{"Bibliographic":{"Title":"Atmospheric diffusion in an urban area","Authors":"","Publication date":"1970","Publisher":""},"Administrative":{"Date created":"08-17-2023","Language":"English","Rights":"CC 0","Size":"0000008489"},"Pages":["A\nQC\n880\nA4\nNOAA Research Laboratories\nno.33\nAir Resources\nAtmospheric Turbulence and Diffusion Laboratory\nOak Ridge, Tennessee\nMay 1970\nATMOSPHERIC DIFFUSION IN AN URBAN AREA\nATMOSPHERIC SCIENCES\nF. A. ) Gifford, Jr.\nLIBRARY\nJUL 19 1972\nN.O.A.A.\nU. S. Dept. of Commerce\nU. S. DEPARTMENT OF COMMERCE\nNATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION\n'12 3748","A\nQC\n880\nA4\nAtmospheric Diffusion in an Urban Area\nno. 33\nPaper presented at the 2nd IRPA Conference\nBrighton, England\nMay 5, 1970\nby\nF. A. Gifford, Jr.\nAir Resources Atmospheric Turbulence\nand Diffusion Laboratory, ESSA\nOak Ridge, Tennessee\nA number of urgent practical problems require computing levels of urban\nair pollution: for example, the design of \"air quality control regions;\" the\nestablishment of air pollution control regulations; operational (that is,\nreal-time) air resource management; siting of power plants (both nuclear and\nconventional) ; and many others. A recent and interesting application in-\nvolves the calculation of dosages arising from the proposed domestic and\nindustrial use of natural gas containing trace quantities of radioactivity.\nThe impact of this on populations will be discussed by Dr. Jacobs and his\ncolleagues in a later paper (see Abstract No. 95). In what follows I will\ndescribe a method of calculating the dilution, or diffusion by the atmosphere\nof gases from such an urban area source.\nUrban pollution can be thought of as arising from two kinds of sources:\n(1) isolated, elevated point sources such as tall stacks; and (2) the distribu-\nced area source. The first type has been extensively treated, for instance in\nMeteorology and Atomic Energy - 1968 (TID 24190). The second has been discussed\nby several authors following Lucas' (1956) early study. These studies have\napproached the area-source problem either by an integration of a point-source\ndiffusion formula over an area, or else by using a numerical approximation LC\nthe diffusion equation.\n33\ntran 2.\nintribution its.\n7\n:","- 2 -\nAt Oak Ridge we have taken a somewhat different approach. For the steady-\nstate case and with the x-axis in the direction of the mean wind u (and with\nv = w = 0) the diffusion equation appropriate to an area source at the surface\nis\n( 1)\nbecause only the vertical diffusion contributes significantly to the process.\nXA is the concentration, (g or cc)m-3. The mean wind, u, and the vertical eddy\ndiffusivity, Kz are functions of height, and we assumed power laws for these;\n( 2 )\n( 3 )\nOur procedure is to look for a transformation of the independent variables of\nthe above system of equations. Namely the following new variables are de- -\nfined:\n(==z/z(x)\nE=X\n( 4 )\nand the arbitrary function 2(x) is determined such that the resulting differ-\nential equation will be soluble by the classical method of separation of\nvariables. The required condition on 7. (x) turns out to be\n( 5 )\nThis transformation, known as a similarity transformation, reduces the mathe-\nmatical problem to that of solving two ordinary differential equations, because\nthe variables are separable. These ordinary differential equations are, however\n,","- 3 -\nfar from elementary. So instead of solving them in detail we have proceeded\nwith a partial analysis of the problem as follows.\nThe continuity equation for an area source of arbitrary strength Q(x) is\n{Q(x)}\nd\n( 6 )\n=\no\no\nwhere X is the distance from a point to the upwind edge of the city. If the\npower law for u and the similarity form for XA are introduced, equation (6)\ncan be solved for the ground-level concentration distribution,\n( 7 )\nwhere *AO is defined by the imposed similarity condition\nFor any given meteorological conditions\n= dc\n( 8 )\no\nis a constant parameter and is estimated to vary between 1/2 and 1. Combin-\ning this with the relation between Z and X determined from the similarity trans-\nformation gives a solution to the area source problem up to a constant which\ncan be approximated in various ways.