases, and decreases with increasing relative humidity. The observed [NH(3)][HNO(3)] products exceeded values predicted by theoretical equilibrium constants, due to a local excess of ammonia concentration.     

Measurement and analysis of the relationship between ammonia, acid gases, and fine particles in eastern North Carolina

An annular denuder system, which consisted of a cyclone separator; two diffusion denuders coated with sodium carbonate and citric acid, respectively; and a filter pack consisting of Teflon and nylon filters in series, was used to measure acid gases, ammonia (NH3), and fine particles in the atmosphere from April 1998 to March 1999 in eastern North Carolina (i.e., an NH3-rich environment). The sodium carbonate denuders yielded average acid gas concentrations of 0.23 microg/m3 hydrochloric acid (standard deviation [SD] +/- 0.2 microg/m3); 1.14 microg/m3 nitric acid (SD +/- 0.81 microg/m3), and 1.61 microg/m3 sulfuric acid (SD +/- 1.58 microg/m3). The citric acid denuders yielded an average concentration of 17.89 microg/m3 NH3 (SD +/- 15.03 microg/m3). The filters yielded average fine aerosol concentrations of 1.64 microg/m3 ammonium (NH4+; SD +/- 1.26 microg/m3); 0.26 microg/m3 chloride (SD +/- 0.69 microg/m3), 1.92 microg/m3 nitrate (SD +/- 1.09 microg/m3), and 3.18 microg/m3 sulfate (SO4(2-); SD +/- 3.12 microg/m3). From seasonal variation, the measured particulates (NH4+, SO4(2-), and nitrate) showed larger peak concentrations during summer, suggesting that the gas-to-particle conversion was efficient during summer. The aerosol fraction in this study area indicated the domination of ammonium sulfate particles because of the local abundance of NH3, and the long-range transport of SO4(2-) based on back trajectory analysis. Relative humidity effects on gas-to-particle conversion processes were analyzed by particulate NH4+ concentration originally formed from the neutralization processes with the secondary pollutants in the atmosphere.     

Atmospheric phase distribution of oxidized and reduced nitrogen at a forest ecosystem research site

Atmospheric concentrations of gaseous NH3 and HNO3 and of particulate NH4+ and NO3- were measured during various seasons at a forest ecosystem research site in the "Fichtelgebirge" mountains in Central Europe. Air masses arriving at this site were highly variable with respect to trace compound concentration levels and their concentration ratios. However, the distributions of NH4+ and NO3- within the aerosol particle size spectra exhibited some very consistent patterns, with the former dominating the fine particle concentrations, and the latter dominating the coarse particles range, respectively. Overall, the particulate phase (NH4+ + NO3-) dominated the atmospheric nitrogen budget (particulate and gas phase, NH4+ + NO3- + NH3 + HNO3) by more than 90% of the median total mixing ratio in winter, and by more than 60% in summer. The phase partitioning varied significantly between the winter and summer seasons, with higher relative importance of the gaseous species during summer, when air temperatures were higher and relative humidities lower as compared to the winter season. Reduced nitrogen dominated over oxidized nitrogen, indicating the prevailing influence of emissions from agricultural activity as compared to traffic emissions at this mountainous site. A model has been successfully applied in order to test the hypothesis of thermodynamic equilibrium between the particulate and gas phases.     

Use of (15)N-labelled nitrogen deposition to quantify the source of nitrogen in runoff at a coniferous-forested catchment at Gårdsjön, Sweden

To determine the source of dissolved inorganic nitrogen (N) in runoff, approx. 35kg N enriched with the stable isotope (15)N (2110 per thousand delta(15)N) was added to a mature coniferous forested catchment for one whole year. The total N input was approx. 50kg ha(-1) year(-1). The enrichment study was part of a long-term whole-catchment ammonium nitrate addition experiment at G?rdsj?n, Sweden. The (15)N concentrations in precipitation, throughfall, runoff and upper forest floor were measured prior to, during, and 3-9years following the (15)N addition. During the year of the (15)N addition the delta(15)N level in runoff largely reflected the level in incoming N, indicating that the leached NO(3)(-) came predominantly from precipitation. Only 1.1% of the incoming N was lost during the year of the tracer addition. The cumulative loss of tracer N over a 10-year period was only 3.9% as DIN and 1.1% as DON.     

