Skip to main content

The conservative volume element

  • Chapter
Urban Air Pollution Modelling

Part of the book series: Air Pollution Problems Series ((AIRPP))

  • 244 Accesses

Abstract

Modern methods of atmospheric research, including air pollution calculations, are based on well-known physical laws related to what is usually called a ‘volume element’, ‘parcel’ or ‘box’ of air. Such an element is a volume of identifiable air that maintains some sort of integrity as it moves around from point to point.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Abeles, F. B., Cracker, L. E., Forrence, L. E. and Leather, G. R. (1971). Fate of air pollutants: removal of ethylene, sulphur dioxide and nitrogen dioxide by soil. Science,173, 914–16

    Article  CAS  Google Scholar 

  • Altshuller, A. P. (1975). Evoluation of oxidant results at CAMP sites in the United States. J. Air Pollut. Control Assoc.,25, 19–24

    Article  CAS  Google Scholar 

  • Altshuller, A. P. and Bufalini, J. J. (1965). Photochemical aspects of air pollution: a review. Photochem. Photobiol., 4, 96–146

    Article  Google Scholar 

  • Altshuller, A. P. (1971). Photochemical aspects of air pollution: a review. Environ. Sci. Technol.,5, 39–64

    Article  CAS  Google Scholar 

  • Anthes, R. A., and Seaman, N. (1976). Diffusion of a passive contaminant over complex terrain under stable and unstable conditions. Proc. 3rd Symp. Atmos. Turbulence, Diffusion Air Quality, Raleigh, N.C., 19 to 22 October 1976., Am. Meteorol. Soc., Boston, Mass., pp. 449–454

    Google Scholar 

  • Ashmore, B. C., Burnett, M. G., and Tyler, B. J. (1962). Reaction of nitric oxide and oxygen. Trans. Faraday Soc.,28, 685–91

    Article  CAS  Google Scholar 

  • Atkins, D. H. F., Cox, R. A., and Eggelton, A. E. J. (1972). Photochemical ozone and sulphuric acid aerosol formation in the atmosphere over southern England. Nature (London),235, 372–6

    Article  CAS  Google Scholar 

  • Becus, G. A. (1978). A stochastic model of air pollution. Proc. 13th Int. Colloq. Inst. Natl Rech. Chim. Appl., Paris, 25 to 28 April 1978, Preprint

    Google Scholar 

  • Bergstrom, R. W., Jr., and Viskanta, R. (1973). Modelling the effects of gaseous and particulate pollutants in the urban atmosphere, part I, thermal structure, part II, pollutant dispersion. J. Appl. Meteorol.,12, 901–18

    Article  CAS  Google Scholar 

  • Bilger, R. W. (1974). Oxidants and their precursors in the atmosphere. Dep. Environ. Conservation, Canberra, Aust. Publ., part I, 61 pp., part II, 63 pp.

    Google Scholar 

  • Bird, R. B., Stewart, W. E., and Lightfoot, E. N. (1964). Transport Phenomena, Wiley, New York, 780 pp.

    Google Scholar 

  • Blackadar, A. K., and Dutton, J. A. (1970). Tracers in the air. Weatherwise, Aug., 182–5

    Google Scholar 

  • Brock, F. V. (1962). Analogue computing techniques applied to atmospheric diffusion: continuous-area source. Proc. Symp. Air over Cities, Cincinnati, Ohio, 6 to 7 November 1961; SEC, Tech. Rep., No. A62–5, pp. 173–88

    Google Scholar 

  • Calvert, J. G., Demerjian, K. L., and Kerr, J. A. (1973). The effect of carbon monoxide on the chemistry of photochemical smog systems. Environ. Lett., 4, 281–95

    Article  CAS  Google Scholar 

  • Cermak, J. E. (1971). Laboratory simulation of atmospheric boundary layer. Aircraft Ind. Assoc. Am. J.,9, 1746–54

    Google Scholar 

  • Chang, P. C., Wang, P. N., and Lin, A. (1971). Turbulent diffusion in a city street. Proc. Symp. Air Pollut., Turbulence Diffusion, Las Cruces, N. M., 7 to 10 December 1971, New Mexico State Univ. Press, Las Cruces, pp. 137–44

    Google Scholar 

  • Chovin, P., and Roussel, A. (1973). Physicochimie et Physiopathologie des Polluants Atmosphériques, Masson, Paris, 303 pp. (in French)

