2002 International Radon Symposium Proceedings
Effect of Activity Patterns on Radon Exposure
Willard E. Hobbs, Ph.D.
Radon Reduction & Research
Santa Barbara, CA 9.310.5
ABSTRACT
An important goal of those concerned with air pollution is to estimate the timeweighted average exposure
to various indoor air pollutants. Various studies have measured the concentration of pollutant for indoor
environments, but without regard to the presence of humans. Other studies have used diaries and other records
to evaluate the activity patterns relative to various environments, indoor and outdoor. In this presentation I will
show how the results of these studies can be combined analytically to provide estimates of the distribution of
human exposures to radon. This is a big step beyond the earlier approaches, which have used random sampling
to computationally estimate the exposure distribution (Ref. 1). As an example, I will use residential radon
concentrations and activity patterns associated with people in the State of California. For both populations,
homes and people, there have been detailed studies made using samples of size larger than 3,000. The relatively
large sample size was needed to consider various strata. For homes, they considered such things as housing
type, climate, and geologic province. For people, they considered such things age, gender and income level. The
salient points of these studies will be reviewed. In both cases state officials arc satisfied that the obtained
distributions accurately reflect the populations. I focus on the residential environment because it is the
environment where we spend the most time and the one where people receive their largest dose of natural
radiation (from radon, of course). The procedure presented is to evaluate the exposure distribution by averaging
over all home concentration levels and all human activity patterns. It reduces to a type of convolution of these
two distributions. The home radon concentration levels are well approximated as a lognormal distribution and
the athome fraction of a day may be approximated as a histogram. Corrections are made for the concentrations
because people spend the nighttime hours at home when radon levels are twice their dayaverage recorded
levels. With these assumptions, an analytic formula for the daily human exposure distribution per unit radon
(pCidaylliter) may be analytically calculated. It is a single peak distribution which is broader that a lognormal
distribution. Albeit, the arithmetic average for California is a modest 0.9 pCi/L with less than one percent of
population predicted to have a timeweighted exposure greater than 4.0 pCi/L. Because the procedure is
analytic, it may be evaluated using ubiquitous spreadsheet software requiring minimal computer resources. It
would be interesting to compare the recent updates to the California activity patterns with those found in Iowa
(reported at last year's AARST meeting). Nevertheless, it is not believed that activity patterns vary significantly
from state to state, and therefore, Californian patterns can be used to estimate human exposure for radon in
other states.
1. M. D.Koontz, W. C. Evans, and C.R. Wilkes, "Development of a Model for Assessing Indoor Exposure
to Air Pollutants," GOEMET Technologies, Inc., Report A933157, California Air Resources Board,
2020 L St, Sacramento, CA, January 1998.
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2002 International Radon Symposium Proceedings
INTRODUCTION
An important goal of those concerned with air pollution is to estimate the timeweighted average exposure to
various indoor air pollutants. Numerous studies have measured the concentration of pollutants for indoor
environments, but usually without regard to the presence of humans. Other studies have used diaries and records
to evaluate the activity patterns and access the time in various environments both indoor and outdoor. In this
paper I will show how the results of these studies can be combined analytically to provide accurate estimates of
human exposures. I will use activity patterns and residential radon concentrations associated with people and
houses in the State of California.
I consider the residential environment because it is the one where we spend the most time and the one where
people receive their largest dose of radon radiation. The average Californian spends approximately 17.2 hours
per day in a residence. Because of the design and use of homes, of all building types, the exposure to radon is
highest in residences. In homes radon concentrations average an order of magnitude greater than outdoor levels.
High nighttime levels driven by the stack effect dominate the high residential levels. A factor relating to high
residential radon levels is that ventilation systems in homes are not regulated. Air exchange often occurs
inadvertently (by default) allowing unhealthy conditions to develop and linger. Air handling units in
commercial and public building are regulated, maintained, and used. This usually keeps radon concentrations in
those buildings at negligible levels.
The procedure presented here is to convolute the indoor radon concentration distribution with the activity
patterns that show the distribution of time spent in residences. The residential concentration distribution uses
data generated by the California Department of Health Services and timedependent data that I gathered. Like
many indoor and outdoor pollutants radon concentrations are accurately modeled with a lognormal distribution
function. The mean radon concentration is increased by a factor to account for the higher nighttime levels when
the occupants are present. We begin the next section with a brief discussion of the data and its approximation.
The activity profiles are the focus of this paper. We make three approximations of the distribution of time spent
at home by the people of California. Each divides the day into different subsets of portions of day spent at
home. The division doesn't make a significant difference, as the resulting distribution of exposures is essentially
the same for each. In the conclusion the way the exposures vary with the details of the assumed input functions
and other implications of this analysis are discussed.
