Rainout-Washout Model for Variation of Environmental Gamma-Ray Intensity by Precipitation

Transcription

1 Journal of NUCLEAR SCIENCE and TECHNOLOGY, 19[5], pp. 393~409 (May 1982). 393 Rainout-Washout Model for Variation of Environmental Gamma-Ray Intensity by Precipitation Nobuyoshi TAKEUCHIt and Akira KATASE Faculty of Engineering, Kyushu University* Received July 29, 1981 A rainout-washout model is proposed in order to forecast the variation of the intensity of environmental g-rays and study the behavior of radioactive nuclei in the atmosphere on rainy days. This model divides the atmosphere into two parts of in cloud and under cloud. Simultaneous differential equations are formulated to give the time variations of the concentrations of daughter nuclei of 222Rn during precipitation in each state of free atoms or ions, aerosol particles, cloud droplets and rain drops. Coefficients used in the equations for removal of daughter nuclei from one state to other one and for washout by rain drops are estimated from published data. Variations of various concentrations are obtained. Counting rates of a Ge (Li) detector are calculated for 352 kev (214Fb) and 609 kev (214Bi) g-rays. They are mainly due to g-rays from daughter nuclei accumulated on the earth's surface, most part of which is brought by rainout in cloud. Experimental variations of counting rates are well reproduced on rainy days. For the forecast of the variations it is necessary to measure rainfall rates, concentrations of 222Rn and cloud base heights at short interval. KEYWORDS: rainout, washout, gamma radiation, radon 222, rainfall, counting rate, aerosol, cloud droplet, variation, environment, precipitation I. INTRODUCTION In various nuclear facilities, the environmental nuclear radiation is measured to monitor radiation doses the general public receives and to detect the release of radioactive nuclei from them. The intensity of natural r-rays fluctuates and especially makes large changes with rainfalls(1)(2). Therefore, it is difficult to distinguish if small changes in the intensity of r-ray are due to artificial radioactive nuclei from nuclear facilities. When it rains, the distinction is not easy even for large increases of radiation dose to be natural ones or not. Then it will be useful that the variation of the intensity of natural g-rays can be predicted by some means, at least on rainy days. The increase of g-ray intensity on rainy days is induced by the phenomena of rainout and washout(3) of daughter nuclei of 222Rn in the atmosphere. These phenomena also remove radioactive nuclei which will be discharged into the atmosphere at accidents of nuclear facilities or explosions of atomic bombs. Therefore, the study of these phenomena is considered to be very important not only to expect the magnitude of increase in the -ray intensity on rainy days, but also to give the information on the behavior of radio- g active substances in the atmosphere. The phenomenum of rainout is related to the mechanism of rain drop formation in cloud. If the intensity of g-rays on rainy day is closely connected with the rainout process in cloud, its study may give fresh insight into occurrences in cloud. Damon & Kuroda(4) have measured the natural radioactivity in rain water, and prot Present address : Fuji Electric Co., Ltd., Hzno-shz, t okyo 191. * Hakozaki, Higashi-ku, Fukuoka-shi

