0 p-2y-y —~ (A; # A)n; = 0 for i>1 (2) » we introduce the following ions: = HE, where F, is the exhalation 1 Rn™ atoms from the ground This condition means that the Rn™ and Rn™ in a vertical air to the exhalation rate of its ea. °t > 1. This condition reflects n of newly formed Po™ or Po™* air and their deposition on the = 0 for: > 1. This takes into that all atoms and carrier par’ products reaching the ground mn will be deposited. )7 0 fori=1,2,3..., a& consequence of radioactive coefficient K is quite variable rding to the vertical variations ad atmospheric stability. Some layers can be distinguished slope of the function K (z). In or near the earth’s surface K with altitude, following an ear or power law of z. Apdient wind height, dK/dz dees nearly independent of altir troposphere under normal to the high stability of the gain decreases rapidly above nd is likely to approach a lue in the lower stratosphere. and velocity and temperature —_ Oo oS —_ o = — AVN 3801 10° Turbulent diffusion coefficient K(cm?/s) — aan aRa empoBesa dreerie ae pemimetnbsa ealina or aeemai dn c tn) cpeeettmme mab eur sumptions the equilibrium vertin™, Rn™, and their decay produined from the following system uations: INTERNATIONAL SYMPOSIUM ON TRACE GASES AND RADIOACTIVITY al * +m : the same removal rate ean be ee hort-lived Rn™ decay products eay products A, >> A,. For Pb®™° Icm 10cm Im 10m 100m 1km km 30km Altitude Fig. 1. Vertical profiles of the turbulent diffusion coefficient. profiles with time result in fluctuation of K by about 2 or 3 orders of magnitude in the ground layer and by about 1 or 2 orders of magnitude in the upper troposphere. The influence of these uncertainties on the vertical distribution of the natural radionuclides was estimated from solutions of (2) for twenty different K profiles. These profiles cover the total range of fluctuation of the turbulent diffusion coefficient that seems to be possible according to the diffusion diagram given by Lettau [1951]. Five characteristic K profiles which correspond to typical conditions of turbulence in the troposphere are shown in Figure 1. The K pro- rapid decrease of the turbulent diffusion coeffi- clent was assumed in the tropopause region approaching a constant value of K = 3 x 10* em’/ sec between 20 and 30 km. In either case the gas kanetic diffusion coefficient, which is about 0.05 em’/sec for Rn™ and Rn™ atoms, can be neglected, NUMERICAL TREATMENT We use the abbreviations r,* file SSN is an exampleof strong vertical mixing, Putting weak vertical mixing throughout the lower troposphere. For JWN,diffusion in the ground layer was assumed to be very weak, which is , = mh, and the profile WNN is an example of rather typical for a strong inversion near ground. The profile NNN is likely to be representative of normal turbulence conditions throughout the troposphere. In all these five typical cases a Ay for =A, tA v= for 1 vp > 1 i-l ¢g, = apt , , Ag yy ve} and defining a,,, recursively by Oia» = r,* A, _ 2~> 1 r,* Or ysl ¥ = lye eryut — We e- ° we ~ (3) yoo. an Los : 1 (4)