CALIFORNIA DATA
Residential Radon Concentrations There have been two major statewide surveys of residential radon
concentrations in California. The first by Liu, et al. involved 3 10 yearlong alphatrack measurements and the
second by ~uinton*involved about 3000 charcoal canisters in summer and autumn shortterm screening
measurements. In both of these data sets 1.9% of the measurements were above 4.0 pCiIL. The reason for the
close agreement is the timeofyear for the screening measurements, occurring during the hottest portion of the
year when the stack effect is weakest.
'
a
studied the data sets and found that the best parameters arc a geometric mean of 0.65
Hobbs and ~ c a d have
pCiIL and a geometric standard deviation factor of 2.4. Their method for analyzing the data does not include
measurements with magnitude less than 1.0 pCi/L and is designed to predict the proportion of homes with
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36
2002 International Radon Symposium Proceedings
elevated radon concentrations. For example, the above parameters give a fraction of homes with radon levels
above 4.0 pCilL as 1.9%, agreeing with the observations.
In this paper the geometric mean found by Hobbs and ~ e a d is
a ~increased to 1.08 pCiIL to account for the
higher nighttime levels. Nero, et aL4 have shown that radon levels in houses follow a lognormal distribution. A
simple approach to such a distribution is to note that the logarithms of the measurements follow a standard
normal (Gaussian) distribution. The geometric standard deviation is therefore a factor within which
approximately 68% of the distribution lies. (For the assumed California distribution this would be between
1.0812.4 = 0.45 pCilL and 0.65x2.4 = 2.59 pCiIL or approximately 0.5  2.6 pCi/L.)
This paper considers situations where the population of homes is well characterized by a single lognormal
distribution. The Hobbs and ~ e a d a 'analysis found that regions with large geometric standard deviations were
often associated with radon "hot spots." These are situations where the distribution of radon concentrations is
characterized by a sum of two lognormal distributions, one with a significantly larger geometric mean. Here, I
assume that this is not the case.
Activity Patterns The California Air Resources Board has sponsored two surveys whereby 24hour time diaries were administered to a modified random sample of California residents. The
first by Jenkins, el at.' involved a target population of adults and adolescents and provided
1,762 location,activity profiles. The second by Phillips, et a t . involved a target population of
children and provided an additional 1,200 location/activity profiles, for a total of 2,962 profiles.
The two surveys are complimentary in that virtually identical schemes were used for recording
both location/activity information and selected characteristics of the participants.
For this research I accessed the California activity profiles using the computer code CPIEM (California
Population IndoorAir Exposure Model) developed by Koontz, et al. The code itself was not run; only the 24hour activity input file was used. This gave the time spent in the participant's residence as well as other persons'
residences. Other location codes are included as well as activity levels but these were not used. Various
demographic strata have been analyzed and the data arc believed to be an accurate representation of California
activities.
TIME IN RESIDENCE AND RADON EXPOSURE
To calculate the average exposure conceptually I make a choice of a random Californian. The radon in his
house will be randomly chosen from the distribution of indoor radon levels and the fraction of time he spends in
the house will be randomly chosen from the distribution of activity profiles. I assume that these two factors are
independent. The time in residences is represented as a fraction of a dayfbetween 0 and 1. The distribution
must include the two limits because there are individuals (relatively few) who do not spend any time in a
residence/=O and others (relatively many) who do not leave h o m e p l .
The distribution of timeaverage radon exposure for the individuals who do not leave home is simply the
distribution of radon concentrations in California homes. Since we are calculating residential exposure, people
who do not enter a residences, do not receive any exposure. Consider the subset of the population that spends
exactly half their day in a residence. For this fraction of people to receive a timeaverage exposure of 2 pCiIL,
they would need to be in homes with an average radon concentration of 4 pCiIL. Recall that the radon geometric
mean has been increased because the half a day that individuals spend in residences usually includes the
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37
2002 International Radon Symposium Proceedings
nighttime when radon levels are higher. The details of how the distributions are convolution are included in the
Appendix.
DeltaFunction Approximation Figure 1 shows an approximation to the distribution of day fraction from the
California surveys. It is represented as a bar chart where the height of each bar is the number of records
reporting a given percent plus or minus onehalf percent. The top bar has the largest value; 181 respondents
report spending more that 0.995 of a day at home. (A closer examination shows that 164 spent all day at home
while 17 reported spending less than 0.005 day = 7 min 12 sec not at home.)
Assuming that the number of people at each percentage spent exactly that fraction of a day in a residence, the
exposure to the population can be calculated. The lognormal distribution for the radon concentration x in
California homes is
Where p and CJ are the natural logarithms of the geometric mean and geometric standard deviation. If/n is the
fraction of the population that spends fraction yn of the day in residences, the distribution function is
an(y) = fn 6 ( y y,,) and the corresponding exposure en(x) is
N.B., the expression ynp is the log of the product of dayfraction yn and the geometric mean e" (see footnote 8).