    Google Scholar 

  • Clyne, M. A. A., Thrush, B. A., and Wayne R. P. (1964). Kinetics of the chemiluminescent reaction between nitric oxide and ozone. Trans. Faraday Soc., 60, 359–70

    Article  CAS  Google Scholar 

  • Coffey, P. E., and Stasiuk, W. N. (1975). Evidence of atmospheric transport of ozone into urban areas. Environ. Sci. Technol.,9, 59–62

    Article  CAS  Google Scholar 

  • Derwent, R. G. (1971). The relationship between chimney heights and the extent of oxidation of nitric oxide to nitrogen dioxide in the plume. Warren Spring Lab., Stevenage, Rep., No. LR-159 (AP), 9 pp.

    Google Scholar 

  • Derwent, R. G., and Stewart, H. N. M. (1973a). Air pollution from the oxides of nitrogen in the United Kingdom. Atmos. Environ.,7, 385–401

    Article  CAS  Google Scholar 

  • Derwent, R. G. (1973b). Elevated ozone levels in the air of central London. Nature (London) ,241, 342

    Article  CAS  Google Scholar 

  • Dickerson, M. H. (1975). MASCON—a mass-consistent atmospheric flux model for regions with complex topography. Lawrence Livermore Lab., Univ. Calif:, Preprint, No. UCRL-76157, Rev. 1, 14 pp.

    Google Scholar 

  • Djuric, D., and Thomas, J. C. (1971). A numerical study of convective transport of gaseous pollutants in the vicinity of tall buildings. Proc. Symp. Air Pollut., Turbulence Diffusion, Las Cruces, N. M., 7 to 10 December 1971, New Mexico State Univ. Press, Las Cruces, pp. 24–34

    Google Scholar 

  • Donaldson, Coleman du P., and Hilst, G. R. (1972). Effect of inhomogeneous mixing on atmospheric photochemical reactions. Environ. Sci. Technol.,6, 812–16

    Article  CAS  Google Scholar 

  • Dreyer, H. S., Smith, S. U., Wald, G. A., Hoydysh, W. G., and Pulis, L. C. (1977). A sensitivity study of the DEPICT computer program. J. Air Pollut. Control Assoc.,27, 1203–1205

    Article  Google Scholar 

  • Egan, B., and Lavery, T. F. (1973). Application of a numerical simulation model to the dispersion of vehicular emissions near highways. Proc. 3rd Int. Clean Air Congr., Düsseldorf, 6 to 10 October 1973, VDI-Verlag, Düsseldorf, pp. B7 — B9

    Google Scholar 

  • Egan, B. A., and Mahoney, J. R. (1971). A numerical model of urban air pollution transport. Proc. Am. Meteorol. Soc.—Air Pollut. Control Assoc. Meet. Air Pollut. Meteorol., Raleigh, N. C., 5 to 9 April 1971, pp. 8–12

    Google Scholar 

  • Egan, B. A. (1972a). Numerical modelling of advection and diffusion of urban area surface pollutants. J. Appl. Meteorol., 11, 312–22

    Article  Google Scholar 

  • Egan, B. A. (1972b). Application of a numerical air pollution model to dispersion in the atmospheric boundary layer. J. Appl. Meteorol., 11, 1023–39

    Article  Google Scholar 

  • Eschenroeder, A. Q., and Martinez, J. R. (1971). Concepts and applications of photochemical smog models. Gen. Res. Corp., Santa Barbara, Calif, Tech. Memo., No.1516, 124 pp.

    Google Scholar 

  • Eschenroeder, A. Q., Martinez, J. R., and Nordsieck, R. A. (1972). Evaluation of a diffusion model for photochemical smog simulation. Gen. Res. Corp., Santa Barbara, Calif., Publ. No. 68–02–0336; US Environ. Prot. Agency, Rep. No. EPAR4–73–012a, 211 pp.

    Google Scholar 

  • Fabrick, A. J., and Sklarew, R. C. (1975). Cross evaluation of regional air pollution models. Proc. 68th Annu. Meet. Air Pollut. Control Assoc., Boston, Mass., 15 to 20 June 1975, Paper, No. 75–04.6, 15 pp.

