Radon 222 and Tropospheric Vertical Transport

Radon 222 is an inert gas whose loss is due only to radioactive decay with a half life of 3.83 days (5.51-day exponential lifetime). It is a very useful tracer of continental air because only ground level continental sources are significant. Thus it is similar in several ways to many air pollutants (e.g., NO,, (NO + NO2), SO2, and certain hydrocarbons). Previously published measured (cid:127)22Rn profiles are analyzed here by averaging for the summer, winter, and spring-fall seasons. The analysis shows that in summer, about 55% of the 222Rn is transported above the planetary boundary layer, considerably more than during the other seasons. Similarly, in summer, about 20% rises to over 5.5 km (500 mbar). The average profiles have been used to derive vertical eddy diffusion coefficients with maximum values of 5-7 x l0 s cm'- s-x in the midtroposphere and 8 x 10 3 to 5 x 10 '(cid:127) cnl 2 s-x near the surface. for the spring-fall show both similarities to and differences from the summer similar but extends upward to 5 km. In the winter case, the slope in the winter and in the spring and fall to give climatologically meaningful averages. The seasonal difference shown here should be regarded only as qualitative.

to a few specific measurements of 222Rn and its decay daughters or limited only to transport within the PBL. On the other hand, eddy diffusion coefficients derived from excess •'•CO2 do not have enough vertical resolution in the troposphere [Davidson et al., 1966;Seitzet al., 1968].
In this paper we try to compile a statistically more meaningful average vertical profile of 222Rn measured in the troposphere. Special emphasis will be given to the 222Rn distribution in the summer in order to test various models and parameterizations of the vertical transport associated with cumulus clouds. A corresponding eddy coefficient will be derived from the average 222Rn profile.
The lifetime and source characteristics (i.e., emitted at the surface) of 222Rn are of the same order as many air pollutants such as NO,,(NO + NO2), propane, butane, and other moder-. ately reactive hydrocarbons. We will discuss the implications of applying the derived eddy coefficients to trace gases with various lifetimes.

COMPILATION OF MEASURED 222 RN PROFILES
We have made a literature search of measured vertical profiles of 222Rn. Since our primary interest is to characterize the vertical transport from the surface to the tropopause, profiles that do not reach beyond the top of the PBL are excluded in this paper. These data, mostly taken from meteorological towers, will be addressed in a future study. Measurements made over the ocean are also excluded because of a scarcity of data. Most of the 222Rn in the maritime air is advected from continents and is deposited over oceans as 2•øPb. Measurements of 222Rn and 2•øPb in the maritime air will be valuable for studying transport processes over oceans [Kritz, 1983].
The published profiles of 222Rn made over continental land masses are shown in Figures 1-5. The activity, converted to a standard of picocuries per cubic meter (STP) where necessary, is proportional to the mixing ratio of 222Rn and is plotted as a function of height above ground rather than above sea level.  Figure 3. The morning-to-midday period is represented by curves A-E, late evening by curve F, and afternoon by curve G, but all are within a 1-week period. The large day-to-day variation is clearly evident, as is the dividing feature just below 2 km. According to these authors the diurnal variation is not important above the 2-km break. The 95% confidence level in the counting statistics is about 5 pCi m-3, and radon is inferred from the daughter measurements.
A similar set of four profiles [Larson, 1974] were made over the Yukon Valley of Alaska during February 1972 and are shown in Figure 4. The standard deviation in counting ranges from 1 to 5 pCi m -3 and times of day are not given. Conditions for curves A-C were dominated by a high-pressure system with a low-level inversion, while curve D represented a new air mass advected into the area. Throughout the measurement period a snow cover of 58.4 cm persisted, and the author used the large radon concentration near the surface to argue that emanation is not severely inhibited by frost and snow cover.

DISCUSSION
The average summertime '-'-'-Rn mixing ratio profile shows the least decrease with height compared to the other two seasons. This is consistent with the generally accepted fact that vertical mixing is more efficient in the warmer season because of the solar heating-induced mixing. The difference between the summer profile and the other two profiles should not be regarded as quantitative, because of the sparseness of data in nonsummer seasons, as discussed above.
The slope of the summer profile has some interesting features. It starts relatively steeply below 3 km and gradually levels off between 3 and 8 km. Above that the influence of the stable tropopause starts to become important. The locations of the tropopause in this figure are not well defined because individual tropopause altitudes, where given, range from about 9 to 16 km. Most of the measurements did not reach above the tropopause.
Because of poor height resolution, it is difficult to identify mechanisms that contribute to the steep slope below 3 km. The slow exchange between the PBL and the overlying free troposphere must contribute in part [Wilkening, 1970]. Since the top of the PBL usually increases during the daytime [Kaimal et al., 1976] and the 222Rn measurements were made at various daytime hours, the average profile of 22eRn below 2 km should not be considered to represent daytime turbulent diffusion within the PBL, which is known to be fast [e.g., Kairnal et al., 1976]. It should only be regarded as representing the effective mixing that includes both daytime and nighttime atmospheric processes. On the other hand, since none of these data were taken at night, the average profile definitely has a daytime bias. This bias significantly affects the e2eRn distribution in the PBL; above it the effect is probably small.
Between 3 and 8 km the summer ee:Rn mixing ratio decreases by about 60%, in comparison to an 80% decrease between the surface and 3 km. Clearly, efficient vertical transport in the 3-to 8-kin region is required. The vertical transport can be either by advection or by turbulence, or both. In fact, below 8 km the profile, to a certain extent, resembles the tracer profile calculated by the advective cumulus cloud model of Gidel [1983]. In that model, Gidel   In view of the large standard deviation and lack of other independent methods to test the representativeness of the average 222Rn profiles compiled here, they cannot be claimed to be statistically meaningful. However, these profiles are by far the most extensive data compiled for a tropospheric tracer with simple chemistry. In the following section, we will assume that the 222Rn profiles are representative of the average distributions over the continents and can be used to derive vertical eddy coefficients.

