146 Health Physics from '*’Cs deposition density estimates. However, as described in Becket al. (2010), the assumed degree of fractionation was very important for estimating '’’Cs deposition density from exposure-rate measurements at some atolls heavily impacted by Bravo. August 2010, Volume 99, Number 2 Table 1. Fitted parameter values of a, and A, for use in eqn (2) to describe the variation of the exposure rate with time after detonation according to Hicks’ (1981, 1984) data for fractionated debris (R/V = 0.5) for Bravo (thermonuclear tests) and Tesla (nonthermonuclear tests). The values of a, are normalized to an exposure rate of 1 mR h™' at H+12. Thermonuclear tests Estimation of the total exposure from fallout In order to estimate the total exposure from fallout from an estimate of exposurerate at any specific time, we used the temporal variations of exposure rate given by Componentof exponential 1 2 3 4 5 6 7 8 9 10 Hicks (1981, 1984) in a manner described below. First, we developed analytic expressions of the temporal variation of the normalized exposure rate for both Bravo and for a non-thermonuclear test (Tesla) that was conducted at the NTS for the purposes of deriving the exposure over any interval of time (post-detonation) from the data provided by Hicks (1981, 1984). The Hicks dy (mR h7') 9.30 3.35 xX 1.65 X 5.00 X 1.85 x 3.50 X 9.58 X 1.38 x 1.40 x 7.37 X 10' 10' 10° 10° 10° 107! 10°? 10°? 1077 107° Non-thermonucleartests A, (hy ay (mR hy 2.25 10° 830x107! 830x107! 3.88 x 107! 9.67 X 10°? 2.28 x 10°? 5.83 x 1077 1.43 x 1073) 3.05 x 107 2.66 X 107° 1.02107 3.2610! 1.00 x 107° 1.68 x 10° 9.57 x 107! 3.04 x 107! 8.08 x 10° 8.75 x 107° 9.28 x 107° 2.38 x 107° Ay (hy 1.86 6.44 6.44 1.34 8.99 2.03 4.35 7.58 4.05 1.00 x x x x x x x x x x 10° 107! 107! 107! 107° 107? 1073 107" 107° 107° of | mR h! at H+12, but do not take weathering effects into account, were fit to 10-component exponential functions such that a mathematical integration could be easily accomplished. The form for the fitted functions of the exposure rate was: 10 EQVE12 = dae, (2) n=1 Exposure Rate (normalized to H+12) exposure-rate data, which are relative to an exposure rate where t=the time elapsed since the time of the detonation of the device (h); E()/E12 = the ratio of the exposure rate at time ¢ to the exposure rate 12 h after detonation, ex- pressed in mR h|; Time post-detonation (h) a, =the coefficient to the n” exponential term; and X, =the decay constant for the n™ exponential Fig. 1. Variation with time of the normalized exposurerates for six thermonuclear tests and a non-thermonuclear test (Tesla) for a fractionation level, R/V, of 0.5 (Hicks 1981, 1984). The fitted regression values for a, and A, for Bravo and Tesla are given in Table | for k/V = 0.5. As shown in Fig. 1, exposure-rate data for six thermonucleartests (Hicks 1984) are highly similar. For that reason, we concluded that the single set of regression parameters, R/V = 0.5 curves is small. We used the R/V = 1.0 decay rate regression fit to calculate total exposure and E12 values for close-in distances and short TOAsof fallout where we assumed R/V to be greater than 0.5. In the absence of similar data for any non-thermonuclear tests term (h'). shown in Table 1, would be suitable for all 16 thermonuclear tests listed in Simonetal. (2010a, Table 1). The regression parameters shown in Table | correspond to a degree of fractionation (R/V) of 0.5, typical of fallout at relatively large distances from the site of detonation where most of the deposited activity was associated with relatively small particles (<50 um diameter). Wealsofit Hicks’ data for Bravo for R/V = 1.0 and used those values for the higher fractionation ratios. As shownlater, the difference in decay rates between the R/V = 1.0 and at Bikini or Enewetak, we concluded that the data derived by Hicks (1981) for the Tesla test conducted at the NTS would adequately reflect the decay rate and nuclide composition of the four non-thermonucleartests (Simon et al. 2010a, Table 1) that deposited relatively low levels of fallout in the Marshall Islands. As shown in Fig. 1, the decay rate for Tesla is very similar to that for the six thermonucleartests. We subsequently took into account the influence of weathering on the temporal variation of the exposure