    Google Scholar 

  • Friedlander, S. K., and Seinfeld, J. H. (1969). A dynamic model of photochemical smog. Environ. Sci. Technol.,3, 1175–181

    Article  CAS  Google Scholar 

  • Fromm, J. E. (1969). Practical investigation of convective difference approximations of reduced dispersion. Phys. Fluids, 12, suppl. II, 3–12

    Google Scholar 

  • Galbally, I. E. (1971a). Surface ozone observation at Aspendale, Victoria, 1964–70. Atmos. Environ.,5, 15–25

    Article  CAS  Google Scholar 

  • Galbally, I. E. (1971b). Preliminary discussion on some oxidant measurements at Vlaardingen,the Netherlands. Atmos. Environ.,5, 187

    Article  Google Scholar 

  • Georgii, H. W., Busch, E., and Weber, E. (1967). Untersuchung über zeitliche und räumliche Verteilang der Immission-Konzentration des Kohlenmonoxid in Frankfurt am Main. Ber. Inst. Meteorol. Geophys., Univ. Frankfurt, No.11, 60 pp. (in German)

    Google Scholar 

  • Gifford, F. A., and Hanna, S. R. (1975). Modelling urban air pollution. Atmos. Environ.,9, 267–75

    Article  CAS  Google Scholar 

  • Goodin, W. R. (1975). A computational study of the transport of air pollutants in a mixing layer. School Eng. Appl. Sci., Univ. Calif., Los Angeles, Calif., Thesis

    Google Scholar 

  • Goodin, W. R., McRae, G. J., and Seinfeld, J. H. (1976). Validity and accuracy of atmospheric air quality models. Proc. 3rd Symp. Atmos. Turbulence, Diffusion Air Quality, Raleigh, N.C., 9 to 12 October 1976, Am. Meteorol. Soc., Boston, Mass., pp. 366–73

    Google Scholar 

  • Grennfelt, P. (1975). Measurement of ozone in Gothenburg, January 1972 to August 1973, and studies of covariations between ozone and other pollutants. Swed. Water Air Pollut. Res. Lab., Gothenburg, Publ., No. B, 221, 9 pp. + appendixes

    Google Scholar 

  • Gronskei, K. E. (1974). Requirements of air quality models for land use planning. Proc. 5th Meet. North Atlantic Theory Organ. — Comm. Challenges Modern Soc. Expert Panel Air Pollut. Modelling., Roskilde, 4 to 6 June 1974, pp. 11–1–11–29

    Google Scholar 

  • Halliday, E. C., and Venter, G. (1971). A numerical experiment in simulating the transport of sulphur dioxide through the atmosphere (by D. Randerson). Atmos. Environ., 5, 815–18, discussion

    Google Scholar 

  • Hameed, S. (1974). Atmos. Environ.8,555–61, discussion

    Article  CAS  Google Scholar 

  • Hawke, G. S., and Iverach, D. (1974). A study of high photochemical pollution days in Sydney, N.S.W. Atmos. Environ.,8, 597–608

    Article  CAS  Google Scholar 

  • Hecht, T. (1973). Workshop on Mathematical Modelling of Photochemical Smog, US Environ. Prot. Agency, Rep. No. EPA–R4–73–010, 42 pp., appendix A

    Google Scholar 

  • Hecht, T. A., and Seinfeld, J. H. (1972). Development of validation of a generalised mechanism for photochemical smog. Environ. Sci. Technol.,6, 47–57

    Article  CAS  Google Scholar 

  • Hilst, G. R., Donaldson, Coleman du P., Teske, M., Contiliano, R. and Freiberg, J. (1973). The development and preliminary application of an invariant coupled diffusion and chemical model. Aeronaut. Res. Ass. Princeton Inc., US Natl Aeronaut. Space Admin., Contract. Rep., No. NASA-CR-2295, 82 pp.

    Google Scholar 

  • Hirt, C. W., and Cook, J. L. (1972). Calculating three-dimensional flows around structures and over rough terrain. J. Comput. Phys.,10, 324–40

    Article  Google Scholar 

  • Hotchkiss, R. S. (1971). The numerical calculation of three-dimensional flows of air and particulates about structures. Proc. Symp. Air Pollut., Turbulence, Diffusion, Las Cruces, N.M., 7 to 10 December 1971, New Mexico State Univ. Press, Las Cruces, pp. 35–42

    Google Scholar 

  • Hotchkiss, R. S., and Harlow, F. H. (1973). Air pollution transport in street canyons. US Environ. Prot. Agency, Rep., No. EPA–R4–73–029, 117 pp.