\nIr. practice we have accually worked with the following form of che equation.\nSince area-source information is often available in the form of a checkerboard","- 4 -\ngrid pattern (this is the case for the Los Angeles natural gas source data\nthat we will consider), we evaluate the above equation over N equal inter-\nvals of X in the form\n( 9 )\nwhere S = (m+1)/(2+m-n) and X = NAX. This is equivalent to equation (7). The\nactual values of m and n are readily determined from the usual \"turbulence\ntypes, 11 for instance those referred to by Mr. Beattie and Miss Bryant earlier\ntoday (Paper No. 49).\nUse of this area-source equation is illustrated by a computation of\nground-level concentrations for the Los Angeles area arising from a given source\ndistribution of natural gas based on actual gas consumption data. Although we\nwere primarily interested in long-term, annual or seasonal means, we have\napplied the equation to a short period in the following example. This is be-\n-\ncause we wanted to compare this equation with the results of a more elaborate\nnumerical solution of the complete diffusion equation by Mr. Robert Lamb of\nUCLA. He has kindly provided us with a calculation from his model, using our\nnatural gas source data, of concentrations averaged over a period of 16 hours. .\nThis is much the more severe test of our model, because concentration over a\nlong-term average tends to be strongly proportional to local source strength\nin any model, even such a complicated one as the UCLA model.\nThe result of this comparison is illustrated in Figure 1. Our model (which\ntakes several seconds of a high-speed computer time or E few minutes hand cal- -\nculation to evaluate) seems to be giving area-source concentration values of","- 5 -\nthe same order as the UCLA model, perhaps a factor of two higher. The UCLA\nmodel, in common with several complex area-source models recently presented,\nrequires of the order of 10 minutes computer time. Figure 2 shows a scatter\ndiagram presentation of the same information. The open points come from the\ntop three rows of the data from Figure 1. We suspect that the UCLA model is\ncomputing higher values there because it takes into account flow convergence\ncaused by the ring of mountains there. of course, we don't know which model\nis giving the most satisfactory values. There are as yet no entirely satis-\nfactory observational data for comparison. However we are confident, based\non the above and several other comparisons with various other area-source\nmodels, that our solution is a valid one, and has the virtue of being quite\nsimple to apply.\nA complete account of this work will be prepared for publication. The\nresearch was performed under an agreement between the Environmental Science\nServices Administration and the U S. Acomic Energy Commission.","ORNL-DWG 70 - 9558\n250\n200\n10\n4.0\n5.0\n4.0\n4.0\n3.0\n4.1\n4.2\n2.4\n2.1\n1.5\n300\n300\n100\n100\n50\n5.2\n7.1\n6.2\n5.4\n5.7\n5.2\n4.8\n3.7\n5.4\n5.7\n5.4\n5.7\n5.7\n3.7\n2.8\n1.9\n400\n400\n350\n390\n400\n200\n150\n100\n6.0\n7.0\n8.0\n7.0\n7,0\n7.0\n6.0\n3.0\n2.5\n2.0\n1.5\n4.5\n6.5\n9.8\n7,7\n7.9\n7.7\n6.5\n4.3\n3.8\n4.3\n2.5\n300\n450\n800\n500\n550\n550\n450\n250\n250\n350\n150\n4.0\n7.0\n8.0\n7.0\n6.8\n7.0\n4.5\n3.3\n2.5\n2.0\n1.0\n6.2\n10.9\n14.4\n9,7\n8.2\n8.9\n6.6\n6.0\n5.6\n3.0\n2.8\n500\n900\n1200\n600\n500\n625\n400\n400\n400\n150\n200\n5,0\n5.0\n6.2\n6.2\n0.5\n6.9\n2.5\n5.7\n3.5\n3.0\n1.3\n12.5\n12.0\n10.4\n10.0\n10.0\n6.5\n2.8\n9.0\n6.9\n5.7\n3.6\n1170\n1000\n900\n700\n650\n600\n425\n350\n500\n200\n175\n0.5\n2.7\n4.6\n5.0\n4.5\n4.3\n3.3\n2.7\n2.0\n0.6\n2.7\n6.1\n9.8\n9,4\n9.9\n8.6\n6.9\n5.5\n5.4\n2.1\n150\n450\n800\n650\n650\n575\n425\n350\n400\n50\n2.7\n3.2\n3.0\n3.0\n3.0\n2.6\n1.0\n5.4\n8.4\n7.2\n7,4\n7.8\n6.3\n2.5\n450\n700\n500\n500\n550\n425\n50\n2.5\n1.8\n1.7\n1.1\n0.9\n1.5\n6.3\n5.5\n3.2\n1.9\n5.9\n3.6\nGRID = 4X4 miles\n600\n400\n150\n500\n200\n0.5\n0.7\n0.9\n0.9\n0.5\n0.4\n0.7\n3.1\n3.3\n3,6\n1.3\n0.9\n300\n250\n275\nLOS ANGELES RESIDENTIAL NATURAL GAS.\nFigure 1","ORNL-DWG 70-9559\n16\n14\n12\n10\n8\n6\n4\nA TOP 3 ROWS\n2\no\n8\n10\n12\n14\no\n2\n4\n6\nCONCENTRATION cmÂ³/m3 - UCLA CALC.\nFigure 2"]}