An extended regression approach to estimating loads and their uncertainties in great barrier reef catchments

Abstract

There are n umerous load estimation methods available, some of w hich are captured in various online t ools. However, m ost estim ators are subject to large biases statistica lly, and t heir ass ociated uncertainties are often not rep orted. Th is makes in terpretation d ifficult an d th e estimatio n o f trend s o r determination of optimal sampling regimes impossible to assess. In this paper, we first propose two indices for measuring the extent of sampling bias, and then provide steps for o btaining reliable l oad estimates by minimizing t he bi ases an d making use of p ossible predictive variables. The load estimation procedure can be summarized by the following four steps. (i) output t he flow rat es at re gular t ime intervals (e. g.10 m inutes) using a t ime seri es model t hat captures all the peak flows; (ii) output the predicted flow rates as i n (i) at the concentration sampling times, if the corresponding flow rates are not collected; (iii) establish a predictive model for the concentration data, which incorporates all p ossible predictor variables and output the predicted concentrations at the regular time intervals as in (i); and (iv) obtain the sum of al l the products of the predicted flow and the predicted concentration over the regular time intervals to represent an estimate of the load. The key step to this approach is in th e development of an appropriate predictive model for concentration. This i s achi eved usi ng a ge neralized regression (rating-curve) a pproach wi th a dditional predictors t hat capture unique features in the flow data, namely the concept of the first flush, the location of the event on the hydrograph (e.g. rise or fall) and cumulative discounted flow. The latter may be thought of as a m easure of constituent e xhaustion occ urring during flood e vents. The m odel also has the ca pacity to accomm odate autocorrelation in model errors wh ich are t he result of intensive sampling during floods. Incorporating this additional in formation can sig nificantly i mprove th e pred ictability o f co ncentration, and u ltimately th e precision with which the pollutant load is estimated. We also provide a measure of the standard error of the load estimate which incorporates model, spatial and/or temporal errors. This method also has the capacity to incorporate measurement error incurred through the sampling of flow. We illustrate this approach using the concentrations of total suspended sediment (TSS) and nitrogen oxide (NOx) and gauged flow data from the Burdekin River, a catchm ent de livering to th e Great Barrier R eef. The sam pling biases for NO x concentrations range from 2 to 10 times indicating severe biases. As we expect, the traditional average and extrapolation methods produce much higher estimates than those when bias in sampling is taken into account. Show more