2 394 J. Nucl. Sci. Technol., posed a three-phase model to account for its specific activity. One of the phases is a state of free atoms produced from the decay of radon and daughter nuclei. The second one is a state of condensation droplets or aerosol particles. The third phase is that of rain drops. The free ions are easily attached to particulate matter suspended in the atmosphere and then they are transferred to rain drops which grow from the condensation droplets. The free ions take sometimes a path way directly to rain drops. They obtained a close agreement on a relation of total activity of rain drops with rainfall rates between the measurements and the expected values. Gat et al.(5) have used a three-phase model of free atoms, aerosol particles and rain to deduce the variations of concentrations of the daughter nuclei in the atmosphere during rainfall. They calculated those variations for a wide range of the values of parameters used in the model and measured activity ratios of the airborne '4Pb to 21413i in order to compare with the calculated results discussing the validity of values of parameters. Two phenomena of rainout and washout(3) have been considered as principal mechanisms which scavenge radioactive nuclei from the atmosphere. Rainout takes place in cloud and washout under cloud. Both phenomena play an important role not only for the removal of radioactive nuclei from the atmosphere, but also for that of dust and pollutants. The idea of Damon & Kuroda corresponds rather to rainout and that of Gat et al. to washout. They both did not clearly distinguish these two phenomena. The phenomena of washout have been studied experimentally and theoretically by many authors(13)-(20). Washout coefficients have been investigated in relation to radii of rain drops and aerosol particles. Experimental variations of the coefficient with the radii do not agree with theoretical ones". The scavenging of radioactive nuclei, aerosol particles and others by rain drops in cloud is called rainout. Its mechanism is complicated one and also has been studied by many authors(13)~(20). The mechanism is considered to be more difficult to be made clear than the washout, because the process of growing of cloud droplets to rain drops contains many factors. The mechanism of both rainout and washout is not solved theoretically, but there are some experimental results which give values of coefficients related to these phenomena. In the present paper, the details of the phenomena are not taken into considerations, but an attempt is made to connect the variation of g-ray intensity by rainfall with some available quantities. Which quantities are important is studied. Only the principal phenomena in the atmosphere are taken into consideration in assuming a model. By this model, the variations of concentrations of radon-daughter nuclei are also studied. II. RAINOUT-WASHOUT MODEL The intensity of natural environmental g-rays increases on rainy days(2). This is principally induced by accumulations of 214Pb and 214Bi nuclei on the ground which are floating in the atmosphere produced as decay products of 222Rn and are carried to the ground by rain drops. Radon atoms exhalate from the ground and propagate to the upper atmosphere by turbulent diffusion, the coefficient of which depends on meteorological conditions of the atmosphere. The concentration distributions of "'Rn atoms have been calculated as a function of altitude by Jacobi & Andre(21) for five mixing conditions of the atmosphere. Because of short half-lives of radon decay products, radioactive equilibrium is established between 222Rn and daughter nuclei in a few hours. If the concentration of 54

3 Vol. 19, No. 5 (May 1982) 395 radon atoms varies slowly, those of daughter nuclei change with it. Even when the mixing conditions happen to change in the atmosphere, the assumption of radioactive equilibrium between 222Rn and daughter nuclei is reported to be reasonable above a few meters on the groundo(22). The radon daughter nuclei are transferred from the atmosphere to rain drops on rainy days by rainout in cloud and by washout under cloud. Both two phenomena should be considered simultaneously, when the variation of environmental ć-ray intensity is tried to be predicted. A rainout-washout model (an R-W model) is proposed. The model divides the atmosphere into two regions of in cloud and under cloud. The daughter nuclei are produced as ions in general. They are easily captured by aerosol particles. Some daughter nuclei will remain as free atoms or ions in the atmosphere. In cloud some of aerosol particles become nuclei of cloud droplets and some adhere to droplets. Free atoms and ions have possibility to be attached to them. They grow in radii depending on the complex meteorological conditions in cloud to fall to the ground through cloud capturing other cloud droplets which contain radon daughter nuclei. On the other hand, falling rain drops under cloud take in them free atoms or ions and aerosol particles by numerous mechamisms which include inertial impaction, interception, Brownian diffusion, thermophoresis, diffusiophoresis and electrostatic charge collection". The radon daughter nuclei are scavenged by rainout in cloud and washout under cloud from the atmosphere to the ground. This scheme is represented in Fig. 1 as an R-W model. The meanings of symbols in the figure are listed in Table 1. Fig. 1 Schematic representation of rainout-washout model In the construction of the scheme in Fig. 1, the following assumptions have been made. At first the processes in Fig. 1 are taken to be irreversible. The formation of free atoms, for instance, is neglected from cloud droplets or rain drops by the evaporation of water. The generation of aerosol particles is also neglected from rain drops by their breakups. As the second assumption, when rain drops fall from cloud scavenging radon daughter 55

4 396 J. Nucl. Sci. Technol. nuclei under cloud and reach the ground, the rain water filters into the ground and the daughter nuclei in it are assumed to remain near the earth's surface adsorbed by soil. The uniform spread of the atmosphere is assumed in the horizontal direction. The rainout of radon atom in cloud is considered to be small and few radon atoms are scavenged by washout(13). The distribution of radon concentration is taken to be constant during precipitation. The mixing condition of the atmosphere is assumed not to change during precipitation, because the information is not available on the variation of the mixing condition when it rains and the inclusion of Table 1 List of symbols used in rainoutwashout model in Fig. 1 this effect in the present model makes the problem complicate. Then the following simultaneous differential equations are formulated for the concentrations of radon daughter nuclei at a position in the atmosphere. All of the concentrations vary according to the altitude. (1) For the concentrations in the state of free atoms or ions in cloud : ( 1 ) ( 2 ) ( 3 ) (2) For the concentrations in the state of aerosol particles in cloud : ( 4 ) ( 5 ) ( 6 ) (3) For the concentrations in the state of cloud droplets in cloud : 56