Summing over all the fractions for each percent of day, the total exposure distribution is
100
~ ( x ) = ~ ' / c ( . ~ . Y I P . ~.
(3)
l=l
This is a sequence of lognormal functions with decreasing means and amplitudes equal to the relative fractions
of the population. The resulting exposure distribution and the original home concentration distributions are
shown in Figure 2.
The distribution function for the fraction of a day spent in a resident by a Californian is the Green's function
which, when convoluted with the home radon concentration distribution, gives 'the exposure distribution. In the
above analysis the Green's function is approximated as a sum of 101 delta functions. One approach at this point
would be to find a smooth ftmction that could then be analytically convoluted and the exposure thereby
evaluated.
Histoeram Approximation I have chosen to approximate the dayfraction function in even simpler terms. Figure
3 shows a histogram for the dayfractions divided into 10 bins, each with a width lo%, plus a bottom bin for 0%
and a top bin for 100%. [The 164 people with activity profiles showing that they do not leave home are in this
top category. They are not a bin but are represented by a delta functionF,00Â¡/06(ly.] This histogram
expression may be evaluated using the lognormal cumulative distribution function
Where the symbols have the same meaning as before. The result for the exposure distribution is
American Association of Radon Scientists and Technologists, Inc.
2002 International Radon Symposium Proceedings
10
4 x 1 = F,w.c(x,p,o)
+ x(qi41
 n i W c d f (x, i p /10,a) + nl&
i=2
The ni factors normalize the cumulative difference functions and Fi are the proportions of the population in the
10 bins. This exposure and the residential concentration distribution are also shown in Figure 2. It is very close
to the exposures found using the delta functions.
StepFunction Avvroximation An even simpler approximation for the dayfraction function would be a single
step function S(y,a,b). S is equal to 1 when y is between a and b.
a(y) = nS S(y, 0.4,l .O)
Now the exposure is evaluated
e(x) = n, [Ncdf (x, 0.4p, o) Ncdf(x, ^,a)]
(6)
(7)
Again ns is a coefficient to normalize the cumulative difference function. The difference in cumulative
difference functions for the normal curve is found on some calculators (c.g., TI83).
When this curve is also plotted in Figure 2, it is very close to the previous curves. Therefore, this presents a
simple and apparently accurate method for estimating the exposure distribution.
CORRECTION FOR NIGHTTIME RADON ELEVATION
Radon testers with continuous monitors know that the latenight and earlymorning readings should be
somewhat higher than the lateafternoon and earlyevening readings. It is one way to assess the validity of radon
measurements. ~ o b b discussed
s~
this in detail. Most people are in their residences at night, just when indoor
radon concentrations are the highest.
I use a fcmtoTECH RS410F radon survey device that remembers the number of radon counts each half hour. I
looked at my last 39 measurements, corrected for background, and found the following: The average of the last
156 measurements between 5 and 6 AM was 3.42 pCi/L while the last 156 measurements between 5 and 6 PM
was 2.08 pCi/L. Some houses were higher than others so, to account for this, I calculated the ratio of the
measurements for each of the 39 houses. The average of all these ratios is 1.66, which is the factor I used to
increase the California geometric mean for the exposure calculation in this paper.
By looking at the concentration ratio for specific houses, the amount of scatter in the data is reduced. The 95%
confidence interval for the ratio is 1.45 to 1.89. In my area, there is no doubt that the stack effect is the primary
driving force bringing in radon with soil gases during the nighttimc hours.
CONCLUSIONS
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2002 International Radon Symposium Proceedings
In assessing the increased cancer risk from radon, the timeaverage exposure is a more meaningful measure than
average concentration. Let me give a personal extreme example. There was tremendous concern in Santa
Barbara, California, because one school building had several rooms with schoolyear averages above 4.0 pCi/L.
One room had an average above 10 pCi/L. Every night the students went home and the room was shut up.
During the night, the radon concentration in the room would sky rocket to magnitudes grater than 40 pCi/L.
When the heating and ventilation came on in the morning the radon would dissipate. I never recorded a level
during the school day that was greater than 1.0 pCi/L. We did dutifully install a mitigation system for the
building that kept the average concentration in all rooms to negligible levels. But clearly, there was not much
human exposure to begin with.
To assess the exposure in a residence, a rule of thumb is that there is a 75% occupancy rate. The data for
California shows a 72% rate, and it is reasonable to expect that other pans of the USA would be higher. There is
large scatter, however, in residence occupancy rate. As I showed above, a flat distribution from about 40% to
100% is a reasonable approximation for the California activity profiles. The timeaverage exposure 0.73 pCi/L
is about 68% of the average residence concentration 1.08 pCi/L.