EDDY COEFFICIENT
The continuity equation for 222Rn can be written as c9n c9I c9 I c9n

t3t -t3z KzN •zz (n/N) -2n-u• • (1)
where n represents the 222Rn density; N is the background density, which is a function of altitude; K= is the vertical eddy coe•cient; and 2 is the radioactive decay constant (inverse of exponential lifetime). This kind of expression has been traditionally used in the one-dimensional stratospheric and tro•spheric photochemical models [c [ Johnston et al., 1976;Thompson and Cicerone, 1982]. In a more rigorous treatment of vertical transport the advection or mean wind term should be separated from turbulent motion, and only the latter would be parameterized by an eddy coe•cient [c [ Mahlman, 1976;Gidel, 1983]. Nevertheless, a single overall vertical eddy coe•cient has been used profitably in one-dimensional modeling of various stratospheric and tropospheric tracer distributions. The back-ground density at various heights is taken from the spring-fall model of U.S. Standard Atmosphere, Supplement (1966). The last term in (1) is due to zonal transport of 222Rn, where u= denotes the mean zonal wind velocity and x is the longitude. To calculate this term, we assume the average summer profile to be the average steady state profile over the United States.
Since there is negligible transport of 2::Rn from the ocean to the continent, the last term can be approximated by the transport of continental ::2Rn to the ocean, i.e., u=n/l, where l •-5000 km is the longitudinal width of the U.S. continent. With many discontinuities in the 22:Rn profiles that are artifacts due to data averaging, a negative or unreasonable eddy coefficient may result. Without an objective method to smooth the e::Rn profiles, we elect to solve (!) as follows.
Equation ( The eddy coefficients for the other two seasons show the same general behavior as for the summer case, but with generally lower values, as expected. The detailed behavior is even more suspect because of the smaller number of data. Inclusion of the last term of (1) (i.e., horizontal divergence) increases the calculated eddy coefficient significantly in comparison to the eddy diffusion coefficient calculated without the term.
To evaluate the vertical transport of air pollutants, such as One should use these estimates with caution, since the removal process of the trace gas is assumed here to be independent of atmospheric motion. This is obviously not true for many soluble atmospheric gases, such as SO2 and HNO3, that are removed by heterogeneous processes closely related to atmospheric motions. For instance, condensation and precipitation tend to occur frequently in the ascending air but not descending air. s -• between 2 and 10 km. However, as was noticed by Machta [1974], Bolin and Bischof assumed a constant density with height. Using the standard atmosphere, Machta [1974] deduced an appreciably smaller eddy coefficient, 5 x 104 cm z s-x, from Bolin and Bischof's CO: data. This value should be regarded as an annual average vertical eddy coefficient between 2 and 10 km in the latitude band of about 50ø-70øN.

Averaging our eddy coefficients between 2 and 10 km gives a
value that is about 6 times that of Bolin and Bischof's. Part of the difference is probably due to the fact that most :::Rn data were taken at lower latitudes, where convective activities are stronger than at 50ø-70øN.
In the analysis of vertical distributions of Aitken particles from several flights, Junge [1963] estimated that the average eddy coefficient is in the range of 105 to 5 x 105 cm: s -x, which is qualitatively consistent with our values.
The eddy coefficients derived from excess x4CO: usually show a smaller value of about 104 to 105 cm: s-x [Davidson et al., 1966;Seitzet al., 1968]. Excess x4CO: was injected into the stratosphere by nuclear bomb tests, mostly in the early 1960's. It is transported slowly into the troposphere and is eventually assimilated by the biosphere and dissolved in the ocean. The excess x4CO: is a different tracer from Aitken particles, and CO:, because it is transported downward from the stratosphere. Its vertical distribution is affected differently from upward moving tracers when advective motion is important. CONCLUSIONS We have compiled 38 measurements of tropospheric vertical distribution. Although these data may not be representative of the average tropospheric profile, the extensive data, especially in the summer, warrant an examination of the vertical transport in the troposphere. Upward mixing in the midtroposphere is efficient, but not nearly as much as predicted by cumulus cloud transport models. Eddy diffusion coefficients deduced from the average 222Rn data show low values near ground level, larger values in the midtroposphere, and a decrease as the tropopause is approached. For a pollutant with a lifetime similar to 22:Rn and a surface source, at least 50% would reach the free troposphere above the PBL in the summer, less during the rest of the year. Additional measurements, with more vertical resolution and extended coverage from the ground to the tropopause over lands and oceans, are desirable from the standpoint of providing more detailed and accurate parameterizations of tropospheric vertical transport.
Because there is a net transport of 222Rn to the oceans and also vertical wind shear, it is desirable to calculate the 22:Rn distribution in a three-dimensional model.