Contribution of primary and secondary sources to organic aerosol and PM2.5 at SEARCH network sites

Chemical tracer methods for determining contributions to primary organic aerosol (POA) are fairly well established, whereas similar techniques for secondary organic aerosol (SOA), inherently complicated by time-dependent atmospheric processes, are only beginning to be studied. Laboratory chamber experiments provide insights into the precursors of SOA, but field data must be used to test the approaches. This study investigates primary and secondary sources of organic carbon (OC) and determines their mass contribution to particulate matter 2.5 microm or less in aerodynamic diameter (PM2.5) in Southeastern Aerosol Research and Characterization (SEARCH) network samples. Filter samples were taken during 20 24-hr periods between May and August 2005 at SEARCH sites in Atlanta, GA (JST); Birmingham, AL (BHM); Centerville, AL (CTR); and Pensacola, FL (PNS) and analyzed for organic tracers by gas chromatography-mass spectrometry. Contribution to primary OC was made using a chemical mass balance method and to secondary OC using a mass fraction method. Aerosol masses were reconstructed from the contributions of POA, SOA, elemental carbon, inorganic ions (sulfate [SO4(2-)], nitrate [NO3-], ammonium [NH4+]), metals, and metal oxides and compared with the measured PM2.5. From the analysis, OC contributions from seven primary sources and four secondary sources were determined. The major primary sources of carbon were from wood combustion, diesel and gasoline exhaust, and meat cooking; major secondary sources were from isoprene and monoterpenes with minor contributions from toluene and beta-caryophyllene SOA. Mass concentrations at the four sites were determined using source-specific organic mass (OM)-to-OC ratios and gave values in the range of 12-42 microg m(-3). Reconstructed masses at three of the sites (JST, CTR, PNS) ranged from 87 to 91% of the measured PM2.5 mass. The reconstructed mass at the BHM site exceeded the measured mass by approximately 25%. The difference between the reconstructed and measured PM2.5 mass for nonindustrial areas is consistent with not including aerosol liquid water or other sources of organic aerosol.     

Measurement, analysis, and modeling of fine particulate matter in eastern North Carolina

An analysis of fine particulate data in eastern North Carolina was conducted to investigate the impact of the hog industry and its emissions of ammonia into the atmosphere. The fine particulate data are simulated using ISORROPIA, an equilibrium thermodynamic model that simulates the gas and aerosol equilibrium of inorganic atmospheric species. The observational data analyses show that the major constituents of fine particulate matter (PM2.5) are organic carbon, elemental carbon, sulfate, nitrate, and ammonium. The observed PM2.5 concentration is positively correlated with temperature but anticorrelated with wind speed. The correlation between PM2.5 and wind direction at some locations suggests an impact of ammonia emissions from hog facilities on PM2.5 formation. The modeled results are in good agreement with observations, with slightly better agreement at urban sites than at rural sites. The predicted total inorganic particulate matter (PM) concentrations are within 5% of the observed values under conditions with median initial total PM species concentrations, median relative humidity (RH), and median temperature. Ambient conditions with high PM precursor concentrations, low temperature, and high RH appear to favor the formation of secondary PM.     

Measurement of organic nitrogen and phosphorus fractions at very low concentrations in wastewater effluents

The purpose of this study was to develop simple, accurate, and inexpensive measurement protocols for dissolved organic nitrogen (DON) and dissolved non-reactive phosphorus (DNRP) at low levels in wastewater effluents. Two protocols are presented--one to measure DON exclusively, and the other to measure DON and DNRP simultaneously. Currently, DON and DNRP are calculated indirectly by subtracting the dissolved inorganic fractions from the total dissolved concentration, resulting in significant errors. To increase the accuracy of DON measurements, effluent sample pretreatment using ion exchange to remove nitrate was applied. Spectrometric methods were selected to measure the inorganic fractions-the second derivative UV spectroscopy method for nitrate, and the malachite green method for orthophosphate. These methods, combined with the optimized persulfate digestion of the samples, can be used to measure total dissolved nitrogen and phosphorus accurately. The measurement ranges attained were 0.05 to 3 mg N/L for DON and 0.01 to 0.5 mg P/L for DNRP.     

Effects of SO2 and NOx emission reductions on PM2.5 mass concentrations in the southeastern United States

Measurements from sites of the Southeastern Aerosol Research and Characterization (SEARCH) program, made from 1998 to 2001, are used with a thermodynamic equilibrium model, Simulating Composition of Atmospheric Particles at Equilbrium (SCAPE2), to extend an earlier investigation of the responses of fine particulate nitrate (NO3-) and fine particulate matter (PM2.5) mass concentrations to changes in concentrations of nitric acid (HNO3) and sulfate (SO42-). The responses were determined for a projected range of variations of SO42- and HNO3 concentrations resulting from adopted and proposed regulatory initiatives. The predicted PM2.5 mass concentration decreases averaged 1.8-3.9 microg/m3 for SO42- decreases of 46-63% from current concentrations. Combining the S042- decrease with a 40% HNO3 decrease from current concentrations (approximating expected mobile-source oxides of nitrogen [NOx] reductions by 2020) yielded additional incremental reductions of mean predicted PM2.5 mass concentration of 0.2 microg/m3 for three nonurban sites and 0.8-1 microg/m3 for one nonurban and two urban sites. Increasing the HNO3 reduction to 55% (an estimate of adding Clear Skies Phase II NOx reductions) yielded additional incremental reductions of mean predicted PM2.5 mass concentration of 0-0.4 microg/m3. Because of the well-documented losses of particulate NO3- from Federal Reference Method (FRM) filters, only a fraction of these incremental changes would be observed.     

