Bias in concentration estimates due to nonconstant flow rate during particulate air sampling

Correction for a nonconstant flow rate during particulate air sampling is often done by taking the arithmetic average of the initial and final flow rates. This average is then used in concentration calculations as if the flow rate had been constant at that value during the entire sampling period. For long-lived activity this approach is reasonable, but for shorter-lived activity and longer sampling times the estimated concentrations can be biased low. This note examines the magnitude of this bias, and also provides expressions for estimating the concentration, given an observed count, assuming an exponential flow rate time-dependence. One expression uses an estimate of the exponential time-dependence, while another expression uses a linear approximation for the flow rate time-dependence. The parameters used in these expressions are estimated from the same initial and final flow rates used in the arithmetic average.