Sample size for seasonal mean concentration, deposition velocity and deposition: a resampling study

Methodologies are described to assign confidence statements to seasonal means of concentration (C), deposition velocity (Vd), and deposition categorized by species/parameters, sites, and seasons in the presence of missing data. Estimators of seasonal means with missing weekly data are determined using the means of the non-missing values as estimates of the missing data. An empirical relationship is established between the probability that a resampled mean lies within a defined percentage of the mean for individual full 13-week seasonal samples and the specific coefficient of variation (CV) categorized by species/parameter, site, season, and the number of valid samples. The concept of a specific critical CV is introduced as the least of the specific CVs for which a confidence statement fails for a prescribed uncertainty and confidence level. Specific critical CVs are estimated by resampling valid weekly data for full 13-week seasons and from simulations of weekly data. Using data from 47 eastern US CASTNET sites, two approaches focusing on specific critical CVs are employed to examine the confidence statements for C, Vd, and deposition. The first evaluated confidence statements for individual seasonal means. The second approach evaluated the impacts of establishing minimum sample sizes on confidence statements for C and Vd. In both cases, confidence statements for Vd have lower uncertainty and higher confidence than for C. Confidence statements for deposition reflect the influence of C more strongly than Vd. When the two approaches are contrasted, confidence statements with the same level of confidence had lower uncertainty using the first approach where individual seasonal means were evaluated. An example of a confidence statement using the first approach is that when data are missing but 7 of the 13 weeks of seasonal data are present, for each CASTNET species, except the more variable NO3−, seasonal means of C and deposition are within ±35% of the true value at least 90% of the time.