Chemical speciation of PM2.5 collected during prescribed fires of the Coconino National Forest near Flagstaff, Arizona

The use of prescribed fire is expected to increase in an effort to reduce the risk of catastrophic fire, particularly at urban/forest interfaces. Fire is a well-known source of particulate matter (PM) with particle sizes < or =2.5 microm (PM2.5), small diameter PM known to affect climate, visibility, and human health. In this work, PM2.5 was collected during seven first-entry burns (flaming and smoldering stages) and one maintenance burn of the Coconino National Forest. Samples were analyzed for organic and elemental carbon, cations (sodium, potassium [K+], and ammonium [NH4+]), anions (nitrate [NO3-] and sulfate), and 48 elements (with atomic weights between sodium and lead). The PM2.5 contained high organic carbon levels (typically >90% by mass), commonly observed ions (K+, NH4+, and NO3-) and elements (K+, chlorine, sulfur, and silicon), as well as titanium and chromium. Flaming produced higher K+ and NH4+ levels than smoldering, and the elemental signature was more complex (20 versus 7 elements). Average organic carbon x 1.4 mass fractions (+/-standard deviation) were lower during flaming (92+/-14%) than during smoldering (124+/-24%). The maintenance (grassland) burn produced lower particle concentrations, lower NH4+ and NO3- levels, and higher K and chlorine levels than did the first-entry fires.     

The degradation of dissolved organic nitrogen associated with melanoidin using a UV/H2O2 AOP

The aim of this study was to examine the simultaneous degradation of dissolved organic nitrogen (DON) and associated colour from wastewater containing melanoidins by an advanced oxidation process (AOP). UV irradiation of H2O2 was used as the mechanism to create the hydroxyl radical for oxidation. Melanoidins are large nitrogenous organic compounds that are refractory during biological wastewater treatment processes. The simultaneous degradation of DON and colour, present as a result of these compounds, was investigated using an AOP. The oxidation process was much more capable of removing colour (99% degradation), dissolved organic carbon (DOC) (50% degradation) and DON (25% degradation) at the optimal applied dose of hydrogen peroxide for the system (3300 mg l(-1)). This indicated that colour and DON removal were decoupled problems for the purpose of treating melanoidin by an AOP and thus colour removal can not be used as an indication of DON removal Colour was caused by organic molecules with molecular weight greater than 10 kDa. Oxidation caused a partial reduction of the DON (41-15% of the total dissolved nitrogen) and DOC (29-14% of the DOC) associated with the large molecular weight fraction (>10 kDa) and almost complete colour removal (87-3% of the total colour). The degraded DON was mostly accounted for by the formation of ammonia (31% of the nitrogen removed from the large fraction) and small molecular weight compounds (66% of the nitrogen removed from the large fraction). The degraded DOC appeared to be mostly mineralised (to CO2) with only 20% of the degraded compounds appearing as small molecular weight DOC.     

Passive sampler for PM10-2.5 aerosol

This study investigates the use of a small passive sampler for aerosol particles to determine particulate matter (PM)10-2.5 concentrations in outdoor air. The passive sampler collects particles by gravity, diffusion, and convective diffusion onto a glass coverslip that is then examined with an optical microscope; digital images are processed with free software and the resultant PM10-2.5 concentrations determined. Both the samplers and the analyses are relatively inexpensive. Passive samplers were collocated with Federal Reference Method (FRM) samplers in Chapel Hill, NC; Phoenix, AZ; and Birmingham, AL; for periods from 5 to 15 days. Particles consisted primarily of inorganic dusts at some sites and a mix of industrial and inorganic materials at other sites. Measured concentrations ranged from < 10 microg/m3 to approximately 40 microg/m3. Overall, PM10-2.5 concentrations measured with the passive samplers were within approximately 1 standard deviation of concentrations measured with the FRM samplers. Concentrations determined with passive samplers depend on assumptions about particle density and shape factors and may also depend somewhat on local wind speed and turbulence; accurate values for these parameters may not be known. The degree of agreement between passive and FRM concentrations measured here suggests that passive measurements may not be overly dependent on accurate knowledge of these parameters.