    Google Scholar 

  • Hoydysh, W. G., and Sabetta, F. (1975). A new procedure for calculating dispersion in complex topographies. Proc. 68th Annu. Meet. Air Pollut. Control Assoc., Boston, Mass., 15 to 20 June 1975, Paper, No. 75–14.4, 14 pp.

    Google Scholar 

  • Jacobson, J. S., and Salottolo, G. D. (1975). Photochemical oxidants in the New York—New Jersey metropolitan area. Atmos. Environ.,9, 321–32

    Article  CAS  Google Scholar 

  • Johnson, W. B., Dabberdt, W. F., Ludwig, F. L., and Allen, R. J. (1971). Field•study for initial evaluation of an urban diffusion model for carbon monoxide. Stanford Res. Inst., Rep. (Project, No. 8563 ), 144 pp.

    Google Scholar 

  • Johnston, H. S., and Jost, D. M. (1949). The kinetics of the rapid gas reaction between ozone and nitrogen dioxide. J. Chem. Phys.,17, 386–92

    Article  Google Scholar 

  • Jost, D. (1970). Survey of the distribution of trace substances in pure and polluted atmospheres. J. Pure Appl. Chem.,24, 643–54

    Article  CAS  Google Scholar 

  • Joynt, R. C., and Blackman, D. R. (1976). A numerical model of pollutant transport. Atmos. Environ.,10, 433–42

    Article  CAS  Google Scholar 

  • Junge, C. (1963). Air Chemistry and Radioactivity, Academic Press, New York, 382 pp.

    Google Scholar 

  • Kanitz, S. (1976). Possibility of formation of photochemical smog in Italy: laboratory synthesis and determination of PAN in the air of Genova. J. Igiene Med. Prev.,8, 324–34

    Google Scholar 

  • Karplus, W. J., Bekey, G. A., and Pekrol, P. J. (1958). Atmospheric diffusion of pollutants: analogue computer study. Ind. Eng. Chem., No.11, 50

    Google Scholar 

  • Kita, T. (1972). A doubt about so-called new-type photochemical smog. Proc. Union J. Sci. Eng. Int. Symp. Air Pollut., Tokyo, 17 to 19 October 1972, pp. 427–40 (in Japanese)

    Google Scholar 

  • Kitabayashi, K., Sugawara, K., and Isomura, S. (1977). A wind tunnel study of automobile exhaust gas diffusion in an urban district. Proc. 4th Int. Clean Air Congr., Tokyo, 16 to 20 May 1977, pp. 192–5

    Google Scholar 

  • Kiyohide, T., and Kimura, F. (1975). Simplified Euler treatment of the diffusion equation and its application to Tokyo area. Proc. Jpn. Meteorol. Soc. Spring Meet., Tokyo, 21 to 23 May 1975, p. 59

    Google Scholar 

  • Lamb, R. G. (1968). An air pollution model for Los Angeles. Univ. Calif, Los Angeles, Calif, M.S. Thesis

    Google Scholar 

  • Lamb, R. G., and Neiburger, M. (1971). An interim version of a generalised urban air pollution model. Atmos. Environ., 5, 239–64

    Article  Google Scholar 

  • Lamb, R. G., and Seinfeld, J. H. (1973). Mathematical modelling of urban air pollution. Environ. Sci. Technol.,2, 253–61

    Article  Google Scholar 

  • Lange, R. (1973). ADPIC—a three-dimensional computer code for the study of pollutant dispersal and deposition under complex conditions. Lawrence Livermore Lab., Univ. Calif, Rep., No. TID-4500, UC-32, 60 pp.

    Google Scholar 

  • Lange, R. (1975). ADPIC—a three-dimensional transport-diffusion model for the dispersal of atmospheric pollutants and its validation against regional tracer studies. Proc. 1st Conf. Regional Mesoscale Modelling, Anal. Prediction, Las Vegas, Nev., 6 to 9 May 1975, Am. Meteorol. Soc., Boston, Mass., 16 pp.