The average residence concentration itself has been increased because of the nighttime stack effect. This, as the
schoolroom example clearly shows, violates the assumption of independence between average radon
concentration and activity patterns. If you go to work during the daytime and sleep at home at night, your
effective radon exposure may be greatly increased.
REFERENCES
1.
K.S. Liu, S.B. Hayward, J.R. Girman, B.A. Moed, and F.Y. Huang, "Annual Average Radon
Concentrations in California Residences," JAir & Waste Management Assoc 41, pp. 12071212, September
1991.
2.
D. Quinton, California Statewide Radon Survey Screening Results, jointly sponsored by US
Environmental Protection Agency and the California Dept of Health Services, Sacramento, California, 1993.
3.
W.E. Hobbs and L.Y. Maeda, "Identification and Assessment of a Small Geologically Localized Radon
Hot Spot," Environment International 22, pp. S809S817, January 1996.
4.
A.V. Nero, M.B. Schwehr, W.W.Nazaroff, and K.L. Revzan, "Distribution of Airborne Radon222
Concentrations in U.S. Homes," Science 234, pp. 992997, 1986.
5.
P.L. Jenkins, T.J. Phillips, E.J. Mulberg, and S.P. Hui, "Activity Patterns of Californians: Use of and
Proximity to Indoor Pollutant Sources," Atmospheric Environment 26A, pp. 2 14 12 148, December 1992.
6.
T.J. Phillips, P.L. Jenkins, and E.J. Mulberg, "Children in California: Activity Patterns and Presence of
Pollutant Sources," Proceedings of the 84thAnnual Meeting of the Air and Waste Management Association,
Pittsburgh, PA, 1991.
7.
M.D. Koontz, W.C. Evans, and C.R. Wilkes, Development of a Model for Assessing Indoor Exposure to
Air Pollutants, Final Report A933157, California Air Resources Board Research Division, Sacramento,
California, January 1998.
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40
2002 International Radon Symposium Proceedings
8.
Theorems for working lognormal distributions are similar to those for the normal distributions except
that multiplication is substituted for addition. In this paper the parameters are designated the natural log of
the geometric mean and the natural log of the standard deviation. The differentials are always assumed for
the probability functions: if z = fee, f (z)dz = f (kx)d(kx)= k f{kx)dx.
9.
W.E.Hobbs, "Ventilation Level from Time Profile of Radon," 1999 International Radon Symposium,
paper 12, Sponsored by AARST, Las Vegas, NV, November 1999.
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2002 International Radon Symposium Proceedings
0.2
0.4
0.6
fraction of day at home
0.8
1
Figure 1. Percentiles for a sample of 2962 Californians
concentration
       step function
 . .histogram
    delta functions
Figure 2. Comparison of timeaverage human exposure to
radon using different activity approximations with the
residential radon concentrations.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 0.9
1
Fraction of day spent at home in California
all
day
Figure 3. Histogram of activity profiles
for sample of 2962 Californians
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2002 International Radon Symposium Proceedings
Appendix
Calculation of Residential Radon Exposure by Convolution
of Home Concentration and Fraction of Day at Home
We proceed by first constructing the cumulative distribution of exposure E(z) which is a expression giving the total probability that a
persons exposure is less than or equal to z. The distributions c(x) and a(y) are assumed to be independent so that the product c(x)'a(y)
is the probability that a person is California has a home with concentrationx and is present in the building fraction y of the day. (A
clear fallacy here is that some pollutants are the result of human activity in the building and, thus, larger values o f y would correlate
with larger values ofx.)
A general formula for the cumulative exposure distribution is, by definition,
E(z) =
\{ c(x)
dc c{y
a(y)
9G
This can be rewritten in two ways,
The probabilities are summed over the appropriate portion of the first quadrant. Note that because of the their assumed independence,
we can write

a:)=
J
1=0
J
:I,
:I>
J a ~ ) f ) i ( r ~ = Ã‡Q J t < . y ) ~ < ( r
,0
)Ãˆ
(3)
a0
The individual cumulative probability distributions for the concentrations and day fractions are evident in this formulation. But they
are not evaluated since this usually doesn't help.
Lcty9=yxin the first expression and xl=xy in the second expression,
j
)'
E(:) = 1 = 0 +),Jo{;)7
^
J J k)_(4)
.%'its'
A = Idl U ~ YX ')a O
The probability density function is found by differentiating with respect to z
The alternate forms appear quite different, but are equivalent. If the two distributions a@) and c(x) are normalized, then e(z) will also
be normalized.
Suppose the activity athome distribution a@) is a normalized step function between fractions b and d (O