5 Vol. 19, No. 5 (May 1982) 397 ( 7 ) ( 8 ) ( 9 ) (4) For the concentrations in the state of free atoms or ions under cloud : (10) (11) (12) (5) For the concentrations in the state of aerosol particles under cloud : (13) (14) (15) (6) For the concentrations in the state of rain drops : These concentrations are denoted by A, B and C for three daughter nuclei respectively and they are the number of atoms per unit volume of the atmosphere and not the concentration in rain water. Their values change as rain drops fall to the ground. For a time r during the fall ; (16) (17) (18) Now the time which rain drops take to reach the ground is denoted by T, and the concentrations A, B and C at the earth's surface are expressed as AT, BT and CT respectively, which are obtained from simultaneous integrations of Eqs. (10)~(18) using a relation between altitudes of falling rain drops and the time t for appropriate initial values of A, B and C. These intial values are the concentrations of daughter nuclei contained in rain drops per unit volume of the atmosphere just at the cloud base and deduced by integrations of Eqs. ( 1 )~( 9) from the top of cloud to the base. In the later section, these values will be deduced under simple assumptions. (7) For the concentrations of radon daughter nuclei per unit area on the earth's surface : 57

6 398 J. Nucl. Sci. Technol., (19) (20) (21) Fluxes of 1-rays at a detector put on the ground are calculated from the values of 139, C, and others as explained in the later section. Equations ( 1 )~(21) can be solved if the distribution of radon atoms in the atmosphere and the values of parameters are known. When it does not rain, the values of coefficients related to rain drops is put equal to zero. The equilibrium concentrations of radon daughter nuclei are obtained from radon distributions deduced by Jacobi & Andre(21). Those concentrations are used as the initial values of concentrations on rainy days. Futhermore, coefficients of turbulent diffusion are known as a function of altitude on rainy days, then turbulent diffusion equations can be combined with the present simultaneous differential equations. This system of equations are too complicated to be solved. In order to make clear the important factors which affect the fluctuation of the intensity of environmental g-rays, this complication is not considered to be appropriate but only makes obscure the phenomena. In order to make more simple the analysis of phenomena without loosing their essential points, the following assumptions have been made. The distribution of radon concentrations is taken to be constant under and in cloud respectively, and the phenomena in cloud happen uniformly through cloud, because the phenomena in cloud are very complex and are difficult to be treated in detail(18)~(20). The symbol O is defined as a product of L and Ct : O=LxCt, where L is an average rate of removal of cloud droplets by falling hydrometeors and other possible processes. The value of O expresses a rate of rainout namely a ratio of the quantity of water, which falls from cloud per unit area and unit time, to water contents contained in a vertical cloud column of unit area. The concentrations of daughter nuclei contained in rain drops are given just at cloud base by OAd/v, OBd/v and OCd/v. These are the initial values of A, B and C and the values of AT, Br and CT are easily obtained by integrating Eqs. (16), (17) and (18) in uniform radon distributions and given by two components. One of them contains daughter nuclei included into rain drops in the process of rainout in cloud, and the other contains those by washout under cloud. They are denoted by the symbols R and W in parentheses, respectively. (22) where (23) (24) (25) where (26) 58

7 Vol. 19, No. 5 (May 1982) 399 and (28) (27) where (29) The removal rates are distinguished in Fig. 1 according to the daughter nuclide, but it is reasonable to abandon such assignment. Then (30) (31) When various concentrations of daughter nuclei are once obtained by solving the simultaneous differential equations, it is possible to calculate the r dose or the g-ray flux on the ground(23). If environmental g-rays are measured with a Ge(Li) spectrometer on rainy days, variations of counting rates by precipitation are experimentally obtained for specified g-rays. The calculation of flux of a specified g-ray is simpler and more accurate than that of dose and the counting rates are deduced. These experimental and theoretical quantities can be compared with each other to see the validity of the present model. The flux of the specified g-ray is derived at a position of a g-detector which is put at a (m) above the ground. A number of g-rays per radioactive decay-an emission rate-is denoted as fl for each specified g-ray of 214pb or214 Bi. A relaxation length in air is less than about 100 m for g-rays of energy below 1 MeV. Contributions to the g-ray flux at the detector is negligible for daughter nuclei in and over cloud compared with that of nuclei under cloud. If the uniform concentration of a specified nuclide in air is denoted as Na, the g-ray flux (b/c, of the specified energy from the nuclide is given by where ji is the attenuation coefficient of air for the g-ray and the height of the detector is neglected. If the nuclide is 214Pb, Na=B'f+B's. The contribution to the g-ray flux from the daughter nuclei in rain drops is obtained by integrating the differential contribution of B or C in the atmosphere. This flux is added to p'a of Eq. (32) to give the g-ray flux 59 (32)