    Google Scholar 

  • Lebedeff, S. A., and Hameed, S. (1975). Study of atmospheric transport over area sources by an integral method. Atmos. Environ.,9, 333–8

    Article  CAS  Google Scholar 

  • Leighton, P. A. (1961). Photochemistry of Air Pollution Academic Press, New York, 300 pp., 456 references

    Google Scholar 

  • Liu, C. Y., and Goodin, W. R. (1976a). A two-dimensional model for the transport of pollutants in an urban basin. Atmos. Environ.,10, 513–26

    Article  CAS  Google Scholar 

  • Liu, C. Y., and Goodin, W. R. (1976b). An iterative algorithm for objective wind field analysis. Mon. Weather Rev.,104, 784–92

    Article  Google Scholar 

  • Liu, M. K. (1977). Development of mathematical models for simulating power plant plumes. Proc. 4th Int. Clean Air Congr., Tokyo, 16 to 20 May 1977, pp. 310–14

    Google Scholar 

  • Liu, M. K., and Seinfeld, J. H. (1975). On the validity of grid and trajectory models of urban air pollution. Atmos. Environ.,9, 555–74

    Article  CAS  Google Scholar 

  • Ludwig, F. L., and Dabberdt, W. F. (1972). Evaluation of the APRAC-lA urban diffusion model for carbon monoxide. Stanford Res. Inst., Rep., 115 pp (Project, No. 8563, Contract, No. CAPA-3–68 (1–69)) (Natl. Tech. Inf. Serv., No. NTIS-PB-210 819 )

    Google Scholar 

  • Magnus, D., and Schechter, H. (1967). Analysis and application of the Padé approximation for the integration of chemical kinetic equations. Gen. Appl. Sci. Lab. Inc., Tech. Rep., No. 642

    Google Scholar 

  • Mahoney, J. R., and Egan, B. A. (1970). A mesoscale numerical model of atmospheric phenomena in urban areas. Proc. 2nd Int. Clean Air Congr., Washington, D.C., 6 to 11 December 1970, (eds H. M. Englund and W. T. Beery), Academic Press, New York, pp. 1152–7

    Google Scholar 

  • Mahoney, J. R., Egan, B. A., and Reifenstein, E. C. (1973). Hackensack Meadowlands air pollution study development and validation of a modelling technique for predicting air quality levels. US Environ. Prot. Agency, Final Rep., No. EPA-450/374–056cn, 92 pp.

    Google Scholar 

  • Marziano, G. L., Sutera, A., Gianolio, L., and Ciprion, M. (1975). Application of a three-dimensional diffusion model to the study of sulphur dioxide distribution in the Venice area and its verification. Proc. Semin. Air Pollut. Modelling, Venice, 27 to 28 November 1975

    Google Scholar 

  • Meroney, R. N., Peterka, J. A., Hatcher, R. V., and Kothari, K. (1977). Gaseous dispersion and turbulence in the wake of clear reactor plants. Proc. 4th Int. Clean Air Congr., Tokyo, 16 to 20 May 1977, pp. 167–70

    Google Scholar 

  • Molenkamp, C. R. (1968). Accuracy of finite-difference methods applied to the advection equation. J. Appl. Meteorol.,7, 160–7

    Article  Google Scholar 

  • Nishida, K., Yamamoto, T., Itakura, Y., and Mizuta, K. (1977). Wind tunnel experiments on atmospheric diffusion of automobile exhaust gases due to highway traffic. Proc. 4th Int. Clean Air Congr., Tokyo, 16 to 20 May 1977, pp. 196–200

    Google Scholar 

  • Nunge, R. J. (1974). Application of an analytical solution for unsteady advective diffusion to dispersion in the atmosphere, I, II. Atmos. Environ.,8, 969–1001

    Article  Google Scholar 

  • Nunge, R. J., and Subramanian, R. S. (1975). Atmospheric dispersion of gaseous pollutants from continuous source—a model of an industrial city. Proc. 79th Natl Meet. Am. Inst. Chem. Eng., Houston, Texas, 19 March 1975, Paper, No.47f, 53 pp.

    Google Scholar 

  • Nunge, R. J., and Vaidyanathan, K. R. (1977). A note on atmospheric dispersion with chemical reaction. Atmos. Environ., 11, 853–6

    Article  CAS  Google Scholar 

  • OCDE (1974). Report on the problem of photochemical oxidants and their precursors in the atmosphere. Environ. Directorate, Paris, France, Doc., No. NR-ENV-74.48, 105 pp.

    Google Scholar 

  • Odaira, T. (1972). Photochemical smog in Tokyo. Tokyo Metropolitan Res. Inst. Environ. Prot., Publ., 72 pp.

