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In a wind-tunnel study, the influence of building width and orientation into the wind was examined through concentration profiles in the near wake of the building. The model building was placed in a simulated atmospheric boundary layer. The effects of building width were examined for buildings having width-to-height ratios ranging from 2 to 22. The effects of oblique orientation were examined for angles ranging from — 30 to +60 deg. For most cases, the source was placed midway along the lee side of the building. The stack height was either at ground level or 1.5 times the height of the building. The lateral plume spread from a point source placed near the center of the building was observed to be largest for a width/height ratio of 10. The influence of the end flow around the sides of the building had less effect for wider buildings. For the ground-level source, an oblique angle resulted in a maximum ground-level concentration increase by a factor of 2–3 at three building heights downstream. Concentrations were increased by less than a factor of 1.5 at ten building heights downstream. For an elevated source, the building influence on ground-level concentrations was quite similar but with an even larger increase.

The plume opacity and droplet diameters of a monodisperse sulfuric acid aerosol were calculated as a function of the initial H 2 SO 4 concentration, initial H 2 O concentration and final gas temperature after cooling from an original stack gas temperature of 300°C. Calculation assumptions include heterogeneous heteromolecular condensation of H 2 SO 4 and H 2 O onto monodisperse nuclei of 0.05 μm dia., three aerosol particle nuclei concentrations of 10 6 , 10 7 and 10 8 cm −3 (at 300°C and 760 mm Hg); and a stack or plume diameter of 6 m. The calculated results show that for the conditions considered and with the stack temperatures in excess of 125°C, initial H 2 SO 4 stack gas concentrations of 10ppm or less will result in calculated opacities of less than 20 % for a plume diameter of 6 m. The results show that the calculated opacity is significantly affected by the initial H 2 SO 4 and initial H 2 O concentrations and the final gas temperature. The increases in the calculated opacities upon cooling of the stack gases are similar in general to the increases in the measured opacities between instack and outstack reported by Nader and Conner (1978) for an oil-fired boiler.

The O3 measurements from the Regional Air Monitoring System (RAMS) in St. Louis in the upwind and downwind flow directions have been used to evaluate the first day impact of the urban plume of St. Louis. The time periods between April and October 1975 and 1976 have been utilized for this purpose. Ozone formation in the urban plume has been evaluated with respect to the distribution of O3 concentrations at RAMS stations downwind. The relationships between O3 concentrations in the urban plume and such meteorological parameters as wind direction, wind speed, temperature, solar radiation intensity and maximum mixing heights have been investigated. Plume widths also have been estimated and related to plume O3 intensities. Incremental O3 formation within the urban plume compared to regional O3 background increases both in frequency and intensity from spring into midsummer and declines again in late summer and early fall. Episodic periods with substantial increments of O3 formation in the plume over background occur especially during the summer months. Aircraft measurements of O3 in the St. Louis plume are discussed by considering first day transport distances, plume widths and O3 profiles beyond the outer stations in the RAMS network. The significance of incremental O3 formation is evaluated in the St. Louis plume on population exposures as well as on fumigations of field crops or forest in rural areas downwind. The strongest effects of O3 formation in the plume occur in the prevailing wind direction. The O3 in the plumes from all of the cities in an interior region of the U.S. is estimated to impact 5–10% of the rural lands in this region on any given day.

Neutral and four different levels of stable stratification (weak to strongly stable i.e. Ri δ = 0.048−0.248 ) were created in the stratified wind tunnel at NIES. The effects of stable stratification on the spread of a plume from a small, circular, ground level release were examined by flow visualization, trace gas concentration measurement, and flow field velocity and turbulence measurements. As stable stratification increased, flow field visualization showed that the turbulence was increasingly suppressed, especially near the surface, and the vertical plume spread was also inhibited with increasing stability. The normalized velocity power exponent, m , increased from 0.17 to 1.04 (for neutral to strong stability), and the u and w components of turbulent intensity were suppressed. The vertical concentration power exponent, p (from C ~ exp (−z p ) ), varied from 1.3 for the neutral case, to 3.0 for the strong stable case. The observed values of p showed reasonably good agreement with the values of p estimated from the half-empirical diffusion equation. The vertical plume spread, σ z , vs distance downwind decreased with increasing stability, appearing as logical extensions of the Pasquill-Gifford chart. However, the horizontal plume spread, σ y , vs distance at first decreased with increasing stability then began to increase as the stability increased from moderate to strongly stable, approaching the neutral case curve. This behavior is caused by the suppression of vertical motion at the stronger stable stratifications which leads to increased plume meandering and plume collapse.

Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585–590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).

The measurements during episodic periods in the St. Louis area in 1975 and 1976 of fine particle sulfur, fine particle mass and ozone are related. Such episodes are concentrated into time periods in the late spring and summer months. During such episodes, particle sulfur is the major constituent of the fine particle mass. The sum of the non-sulfur species in the fine particle mass do not show similar episodic patterns as the fine particle sulfur. Elevated concentrations of fine particle sulfur and of ozone usually occur together within the same episodic time periods. However, the day to day variations in fine particle sulfur and of ozone do differ somewhat within these time periods. Both fine particle sulfur and ozone show the influence of regional scale and local scale atmospheric photochemical processes on their formation during episodic time periods. Regional scale boundary layer processes frequently appear to contribute more to fine particle sulfur concentrations than to ozone formation. Local scale primary emissions also contribute to the ambient fine particle sulfur concentrations at core urban locations.

Ozone plays an important role in the physicochemical interactions between plumes and background air. During two field programs conducted at Cordemais in fall 1984 and at Le Havre in fall 1985, concentration measurements were performed in background air and in the plumes of fossil-fuel fired power plants. In background air, the daily average ozone concentration varied between 15 and 60 ppb depending on solar irradiation, pollution level and atmospheric stability. Maximum values of 100 ppb were observed in industrial area plumes. In the power plant plume, consumption of atmospheric ozone by emitted NO is important during the first 5 km downwind of the power plant but does not totally explain some important formation of NO2 identified at short distances downwind of the power plant.

Several recent assessments have focused on the climate effects of a major nuclear war. Most studies have assumed smoke optical properties which remain constant with time. The optical properties of smoke, however, can change with time due to coagulation within the lofted smoke plumes. We present calculations that model this process and its effect on optical properties on short to intermediate time scales. We treat smoke that is high in elemental carbon content as expected from petroleum-based fuels as well as smoke from vegetative fuels. The model we use is necessarily restricted to spherical particles but our results are in qualitative agreement with the optical effects of smoke from the large forest fires which occurred in Alberta, Canada in the 1950s. If nuclear war smoke is similar (and some data imply that it is), we expect similar optical effects after a war. Our results suggest that coagulation can decrease the absorption cross-section by about 50% in 1 week for a smoke that is half from wood fuel and half from petroleum-based fuel. This decrease might limit the extent of the climate effects of smoke from a nuclear war, even in the absence of rainout of the smoke. The initial smoke size distribution evolves within a few days to a size that may be fit by a log-normal distribution with a mode radius of 0.4μm and a geometric standard deviation of 1.5. Climate model simulations should be initialized with larger smoke size distributions and smaller absorption cross sections than considered previously.

The integral time scale, TC, of the concentration fluctuations in a narrow, meandering (intermittent) plume can be much less than the time scale, TE, of the turbulence in which the plume is immersed, and is generally of the same order of magnitude as the time required for the plume to pass once over a receptor. However the total concentration fluctuation variance is equally strongly influenced by the larger time scale, TE, associated with meandering caused by ambient turbulence. It is shown that observed energy spectra of concentration fluctuations can be fitted by a linear combination of two Markov spectra, one with the time scale of the meandering motions and another with the time scale of the small scale plume motions. The two components are weighted by I and 1 − I, respectively, where I is the intermittency or fraction of time that non-zero concentrations occur.

Four models for the operational prediction of plume visibility have been run by their developers on data from the VISTTA field study at the Navajo Generating Station. The different models give substantially different predictions of plume dispersion, cross-plume concentration integrals, and plume-sky contrast. Two of the models predict plume-sky contrasts which differ qualitatively from those observed. Overall model performance is limited chiefly by dispersion module performance; given observed concentration integrals as inputs, three of the models correctly predict the qualitative features of observed contrast. Much of the observed variation in plume dispersion and concentration integrals appears to have been due to sub-scale fluctuations in atmospheric transport and source emissions. The effects of particles on observed plume contrast were less than the experimental uncertainty.