8 400 J. Nucl. Sci. Technol., pa from nuclei in the atmosphere. A surface concentration of the nuclide on the earth's surface is denoted as Ng, then the r-ray flux 0, of the specified energy is given by For 214Pb, for instance, Ng=Bg. The intrinsic efficiency f2 and the effective area f3 of a Ge(Li) detector depend on the energy and direction of r-ray. Therefore, these value should be obtained by averaging over the angular distribution of r-ray flux at the detector. Now, the values of f2 and fa are assumed to be the averaged ones for the specified r-ray. then the counting rates (cph) Cag and Cgg for pa and pg are given respectively by Total counting rate for this g-ray is In the real mearurements, the counting rate due to the r-ray from nuclei in the ground should be added to Cg. III. VALUES OF PARAMETERS The simultaneous differential equations presented in Chap. II are solved numerically by the Runge-Kutta-Gill method by using the appropriate values of coefficients. The concentrations of radon atoms are determined, then equilibrium concentrations of daughter nuclei before rainfall are obtained from the equations by putting the coefficients L, fw and SW, which are related to rainfalls, as zero. Those values are used as initial values of concentrations on a rainy day to calculate their variations with time for a constant rainfall rate. The concentration of 222Rn in the atmosphere depends on mixing conditions. Several values are read from the figure of Jacobi & Andre(21) and shown in Table 2 for three typical mixing conditions. It is not clear what mixing conditions are on rainy days. Refering to the data under the normal turbulent the specific activities of 222Rn were assumed to be 180 and 200 dpm/m3 in and under cloud, respectively. These values or the concentrations of 222Rn are rather to be taken as adjustable parameters in the present work. (33) (34) (35) Table 2 Specific activities of 222Rn at some altitudes under three typical mixing conditions in atmosphere for exhalation rate of one 222Rn atom/cm2,s quoted from results by Jacobi & Andre Rates of removal express the fraction of radon daughter nuclei which are removed from a state to other state. There are few experiments on the process of transition between states of particles in the atmosphere. It is difficult to select proper values for removal rates. The number of daughter nuclei removed is considered to be proportional to the total number of nuclei in the initial state and may be proportional to the number of particles in the final state to which daughter nuclei transfer. Removal rates will depend on size distributions of particles in both states. Such detailed effects are not taken into 60

9 Vol. 19, No. 5 (May 1982) 401 consideration in the present model and only the average values are used. Furthermore, if the number of particles in the final state does not vary largely in the atmosphere, removal rates are reasonably approximated to be constant. Gat et a1.(5) have used rate constants of transition in their formulae, but sdr and fdr in the present model are not equal to their parameters which are listed in Table 3. The value of r sr was given by Junge", as shown in Table 3 and Ikebe et al.(24) have stated that the mean life of free ions to be captured by aerosol particles is about several tens of seconds. From these values the present one was assumed as 2.1 min-1. Table 3 Values of parameters: Removal rates and washout coefficients The values of "r have been obtained by Hicks(14) from the measurement of the change of concentrations of daughter nuclei in rain drops during precipitation. Makhon'ko(13) listed their values with others. The values useful to the present model are shown in Table 3 and 0.01 min-1 was adopted for sdg and f dg' The washout phenomena have been studied theoretically by Jungem, Greenfield(6), Wang et al.(9) and Davenport et al.(11) Washout coefficients are expected to depend on rainfall rates and size distributions of particles and rain drops. In the measurements by Radke et al.(25), removal rates of aerosol particles by precipitation appear to depend on the kind of particles and vary with particle diameter by several factors with the minimum at about 1 pm. On the other hand, the experimental results of Davenport et al.(11) show a small effect of the particle diameter on the washout coefficient. The data of their two measurements give a relation of 8W=0.0023x R (min-1) (R: rainfall rate in mm/h) for particles with diameter of 3x10-3 to 10 mm. McMahon et al.(7) have chosen xR (min-1) as the best estimate of washout coefficient for particles. Maul(10) has obtained a similar value to that by McMahon et al. for washout coefficient of SO,. These values are tabulated in Table 3 with other experimental values. The effect of the size distribution of rain drops is also not clear. One of the measurements of Davenport et al.(11) shows that the value of washout coefficient is about twice as large as the value calculated by the above relation for sw. This disagreement is perhaps due to the difference of size distribution of rain drops. The above relation is used for sw in the present model, though 61