    Google Scholar 

  • Pandolfo, J. P., Atwater, M. A., and Anderson, G. E. (1971). Prediction by numerical models of transport and diffusion in an urban boundary layer. Cent. Environ. Man, Hartford, Conn., Publ., 139 pp. (Contract, No. CPA-70–62)

    Google Scholar 

  • Pandolfo, J. P., and Jacobs, C. A. (1973a). Vol. I, tests of an urban meteorological pollutant model using carbon monoxide validation in the Los Angeles metropolitan area. US Environ. Prot. Agency, Rep., No. EPA–R4–73–025a, 176 pp.

    Google Scholar 

  • Pandolfo, J. P. (1973b). Vol. II, FORTRAN programme and input–output specification. US Environ. Prot. Agency, Rep., No. EPA–R4–73–025b, 141 pp.

    Google Scholar 

  • Pandolfo, J. P., Jacobs, C. A., Ball, R. J., and Atwater, M. A. (1976). Refinement and validation of an urban meteorological pollutant model. US Environ. Prot. Agency, Publ., No. EPA–600/4–76–037, 32 pp.

    Google Scholar 

  • Pedersen, L. B., and Prahm, L. P. (1973). A method for the numerical solution of the advection equation. Dan. Meteorol. Inst., Air Pollut. Sect., Publ., 36 pp.

    Google Scholar 

  • Pedersen, L. B. (1974). A method for numerical solution of the advection equation. Telhus,26, 594–602

    Google Scholar 

  • Penkett, S. A., Sandalls, F. J., and Lovelock, J. E. (1975). Observations of peroxyacetyl nitrate (PAN) in air in southern England. Atmos. Environ.,9, 139–40

    Article  CAS  Google Scholar 

  • Pielke, R. (1972). Comparison of hydrostatic and anelastic dry shallow primitive equation model. US Dep. Comm., Environ. Res. Lab., Boulder, Colo., US Natl Oceanic Atmos. Admin., Tech. Memo., No. ERL OD-13, 47 pp.

    Google Scholar 

  • Pitts, J. N., and Finlayson, B. J. (1975). Mechanisms of photochemical air pollution. Angew. Chem., Int. Edn Engl.,14, 1–15

    Article  Google Scholar 

  • Plassmann, E., Leisen, P., and Sobotka, H. (1977). Atmospheric dispersion of motor vehicle exhaust gases in urban areas. Proc. 4th Int. Clean Air Congr., Tokyo, 16 to 20 May 1977, pp. 238–41

    Google Scholar 

  • Price, H. S., Varga, R. S., and Warren, J. E. (1966). Application of oscillation matrices to diffusion–convection equations. J. Math. Phys., 45, 301–31

    Article  Google Scholar 

  • Quickert, N., and Dubois, L. (1973). Some factors affecting the ambient ozone concentrations measured in Ottawa. Sci. Total Environ.,2, 81–7

    Article  CAS  Google Scholar 

  • Randerson, D. (1970). A numerical experiment in simulating the transport of sulphur dioxide through the atmosphere. Atmos. Environ.,4, 615–22

    Article  CAS  Google Scholar 

  • Ranzieri, A. J., and Tilden, J. W. (1977). An application of DEPICT (detailed examination of pollutant impact in complex terrain). State Calif. Air Resources Board, Draft

    Google Scholar 

  • Reed, L. E., and Barrett, C. F. (1965). Air pollution from road traffic measurements in Archway Road, London. Int. J. Air Water Pollut.,9, 357–65

    CAS  Google Scholar 

  • Reynolds, S. D. (1973). Urban air shed photochemical simulation model study, vol. I, development and evaluation, appendix D, numerical integration of continuity equations. US Environ. Prot. Agency, Rep. No. EPA–R4–73–030e, 45 pp.; vol. II, user’s guide and description of computer programmes. US Environ. Prot. Agency, Rep. No. EPA–R4–73–030f, 193 pp.

    Google Scholar 

  • Reynolds, S. D., Meyer, J. P., Hecht, T. A., Whitney, D. C., Ames, J., and Yocke, M. A. (1976). Continued research in mesoscale air pollution modelling, II, Refinements in the treatment of chemistry, meteorology and numerical integration procedures. US Environ. Prot. Agency, Publ., No. EPA–600/4–76–016b, 287 pp.

