Concepts, Philosophy and Methods for Development of a General Linear Statistical model for River Water Quality

The modelling of water quality is of considerable importance understanding how to intervene or manage the water quality output from catchments. Modelling methodologies exist from bottom up mechanistic models, through hybrid models to statistical models. Here we will describe a statistical modelling methodology which was developed for forecasting water quality in the Great Barrier Reef catchments using a general linear model in terms of the concepts, philosophy and methods. The conceptual model considers the pathways that exist for constituents (solutes and particulates) in the streamflow to be transported from the soil in the catchment to the stream (Fig. 1). These can be grouped into those flowing over the surface of the soil where there is an interchange between the soil and the surface soil, including exfiltration and flow coming into the stream via groundwater flow mainly as baseflow. The philosophy of this model is to create the most efficacious model using the least complex modelling framework with easily available data. Streamflow components of: the hourly streamflow (Q (m s)); hourly baseflow (q (m s)); the sum of Q minus the long-term mean flow (Q (m s)) were chosen to represent the flow components. Q represents a measure of the catchment condition prior to the flow, with negative values representing dry and positive values wet catchment conditions. The differentials of these flow components with time (t (s)) were calculated. The sign of the differentials represents the rising or falling limb of the hydrograph and the magnitude the rate of change. Integrals of Q, q and Qm were calculated for different lengths of times prior to the measurement time. Transforms of all these components with a power of 0.2 and 2 were calculated. Finally, two orthogonal periodic time-based components sin(2πt/86400P) and cos(2πt/86400P) with P = 365 day were calculated. These covariates are first filtered in a univariate way with the seven constituents: Total Suspended Solids (TSS), Particulate Nitrogen (PN), Dissolved Inorganic Nitrogen (DIN), Dissolved Organic Nitrogen (DON), Particulate Phosphorus (PP), Dissolved Inorganic Phosphorus (DIP) and Dissolved Organic Phosphorus (DOP). With the transforms, this results in 77 possible univariate relationships. These are filtered so only those with an r ≥ 0.1 are selected subsequent analysis using a multivariate additive general linear model. The fitting process also allows the constituent to be transformed and the best model selected with a maximum of five covariates. This process is semi-automated and can result in millions of possible models which reduced in a selection processes to give the model that best fits measured constituent data. The data was split so that validation could be attempted. This model can then be used along with the streamflow data to estimate the constituents in hindcast and forecast mode and uncertainty estimated