10 402 J. Nucl. Sci, Technol., there is a possibility of the change of value by a few factors. Lai et al.(8) have measured washout coefficients in laboratory by using AgCl aerosols. They estimated washout coefficients for free atoms to be about four times their values of 'W. Other data on fw are given in Table 3. When the accuracy of the relation for 3W is considered, it is torelable to use similarly the relation for 3W as a relation for fw too. The precipitation coefficient L signifies a rate of cloud droplets, which fall from cloud per unit time, in a unit volume of the atmosphere. In the present model uniform cloud is assumed. Cloud droplets fall to the ground at a uniform rate anywhere in cloud. The water contents per unit volume in cloud are denoted by L(g/m3), then where K is a constant of The quantity of water is Ct,L (g/m2) in a vertical column of cloud with a unit base area. Falling rain drops decrease this quantity. It was assumed that the cloud lost half of its water contents in 1 h for a constant rainfall rate. One hour may be small or large by a few factors compared with actual values, but that will be scarcely different from them by order. Then This relation is not so different from one expected from the values of L, Ct and R of various clouds(17)(26). Substitution of Eq. (37) to Eq. (36) gives The rainout coefficient also corresponds to a ratio of the number of daughter nuclei, which fall from a unit area of cloud base per unit time, to the concentration in cloud. The water contents in cloud are about 0.5 g/m3 for marine cumulus, 0.3~3 g/m3 for continental cumulus and about 5 g/m3 for cumulonimbus 26). Rainfall rates will vary with the water contents in cloud and rainfalls will not start in cloud of very small water contents. A relation was assumed between rainfall rates and water contents to be From Eqs. (36) and (39), This formula was used in calculations. Scott(17) has proposed a relation between average water contents in cloud and rainfall rates such as Values of O which are derived by Eq. (41) are smaller than the present values derived from Eq. (40) by a factor of about 3 at the rainfall rate of about 1 mm/h. For 5-10 mm/h, there are no large difference in the values of O for both derivations. A value of 360 m/min was used as a falling velocity v of rain drops in most calculations. The variation of average falling velocity with rainfall rate was taken in consideration in some calculations. The falling velocities are tabulated for diameter D of rain drops by Mason(20). From the table, a relation between v and D is approximated to be 62 (36) (37) (38) (39) (40) (41) (42)