    Google Scholar 

  • Reynolds, S. D., Roth, P. M., and Seinfeld, J. H. (1973). Mathematical modelling of photochemical air pollution, I, formulation of the model. Atmos. Environ., 7, 103361; US Environ. Prot. Agency, Rep., Nos. EPA–R4–73–030a–EPA–R4–73–030d

    Google Scholar 

  • Riley, J. J., Liu, H. T., and Geller, E. W. (1976). A numerical and experimental study of stably stratified flow around complex terrain. US Environ. Prot. Agency, Publ., No. EPA–600/4–76–021

    Google Scholar 

  • Roberts, P. J. W., Roth, P. M., and Nelson, C. L. (1971). Contaminant emission in the Los Angeles basin—their sources, rates and distribution. Syst. Appl. Inc., Beverley Hills, Calif., Rep., No. 71-SAI-6

    Google Scholar 

  • Robinson, E., and Robbins, R. C. (1968). Sources, abundance and rate of gaseous atmospheric pollutants. Stanford Res. Inst., Rep.

    Google Scholar 

  • Roth, P. M., Reynolds, P. J. W., and Seinfeld, J. H. (1971). Development of a simulation model for estimating ground-level concentrations of photochemical pollutants. Syst. Appl. Inc., Beverley Hills, Calif, Final Rep., No. 71-SAI-21, 55 pp.

    Google Scholar 

  • Roth, P. M., Roberts, P. J. W., Liu, M. L., Reynolds, S. D., and Seinfeld, J. H. (1974). Mathematical modelling of photochemical air pollution, II, a model and inventory of pollutant emissions. Atmos. Environ.,8, 97–130

    Article  CAS  Google Scholar 

  • Runca, E., and Sardei, F. (1975). Numerical treatment of time-dependent advection and diffusion of air pollutants. Atmos. Environ.,9, 69–80

    Article  CAS  Google Scholar 

  • Runchal, A. K., Bealer, A. W., and Segal, G. S. (1978). A completely random-walk model for atmospheric dispersion. Atmospheric Pollution 1978 ( Benarie, M., ed.), Elsevier, Amsterdam, 137–42

    Google Scholar 

  • Seinfeld, J. H. (1975). Air Pollution: Physical and Chemical Fundamentals, McGraw-Hill, New York, chapter 4, 523 pp.

    Google Scholar 

  • Seinfeld, J. H., Reynolds, S. D., and Roth, P. M. (1972). Simulation of urban air pollution, Photochemical Smog and Ozone Reactions, Adv. Chem. Ser., 113, 58–100

    Article  CAS  Google Scholar 

  • Shannon, J. (1976). Application of the diffusion wind atmospheric dispersion model to the Tulsa urban area. Proc. 3rd Symp. Atmos. Turbulence, Diffusion Air Quality, Raleigh, N.C., 19 to 22 October 1976, Am. Meteorol. Soc., Boston, Mass., pp. 382–8

    Google Scholar 

  • Sheih, C. M. (1977). Mathematical modeling of particulate thermal coagulation and transport downstream of an urban source. Atmos. Environ., 11, 1185–90

    Article  Google Scholar 

  • Shieh, L. J., and Shir, C. C. (1976a). Development of an urban air quality simulation model with compatible RAPS data. IBM Res. Cent., Yorktown Heights, N.Y., Rep., No. RJ-1701-(24555), 147 pp.

    Google Scholar 

  • Shieh, L. J. (1976b). Analysis of input parameters and results of urban air pollution computation. Proc. 3rd Symp. Atmos. Turbulence, Diffusion and Air Quality, Raleigh, N.C., 19 to 22 October 1976, Am. Meteorol. Soc., Boston, Mass., pp. 374–81

    Google Scholar 

  • Shieh, L. J. (1974). A generalised urban air pollution model and its application to the study of sulphur dioxide distribution in the St Louis metropolitan area. J. Appl. Meteorol.,13, 185–204

    Article  Google Scholar 

  • Sklarew, R. C. (1973). Coupling of the photochemistry to an airshed model. Workshop on Mathematical Modelling of Photochemical Smog, US Environ. Prot. Agency, Rep., No. EPA–R4–73–010, pp. 35 – 6

    Google Scholar 

  • Sklarew, R. C., Fabrick, A. J., and Prager, J. E. (1972). Mathematical modelling of photochemical smog using the PIC method. J. Air Pollut. Control Assoc.,22, 865–9

    Article  CAS  Google Scholar 

  • Snyder, W. H. (1972). Fluid models for the study of air pollution meteorology: similarity, facilities, review of literature and recommendations. Div. Meteorol., US Environ. Prot. Agency, Publ., 106 pp.

