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 due to financial constraints and therefore many studies have relied on simulation based methods utilising 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 characterising 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 is 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. Using total phosphorus data from 17 subcatchments in south-eastern Australia, the ability of a model-based approach to estimate the effect of sample size on the precision of mean concentrations is examined. The effect of sample size on the precision of the mean estimate is examined for base and event-flow conditions. The effect of catchment characteristics on the precision of the mean estimates was also examined. 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 while 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. This article is protected by copyright. All rights reserved.