11 Vol. 19, No. 5 (May 1982) 403 In the precipitation of the Wegener-Bergeron process by(20), a mean-volume diameter is given (43) Substituting this relation to Eq. (42), then The falling velocities of each rain drop vary with their diameters, but they were represented in some calculations by the mean-volume velocity given by the above equation. (44) IV. RESULTS AND DISCUSSION 1. Equilibrium Concentrations of Daughter Nuclei of 222Rn without Precipitation Equilibrium values were obtained for respective concentrations without precipitation by solving the simultaneous differential equations where the coefficients related to precipitation were put to be zero. Their values are shown in Table 4. Because the Table 4 Equilibrium concentrations of daughter nuclei of 222Rn in various states for concentrations of 222Rn of x 106 nuclei/m3 (180 dpm/ms) in cloud and x 106 nuclei/m3 (200 dpm/m3) under cloud, without precipitation removal rates of free atoms or ions are large, the concentrations of free atoms are very small compared with other ones. The concentrations of 218Po contained in aerosol particles and cloud droplets are smaller than those of 214Pb and 214Bi due to the short half-life of 218Po. 2. Variations of Concentrations with Time during Precipitation Variations of concentrations with time were obtained for some values of rainfall rate for the above equilibrium concentrations taken as the initial values. The concentrations Af, Bf, Cf, A,s, Bs and C, are independent of precipitation. The values of A'f, B'f and C'f make little changes by precipitation because isr âfw, but those of A;, B; and C's decrease by the effect of washout. The variations of Ad, Bd, and Cd are small because of A<l. From these tendencies, the concentrations of daughter nuclei in cloud do not change largely except for the heavy rainfall rate. The variations of AT, BT and CT with time are shown in Fig. 2(a) for three different heights of cloud base and those of Ag, Bg and Cg in Fig. 2(b). The decreases of BT and Cr with time are due to the decreases of B's and C's After 60 min these values are nearly in equilibrium. The surface concentrations of daughter nuclei Ag, Bg and Cg increase with time due to the accumulation on the earth's surface. 3. Variations of Concentrations with Rainfall Rate Some concentrations after 60 min of precipitation are shown in Fig. 3 as a function of rainfall rate. The values of A's suffer relatively small effects by precipitation because of the short half-life of 218To. For B's and C's, the washout coefficients are the same order as radioactive decay constants. They decrease with rainfall rate by washout. The concentrations BT and CT increase with rainfall rate, but the rate of increase decrease and the value of CT has the maximum. These situations are induced by the large decrease of B; and C's for large rainfall rate. The values of Bg and Cg increase slowly for large rainfall rate. 63

12 404 J. Nucl. Sci. Technol., Fig. 2 Variations of concentrations of daughter nuclei of 222Rn with time for three different cloud-base heights Fig. 3 Variations of concentrations of daughter nuclei of 222Rn after 60 min of start of constant precipitation with rainfall rate 64

13 Vol. 19, No. 5 (May 1982) Fractions of Daughter Nuclei Taken in by Rainout The daughter nuclei in rain drops on the earth's surface are taken in from cloud droplets in cloud by rainout and principally from aerosol particles under cloud by washout. Ratios of the number of nuclei taken in by rainout to the total number are difined as a fraction of concentrations by rainout and were calculated by using Eqs. (22)~(30) at 60 min after the start of rainfall. Results are shown in Fig. 4. The large part of 218po in rain drops is taken in by washout. The 218Po nuclei rained out in cloud easily decay before they reach the earth's surface. The fractions for 214Pb and 214Bi decrease with rainfall rate, because the washout coefficients increase. However, the concentrations in the state of aerosol particles decrease with rainfall rate, and consequently the rainout component does not strongly decrease for large rainfall rate. The magnitude of rainout components depends on the value of rainout coefficient O. This value cannot be determined rigidly at present, but the present value of O is not differ so much from the real one as discussed in the former chapter. The large part of 214Pb and "'Si nuclei in rain drops can be said to be brought to the earth's surface from cloud. The thickness of cloud is large. Rain drops collect cloud droplets through cloud and fall to the ground with abundant daughter nuclei. 5. Effects of Cloud Height on Concentrations in Rain Drops Fig. 4 Contribution of rainout in percentage to concentrations of daughter nuclei of 222Rn in state of rain drops on ground and on Earth's Surface If the altitude of cloud base is high, rain drops fall through larger distance and catch more daughter nuclei by washout. The concentrations of 218Po in the state of rain drops, for which the fraction of washout component is large, increase more steeply with the cloud base height than those of other two nuclides as shown in Fig. 5(a). The latter two concentrations also increase linearly with it, but the variations are not large. On the earth's surface, the surface concentrations of three nuclides similarly increase with cloud base height as shown in Fig. 5(b). The concentration of 214Bi is larger than that of "'Pb due to the accumulation of decay products on the ground. 6. Effects of Values of Removal Rates on Concentrations Only the value of fsr was changed from 2.1 to 1.0 and the concentration were calculated. Those of free atoms or ions increased. The value of C'f became large about eightfold, but those in the state of aerosol particles made little change except A's. Hence, those in the rain drops and on the earth's surface did not change. Values of sdr and f dr were changed from 0.01 to Then, the concentrations in the state of cloud droplets increased and those in the state of rain drops and on the earth's surface was made about twice. On the other hand, when values of sdr and sdr were varied from 0.01 to 0.006, 65