    Google Scholar 

  • Snyder, W. H. (1974). Fluid modelling programme of the Meteorology Laboratory, US Environmental Protection Agency. Proc. 5th Meet. North Atlantic Treaty Organ.–Comm. Challenges Modern Soc. Expert Panel Air Pollut. Modelling, Roskilde, 4 to 6 June 1974, pp. 31–1–31–47

    Google Scholar 

  • Stasiuk, N. W., and Coffey, E. P. (1974). Rural and urban ozone relationship in New York state. J. Air Pollut. Control Assoc.,24, 564–8

    Article  CAS  Google Scholar 

  • Steinberger, H., and Balmor, Y. (1973). Photochemical ozone formation in the atmosphere over southern England. Nature (London),241, 341–2

    Article  CAS  Google Scholar 

  • Steinberger, H., and Goldwater, F. (1972). A sensitive automatic meter for continuous sampling of contaminating oxidants in the atmosphere. J. Phys. E,5, 373

    Article  CAS  Google Scholar 

  • Tauber, S. (1972). Linear algebra in air pollution problems. Atmos. Environ.,6, 279–81

    Article  CAS  Google Scholar 

  • Tauber, S. (1975). On the determination of pollution matrices. Atmos. Environ.,9, 135–7

    Article  CAS  Google Scholar 

  • Tauber, S. (1973). Matrix representation of dynamic air pollution problems. Atmos.Environ., 7, 655–66

    Article  Google Scholar 

  • Tauber, S., and Trau, J. (1973). A vector partial differential equation model for air pollution. Atmos. Environ., 7, 973–7

    Article  CAS  Google Scholar 

  • United States National Air Pollution Control Administration (1970). Air quality criteria for photochemical oxidants. US Natl Air Pollut. Control Admin., Publ., No. AP-63

    Google Scholar 

  • Tauber, S. (1971). Air quality criteria for nitrogen oxides. US Natl Air Pollut. Control.Admin., Publ., No. AP-84

    Google Scholar 

  • University of California (1974). Development of an air pollution model for the San Francisco bay area. Lawrence Livermore Lab., Univ. Calif:, Nat! Sci. Found., 2nd Semiannu. Rep., No. TTD-4500, UC-11, 127 pp.

    Google Scholar 

  • Varga, S. R. (1961). On higher-order stable implicit methods for solving parabolic differential equations. J. Math. Phys.,40, 220–31

    Article  Google Scholar 

  • Viskanta, R., Bergstrom, R. W., and Johnson, R. O. (1976). Modelling the effects of pollutants and dispersion in urban atmospheres. US Environ. Prot. Agency, Publ., No. EPA–600/4–76–002, 123 pp.

    Google Scholar 

  • Weatherley, M.-L. P. M. (1966). Air pollution measurements at Islington, London, in 1964, part 2. Warren Spring Lab., Stevenage, Rep., No. LR-40(1P)

    Google Scholar 

  • Wedding, J. B., Lombardi, D. J., and Cermak, J. E. (1977). A wind tunnel study of gaseous pollutants in city street canyons. J. Air Pollut. Control Assoc.,27, 557–66

    Article  CAS  Google Scholar 

  • Welch, J. E., Harlow, F. H., Shannon, J. P., and Daly, B. J. (1969). The MAC method—a computing technique for solving viscous incompressible transient fluid flow problems involving free surfaces. Los Alamos Sci. Lab., Los Alamos, N.M.,Publ., No. LA-3425, 146 pp. (revised)

    Google Scholar 

  • Wippermann, F., and Yordanov, D. (1972). A perspective for a routine prediction of concentration patterns. Atmos. Environ.,6, 877–88

    Article  Google Scholar 

  • Wisse, J. A., and Velds, C. A. (1970). Preliminary discussion on some oxidant measurements at Vlaardingen, the Netherlands. Atmos. Environ.,4, 79–85

    Article  CAS  Google Scholar 

  • Yoshikawa, A., Katsuhito, Y., and Hirohisa, S. (1973). Gas stagnation in rectangular cavity, part 2. Kuki Chowa Eisei Kogaku,47, 1–10(in Japanese)

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Copyright information

© 1980 Michel M. Benarie

About this chapter

Cite this chapter

Benarie, M.M. (1980). The conservative volume element. In: Urban Air Pollution Modelling. Air Pollution Problems Series. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-03639-4_5

Download citation

Publish with us

Policies and ethics