International audience; The application of a correspondence analysis to an aerosol collected in a simple atmospheric environment permitted the evaluation of the emission sources. A quantitative relation on the chemical composition of the emission sources was obtained from the calculation of the barycentre of sample clusters, and the mean chemical profile of each emission source was determined.

The 1981 VISTTA field study characterized the composition and appearance of particle-rich plumes from three different sources. This paper compares the VISTTA observations with the predictions of two plume visibility models. Observations and predictions are analyzed from the perspective of exact solutions to the equations of radiative transfer for a somewhat idealized atmosphere. These solutions, which explicity relate plume/sky contrast to the composition of plume and background and the geometry of sun, plume and observer, are shown to be consistent with the VISTA observations. The simplified relationships are used as the basis for budgeting radiative transfer by the plume and background, and for analyses of the sensitivity of plume appearance to individual variables. The optics predictions of the two models are less accurate for plumes dominated by particle scattering than they are for plumes dominated by NO2 absorption. Inaccurate prediction of plume particle size distributions can be identified as an important source of error. Inaccurate prediction of background sky radiance is suspected as another.

Measurements of the chemical composition of cloud water have been made as part of a programme to study the chemical development of power plant plumes in trajectories over the North Sea. During a two-day study (28–29 January 1981), the conditions were anticyclonic with light winds advecting the plume from the NE coast of England towards Denmark. The mixing layer overland was capped by stratocumulus beneath a very strong subsidence inversion, which resulted in the plume being entirely trapped within the layer. Low level acceleration occurred as the plume travelled towards the coast, accompanied by a shallowing of the mixing layer. This led to the unusual situation whereby the plume was confined to a shallow (400m) stratocumulus-filled boundary layer throughout most of its travel. The light winds enabled approximately Lagrangian sampling of the plume after about 5 and 22 h travel (~ 100 and 650km from source). The very shallow boundary layer constrained the dilution of the plume to such an extent that even though ambient O3 was consumed within the plume by the reaction with NO, the NO2NOx ratio was still < 0.5 along the plume centre line after 22 h travel. The measurements have been compared with the predictions of a reactive plume model involving both gas phase and solution phase chemistry. The model predicts oxidation rates for SO2 in the ambient air outside the plume to be substantially higher than those within the plume, at values of 0.5–1.0 and ~ 0.04 % h−1, respectively. This leads to the conclusion that nearly all the sulphate in the plume arose from entrainment of sulphate produced in cloud droplets outside the plume. The absence of an effective oxidation mechanism in solution for the conversion of NOx to HNO3 suggests that nitrate in the cloud water was derived from the gas phase oxidation of NOx. HC1 was found to be the major contributor to cloud water acidity in the plume on this occasion. The resultant acidity suppressed the solubility of SO2 and this together with the low oxidant levels inhibited the production of sulphate in solution within the plume. The HCl contribution to acidity had declined markedly after 22h travel and this loss corresponds to a dry deposition velocity of 13 mm s−1.

A mechanism of rainfall augmentation in the lee of big (~ 5000 MWe) power plants due to washout of liquid water content of cooling tower plumes by raindrops, has been studied by means of a one-dimensional plume model. The relative rainfall increase beneath the plume was estimated for various meteorological conditions and total outputs of cooling tower system. Usually the rainfall increase, doesn't exceed 20–40% and extends not more than 5–7 km from the power plant. In favourable conditions rainfall may however increase even 70 % or more over a large area. In such cases the amount of additionally deposited water may several times exceed the total emission from cooling towers. The total, yearly or seasonal increase of rainfall, which is much smaller due to variability of the wind direction, depends on local climatological conditions.