14 406 J. Nucl. Sci. Technol., Fig. 5 Variations of concentrations of daughter nuclei of 222Rn after 60 min of start of precipitation with cloud base height corresponding concentrations became smaller by a factor of about 1.3. Values of removal rates are a little uncertain, but their values do not affect seriously the concentrations in the state of rain drops and on the earth's surface, which influence intensely the intensity of g-ray flux as explained in the next section. 7. Variations of Counting Rates of g-rays by Precipitation Counting rates which are obtained by a Ge(Li) spectrometer for a specified y-ray can be calculated from various concentration distributions as shown in Chap. II. A Ge(Li) detector of 60 cm3 was used to measure the environmental g-rays on rainy days(2). Values of parameters necessary for the counting-rate calculation are shown in Table 5. The values of f2 were measured in a direction of detector axis and these and the value of f3 were used as approximate values to the average ones mentioned in Chap. II. Rainfalls were also measured for every 1 h. An example of results obtained is shown in Fig. 6. The ordinate is peak counting rates (cph) of specified g-rays in g-ray spectra. The abscissa is the time from the start of rainfall and its rates are shown under the line. A histogram written by dotted lines and marked by the letter Y represents the variation of counting rate of 352 kev g-ray of 214Pb measured in July, The letter Z represents similarly those of 609 kev g-ray of 214Bi. The values of counting rates at zero of the abscissa show average counting rates on days without precipitation. Counting rates were calculated from the equilibrium concentrations of daughter nuclei in the atmosphere without precipitation. These values were subtracted from the measured average values and the residues were considered to correspond to the contributions from daughter nuclei in the ground. Table 5 Values of coefficients for calculation of counting rate measured with Ge (Li) spectrometer Various concentrations were calculated for varying rainfall rates in the following way. At first, the equilibrium concentrations were used as the initial values of concentrations 66

15 Vol. 19, No. 5 (May 1982) 407 Fig. 6 Comparison of calculated counting rates for 352 kev ƒá-ray of 214Pb ( x ) and 609 kev ƒá-ray of 214Bi( ž) with measured ones (Y: 214pb, 214Bi) and the simultaneous differential equations were solved for a constant value of rainfall rate as explained before. This value was changed to a new one, then the final values of concentrations in the calculation for the old rainfall rate were used as the initial ones for the new rainfall rate and the equations were solved. Counting rates during precipitation were calculated simultaneously with the calculation of concentrations for g-rays from daughter nuclei in the atmosphere which were in the states of free atoms, aerosol particles and rain drops. These counting rates are shown by two curves in the lower part of Fig. 6. Counting rates were also calculated at the same time for g-ray from daughter nuclei on the earth's surface. These values were added to the sums of the counting rates due to the nuclei in the atmosphere and that due to the nuclei in the ground. Results are shown in Fig. 6 by two curves marked by cross and lozenge for 352 kev of 214Pb and 609 kev of 21413i, respectively. In these calculations, rainfall rates were varied for some time at the interval of 30 min by keeping those for 1 h to be equal to the measured ones, because the results calculated for 1 h interval gave poor fit to the measured variation of counting rate. The concentrations of 222Rn were adjusted to give a good fit and kept constant through the calculations. These values are shown in the figure and are considered to be a little large compared with the values in Table 2, when the exhalation rate of Rn atoms/cm2,s is referred(27). Experimental variations are well reproduced by the calculated one. 67

