Using the precision of the mean to estimate suitable sample sizes for monitoring total phosphorus in Australian catchments

The effect of the sample size on prediction quality is well understood. Recently, studies have assessed this relationship using near‐continuous water quality samples. However, this is rarely possible because of financial constraints, and therefore, many studies have relied on simulation‐based methods utilizing more affordable surrogates. A limitation of simulation‐based methods is the requirement of a good relationship, which is often not present. Therefore, catchment managers require a direct method to estimate the effect of sample size on the mean using historical water quality data. One measure of prediction quality is the precision with which a mean is estimated; this is the focus of this work. By characterizing the effect of sample size on the precision of the mean, it is possible for catchment managers to adjust the sample size in relation to both the cost and the precision. Historical data are often sparse and generally collected using several different sampling schemes, all without inclusion probabilities. This means that an approach is needed to obtain unbiased estimates of the variance of the mean using a model‐based approach. With the use of total phosphorus data from 17 sub‐catchments in southeastern Australia, the ability of a model‐based approach to estimate the effect of sample size on the precision of event and base‐flow mean concentrations. The results showed that for estimating annual base‐flow mean concentration, little gain in precision was achieved above 12 observations per year. Sample sizes greater than 12 samples per event improved event‐based estimates; however, the inclusion of more than 12 samples per event did not greatly reduce the event mean concentration uncertainties. The precision of the base‐flow estimates was most correlated to percentage urban cover, whereas the precision of the event mean estimates was most correlated with catchment size. The method proposed in this work could be readily applied to other water quality variables and other monitoring sites. Copyright © 2014 John Wiley & Sons, Ltd.