A simple model of the origin and transport of ²²²Rn and ²¹⁰Pb in the atmosphere

Abstract.

This paper presents a simple model of the transport of the natural radionuclides ²²²Rn and ²¹⁰Pb through the atmosphere in which it is assumed that the vertical distribution in a column of air moving horizontally over the earth's surface is largely controlled by turbulent diffusion. The inert gas ²²²Rn (half-life 3.82 days), a product of ²²⁶Ra decay in soils, enters the atmosphere by diffusion from land surfaces where it decays via various short-lived radionuclides to ²¹⁰Pb and thence via ²¹⁰Po and ²¹⁰Bi to the stable isotope ²⁰⁶Pb. Individual ²¹⁰Pb atoms in the atmosphere become readily attached to airborne particles and within the troposphere are removed both by wet and dry deposition. Although these processes are extremely complex and result in rapid fluctuations in concentrations and fluxes on short time-scales, the constancy of the mean annual ²¹⁰Pb flux at particular sites suggests that the short-term fluctuations have little significance on these longer time-scales. The model is used to capture the main features of the global transport of ²²²Rn and ²¹⁰Pb at northern mid-latitudes where, on annual time-scales, the transport of air is dominated by a global west-east circulation. Air columns travelling over a large ocean will have very low concentrations when they arrive at the western margin of a large land mass. ²²²Rn concentrations will then build up as the column moves over the land mass, declining again as the column passes over the eastern seaboard. The diffusion equation is solved to give a dynamic picture of the evolution of the ²²²Rn concentration versus altitude profile assuming a constant flux from the land surface, and zero flux from the oceans. Over the land surface the profile develops relatively quickly and, in the steady state, follows an exponential relation. These profiles represent a source term for the production ²¹⁰Pb. Within the troposphere, the ²¹⁰Pb transport equation also includes a sink term representing loss from the aerosol phase by incorporation in water droplets and rain. By fitting the theoretical profiles to measured data from continental USA and Eurasia, it is estimated that the mean ²²²Rn exhalation rate from northern land masses is 1570 Bq m ^{- 2} y ^{- 1} (0.87 atoms cm ^{- 2} s ^{- 1}) and that the mean vertical diffusivity in the atmosphere is 2.7km² d ^{- 1} (3.1 x 10⁵ cm² s ^{- 1}). Further, the mean ²¹⁰Pb residence time in the troposphere is estimated to be about 5 days. Results of the calculations show that over large continental land masses the ²¹⁰Pb inventory is predominantly in the troposphere, but that as the air column moves out over the sea, the stratospheric inventory continues to increase over large distances and is an important factor controlling long-range transport. By mid-ocean it may contain 80% or more of the remaining inventory, and becomes the main source of ²¹⁰Pb to the troposphere. Comparisons with the measured atmospheric fluxes across the USA and Eurasia are used to calculate the mean west-east global circulation velocity at mid latitudes, and intercontinental transport rates for ²¹⁰Pb. The results suggest that as much as 40% of ²¹⁰Pb fallout on the western seaboard of Europe is of North American origin, and that $\sim$30% of fallout on the western seaboard of the USA is of Eurasian origin.