16 408 J. Nucl. Sci. Technol., The forecast for the variations of counting rates of any g-rays by precipitation is considered to be possible as shown in Fig. 6. The variation of g-ray dose by precipitation may be also predicted. The most effective parameter is the concentration of 222Rn in the atmosphere. Counting rates change nearly linearly with it. On rainy days, if the turbulent motion is strong in the atmosphere, the 222Rn nuclei mix well in it and the concentration becomes almost uniform. In this case, the present approximation of the uniform concentration becomes very proper one. The concentration can be measured on the ground and be used in calculations. The cloud base height also affects the counting rates calculated, but this effect is relatively small as shown in Fig. 5. The height may be observed on rainy days to be used in calculations. As for washout coefficients, there are some experiments and these experimental results do not give so different values of coefficient among them. However, few studies of the phenomena of rainout are seen in literature. In the present model, the rainout coefficient O is one of the most serious parameters. This value may be determined from the direct measurements of concentrations of daughter nuclei in cloud droplets and rain drops. On the other hand, the measurements of the variation of g-ray intensity and other related quantities on the ground have possibility to give some insight into the phenomena of rainout in cloud. V. CONCLUSIONS A rainout-washout model has been proposed to describe the behavior of daughter nuclei of 222Rn in the atmosphere on rainy days and to forecast the variation of the intensity of environmental g-rays. The values of coefficients used in the model were estimated from published results on the corresponding phenomena. Variations of concentrations of daughter nuclei by precipitation were obtained in various states in the atmosphere as a function of rainfall rate. Counting rates were calculated for the measurement of specified with a Ge(Li) spectrometer. The variation of counting rate during precipitation g-ray was deduced and was shown to be in good agreement with the experimental results by using the reasonable values of 222Rn concentration in the atmosphere. In order to forecast the intensity of g-rays on rainy days it appears that the concentration of 222Rn and the cloud base height should be measured at short interval together with the rainfall rate. Further study of washout and especially rainout phenomena is required to obtain the more rigid values of coefficients used in the model. Measurements are also necessary on the variations of radon daughter concentrations in various states during precipitation to see how the present simple model simulates the phenomena in the atmosphere. The study of the variation of g-ray intensity by precipitation gives useful information on the behavior of radioactive nuclei and dust in the atmosphere and has possibility to provide insight into the rainout phenomena in cloud. ACKNOWLEDGMENT We would like to thank Professor M. Matoba, Dr. Y. Yoshida and Mr. K. Tsuji for many useful discussions on the present work. - REFERENCES- (1) MINATO, S.: J. Nucl. Sci. Technol., 17[6], 461 (1980). (2) KATASE, A., et al.: To be published. 68

17 Vol. 19, No. 5 (May 1982) 409 (3) JUNGE, C. E.: "Air Chemistry and Radioactivity", (1963), Academic Press, New York. (4) DAMON, P. E., KURODA, P. K.: Trans. Am. Geophys. Union, 35, 208 (1954). (5) GAT, J. R., ASSAF, G., MIKO, A.: J. Geophys. Res., 71, 1525 (1966). (6) GREENFIELD, S. M.: J. Meteor., 14, 115 (1957). (7) McMAHON, T.A., DENISON, P.J., FLEMING, R.: Atoms. Environ., 10, 751 (1976). (8) LAI, K. Y., DAYAN, N., KERKER, M.: J. Atoms. Sci., 35, 674 (1978). (9) WANG, P. K., GROVER, S. N., PRUPPACHER, H. R.: ibid., 35, 1735 (1978). (10 MAUL, P. R.: Atmos. Environ., 12, 2515 (1978). (11) DAVENPORT, H. M., PETERS, L. K.: ibid., 12, 997 (1978). (12) BAKULIN, V. N., et al.: J. Geophys. Res., 75, 3669 (1970). (13) MAKHON'KO, K.P: Tellus, 19, 467 (1967). (14) HICKS, B.B.: J. Appl. Meteorol., 17, 161 (1978). (15) PERKINS, R. W., THOMAS, C. W., YOUNG, J. A.: J. Geophys. Res., 75, 3076 (1970). (16) GARLAND, J.A.: Atmos. Environ., 12, 349 (1978). (17) SCOTT, B.C.: J. Appl. Meteorol., 17, 1357 (1978). YAU, M. K., AUSTIN, M.: J. Atoms. Sci., 36, 655 (1979). (19) YALAMOV, Yu. I., VASILJEVA, L. Yu., SCHUKIN, E. R.: J. Colloid Interface Sci., 62, 503 (1977). (20) MASON, B. J.: "The Physics of Clouds", (2nd ed.), (1971), Clarendon Press, Oxford. (21) JACOBI, W., ANDRE, K.: J. Geophys. Res., 68, 3799 (1963). (22) BECK, H.L., GOGOLAK, C.V.: ibid., 84, 3139 (1979). (23) BECK, H. L. : ibid., 79, 2215 (1974). (24) IKEBE, Y., SHIMO, M.: J. At. Energy Soc. Jpn., (in Japanese), 22[2], 85 (1980). (25) RADKE, L. F., HOBBS, P. V., ELTGROTH, M. W. : J. Appl. Meteorol., 19, 715 (1980). (26) ROGERS, R. R.: "A Short Course in Cloud Physics", (1976), Pergamon Press, Oxford. (27) MEGUMI, K., MAMURO, T.: J. Geophys. Res., 78, 1804 (1973). 69