Airborne measurements were made in and near the plumes of the following mid western coal-fired power plants in 1981: Kincaid in central Illinois in February, La Cygne near Kansas City in March and Labadie near St. Louis in August and September. One objective of these measurements was to obtain data (reported elsewhere) to be used for the evaluation of plume visibility models. The results of the chemical and aerosol measurements are reported here. Good agreement was obtained from different measurement methods for SO2 and sulfate, but not for two different nitrate measurement methods. No more than a few per cent of the NOx emitted by these plants was NO2, and NO2 formation in the plumes could be accounted for by the ozone loss at the observed distances (up to 100 km in winter and 40 km in summer). Sulfate formation rates were in agreement with prior data, and there was no evidence of increased sulfate formation rates in a scrubbed plume (La Cygne). Both aerosol size distributions and sulfur particle size distributions were measured and showed reasonable agreement. The amount of light scattering by particles in the plume was quite variable, in pan because of variations in their mean particle size. The summer measurements were conducted during a rainy and hazy period when the Labadie plume typically could be seen from the ground only within a few km of the source. During this time, the visual impact of the plume was minimal.

A field tracer study was conducted in a hilly area on the coast of California to provide data for evaluating air quality dispersion models. Dual tracers and meteorological measurements were taken both onshore and offshore in order to investigate the transport and dispersion of pollutant plumes released from offshore sources and carried to coastal complex terrain. This paper describes the study design and presents some preliminary conclusions from the data analysis.

Data from a study of buoyant plume interaction with the sea-breeze inversion are discussed with the view of testing inversion penetration criteria. While limited in its aims and the quantity of data available, the study is unusual in that observations of all relevant physical quantities are available. Analysis shows that the Briggs (1969) criterion for penetration is too conservative, while the predictions of Briggs (1975) are too optimistic. Predictions by Manins (1979) are supported. The study demonstrates that plumes can partially penetrate an inversion, with some material being mixed downward and some lost to higher levels.

Underwater releases of toxic or flammable gases occur as a result of industrial accidents (e.g. pipeline breaks or blowouts) or natural (e.g. volcanic) events. The risk associated with such occurrences depends on the gas concentration in the surfacing zone. For gases lighter than air, a rising plume is established above the water surface. The paper presents laboratory measurements of the gas concentration and velocity in the zone-of-establishment as well as in the lower part of the established plume. Theoretical solutions for concentration and plume contour are also given.

The injection of a dense gas stream at ground level into a flowing turbulent atmosphere produces a wide, flat plume that entrains air primarily through its upper surface. A quasi-one-dimensional flow model of an isothermal dense gas plume is developed for the purpose of comparing experiments in wind tunnels and water flumes and field tests in the atmosphere. Comparisons are made for plume width, including the width at the source, and centerline ground plane source gas concentration. All published data are used in this comparison, which cover a factor of about 100 in plume length scale and Reynolds number. Tests conducted by different experimenters were found not to be dynamically similar. Dimensionless model parameters, all of order unity, are selected to give the best agreement among all the experimental data. The dependence of entrainment rate on the plume Richardson number, a key feature of the model, is confirmed in the comparison. The entrainment rate parameter is found to be larger for the field tests than for the laboratory experiments, reflecting the much higher Reynolds number of the former.

Number distribution data for 0.1–45 μm diameter aerosol were obtained using optical counting and sizing probes flown over the Alaskan Arctic during the second Arctic Gas and Aerosol Sampling Program (AGASP-II), flights 201–203. Due to noise present in the lowest size channels of the optical probes, estimates of the H2SO4 component of Arctic haze were not attempted. Large particle (> 0.5 μm diameter) results are presented here. Large particle number and volume concentration were determined along with estimated mass, which was generally 0.3 μg m−3 mass loading sizedistributed aerosol data produced a means for comparing volume geometric median diameters (VGMD) for these higher-mass time intervals. These VGMDs showed that solid crustal particles previously observed during AGASP-II had VGMDs in the 1.2–1.6 μm range and that the shape of these fitted lognormal distributions was essentially constant. This result suggests very-long-range transport from a distant crustal source and, in conjunction with aerosol physical and chemical characterization data, argues against the presence of the Mt. Augustine eruptive particles during AGASP-II Alaskan Arctic sampling.

Three studies are presented that investigate the effect of the number of stacks and of the azimuthal angle between the direction of the wind and the line of stacks on plume rise enhancement. In the first study, observations were made of the merger and motion of thermal pairs. Thermal pairs released in one-above-the-other configurations merged more rapidly and moved faster than thermal pairs released in a side-by-side configuration. In the second study, plume rise measurements were made in a wind tunnel for plumes from two to four stacks. For a given number of plumes, the rise was higher for those cases in which the azimuthal angle was small compared to cases with a larger angle. The third study was an analysis of data from Tennessee Valley Authority field studies. Due to large scatter and the small number of observations, the results are inconclusive for cases with two, three and four plumes. The ten plume cases clearly show higher rise and the rise is larger when the azimuthal angle is small.

Previous investigators of the relationship between measured plume width and sampling time τ (τ ranges from just a few minutes to several hours) have found that width is proportional to τ m , where, in general, 0.2 ⩽ m ⩽ 0.3 . These results are related to the dependency of average in-plume pollutant concentration, ξ, on τ, where ξ ∞ τ p with, generally, −0.7 ⩽ p ⩽ −0.2 . Data previously used to determine exponents m and p have almost exclusively been collected at distances of 10 km or less from a source. Lidar observations of plume width are used here to investigate sampling time effects at distances of 10–68 km downwind. Results of the analysis of the lidar observations indicate that sampling time effects on plume width exist out to at least 68 km. The value of sampling time exponent m was found to be about 0.25. These results are very similar to those found by others at short ( ⩽ 10 km ) pollutant travel distances. No evidence was found to suggest that plume width sensitivity to τ is affected by vertical wind shear. A comparison is made between the results presented here and those previously presented by Hino (1968, Atmospheric Environment2, 149–165). Values of m inferred from Hino's values for p are comparable to lidar-based estimates of m . The effects of pollutant travel distance on the comparison of Hino's analysis with the lidar data analysis are briefly described.

Estimates of maximum ground-level concentrations of SO 2 due to anthropogenic emissions have been made for two National Park Service management areas in southern Florida as part of an interdisciplinary biological effects study for these areas. The nearest major sources of SO 2 are located at least 60 km away on the southern Florida coast so that mesoscale atmospheric transport must occur for the receptor areas to be affected by these sources. A mesoscale atmospheric dispersion modeling system consisting of a three-dimensional mesoscale meteorological model and a three-dimensional Lagrangian particle dispersion model were employed to make the estimates for a realistic worst-case summer meteorological scenario. The temporal and spatial variations of the meteorological fields resulting from the interaction of sea and land breezes with the synoptic flow were simulated with the meteorological model for the southern Florida peninsula. The dispersion characteristics of plumes emitted from four major elevated point sources were then evaluated using the Lagrangian particle model 1. (i) by means of particle dispersion plots and 2. (ii) by computing the 3-h-average ground-level SO 2 concentrations. A comparison was made with concentrations estimated using a plume-trapping formulation and the TVA σ y curves. The study results illustrate the complexity of the dispersion patterns which can occur for travel distances on the order of 100 km in a coastal area due to diurnal effects and mesoscale circulations, and demonstrate the potential of the mesoscale atmospheric dispersion modeling system for studies of air quality in complex terrain.

Filter and cascade impactor samples of suspended particles were collected in-stack and at distances up to 64 km downwind in the plume of a large western coal-fired power plant equipped with both electrostatic precipitators (ESP) and venturi wet particulate scrubbers (VWS) to investigate modifications of the particulate signatures of minor and trace elements during transport. Samples were analyzed for 40 elements by instrumental neutron activation analysis. Precipitator malfunction during the experiment caused greater than normal emission of large particles, and concentrations of As, Zn, Sb, Mo, Ga, W, U, V and Ba in near-plume particles collected on filters were enriched relative to their concentrations in stack particles by factors of 1.4 to 2.5, presumably because of sedimentation of very large particles. Selenium was enriched by up to 6-fold (plume:stack). However, enrichment of elements in the plume relative to more typical in-stack particles were insignificant for all elements except Se, which was enriched 2.3-fold. Concentrations of Se on particles in the stack and plume suggest that most of the Se vapor in stack gases became associated with aerosol particles soon after emission. Thus although significant post-emission modifications of elemental signatures of particles may occur for poorly controlled plants, little change is expected for well-controlled plants equipped with ESPs except for Se. Source signatures measured for Se must account for vapor deposition. Impactor data showed a preferential decrease in the concentrations of the above elements in submicrometer particles; suggesting that either intermodal coagulation or size selective sampling losses were important. The impactor data further suggest that enrichment-particle-size profiles for VWS emissions were not conservative during transport.

The numerical model developed in the first part of this investigation is applied to assess the behavior of sulfur dioxide and sulfate concentration distributions in an urban area using the St Louis Regional Air Pollution Study (RAPS) data. Statistical techniques chosen to determine the accuracy and uncertainty associated with the numerical model results include paired analysis and resampling analysis. The results of the numerical model are also compared with those of RAM, a Gaussian plume model. Finally, the behavior of point and area emission sources in an urban area is assessed to provide an insight into the complex interrelationships between the emissions and meteorological conditions which determine the distribution of ground level concentrations.

With the use of mixed-layer scaling, the near-surface mean concentration and the concentration fluctuations at moderate distances downwind of a stack emitting a highly buoyant effluent are obtained and compared quantitatively with those from a non-buoyant source that is otherwise identical. The environment is a laboratory mixed layer in a state of free convection with mean wind simulated by towing the stack along a horizontal line. Although the buoyant effluent has a much smaller maximum mean groundlevel concentration occurring at a greater downwind distance than the non-buoyant effluent, the decay of mean concentration from that point downwind is found to be exceedingly slow in the buoyant case. The cumulative frequency distributions of sampled concentrations greater than zero for these same two cases are found to be log-normal in only a bimodal sense, with the weaker concentrations having a greater logarithmic range in amplitude than the stronger concentrations. The ratio of the root-mean-square (r.m.s.) concentration fluctuation to the mean concentration, in the central portion of the mean plume, is found to decay with downwind distance. Homogenization associated with both downstream and vertical mixing is believed responsible for the rapid decay observed.

Tracer dispersion experiments conducted in near-neutral stability on the upwind slopes of a small isolated hill are described. Dual tracers were used to give simultaneous plumes from release heights of 0.2H and 0.4H, where H is the height of the hill. Results are compared with a simple Gaussian plume model for flat ground. The increase in crosswind plume spread due to the hill is shown to be in agreement with a linear flow model. The maximum observed concentration is found to be reduced from the predicted flat ground value. As the length scale of the hill is of similar size to the dominant scale of turbulence, this may be explained by enhancement of low frequency meandering of the plume, due to horizontal flow divergence around the hill.

A new, comprehensive model for a chemically reacting plume is presented that accounts for the effects of incomplete turbulent macro- and micromixing on chemical reactions between plume and atmospheric constituents. The model is modular in nature, allowing for the use of different levels of approximation of the phenomena involved. The core of the model consists of the evolution equations for reaction progress variables appropriate for evolving spatially varying systems. These equations estimate the interaction of mixing and chemical reaction and require input parameters characterizing internal plume behavior, such as relative dispersion and fine scale plume segregation. The model addresses deficiencies in previous reactive plume models. Part II is devoted to atmospheric application of the model.

A precipitation band, about 30 km long and 2 km wide, downwind of a nuclear power plant was observed with a millimetric Doppler radar. The three-dimensional radar analysis showed that this band resulted from the growth, by a seeder-feeder process, of a natural snowfall falling in the moist plume produced by the exhaust of the nuclear plant. At the exit from the 0.6 km deep plume, the mean snow precipitation rate was approximately enhanced by a factor of two. This corresponds to an extraction rate of water in the plume by snow scavenging of 600 kg s −1, that is about one third of the water injection rate into the atmosphere by the cooling towers.

Many hot spots can be detected by Channel 3 of the sun-synchronous meteorological satellites NOAA 6–9. This is because that channel is much more sensitive to radiation from bodies in the temperature range 500–1500 K than to scattered sunshine or earth-temperature radiation. Hot bodies occupying only a small fraction of a pixel can be detected. The other channels are designed to receive much greater power from earth radiation (300 K) or scattered sunshine (6000 K). Plumes from chimneys are very difficult to detect because they are small and rapidly diluted and dispersed. Some flukes of illumination make them detectable occasionally; and some infrequent meteorological circumstances make them persistent and large. Ship trails are quite exceptional and very obvious, but they are very rare.