Bayesian uncertainty analyses of great barrier reef catchment water quality model parameters without likelihood assumptions

Abstract

Catchment water quality modelling is used as part of the Paddock to Reef program to assess the impact of land management changes across the Great Barrier Reef (GBR) catchments against water quality targets. It is necessary to have confidence in model performance in order to use them effectively for management and decision-making. Thus calibration, uncertainty and sensitivity analyses of model parameters are critical to optimise their predictive capability and thereby help facilitate better targeting of improved management practices. Average annual loads estimated at end-of-systems (EOS) sites are likely to represent cumulative effects of various water quality processes. As a result, the calibration and uncertainty analyses of model parameters becomes a challenge. Employed together, adaptive Sequential Monte Carlo sampled Approximate Bayesian Computation (SMC-ABC) and machine learning trained surrogate models offer an efficient framework for the calibration and uncertainty analyses of water quality model parameters. The appealing feature of Approximate Bayesian Computation when compared to formal Bayesian analysis is that it overcomes the requirement for an explicit likelihood function. As a compromise, an empirical approach is employed to stochastically sample from the unknown likelihood. This process can be computationally expensive when samples require the evaluation of a numerical models such as a catchment water quality model. To overcome this burden, machine learning techniques can be used to synthesise and train an efficient surrogate model to substitute for the functionality of the primitive model in the ABC algorithm. This paper demonstrates the application of this combination of technologies for the calibration and uncertainty analyses of parameters that represent the transport of fine-sediment and particulate nutrients in two GBR basins namely the Pioneer River and Sandy Creek basins. The comparison between fine-sediment streambank erosion estimated by the selected model along the O'Connell River between 2010 and 2014 against that estimated by the O'Connell River stability assessment (ORSA) was encouraging. Estimate by the selected calibrated model was only 1.6% greater than the ORSA estimate. Average annual fine-sediment and particulate nutrient loads estimated by the calibrated model at the Pioneer River EOS site were within +/-9% of that estimated by the GBR catchment loads monitoring program (GBRCLMP). Average annual fine-sediment and particulate nutrient loads estimated by the calibrated model at Sandy Creek EOS site are within +/-3% of that estimated by GBRCLMP. Analysis of model parameter uncertainty reveals that all GBRCLMP estimated average annual constituent loads lie within the 95% credibility intervals of the modelled data. This work demonstrates that employed together, SMC-ABC and machine learning trained surrogate models offer an efficient and powerful framework for the calibration and uncertainty analyses of GBR water catchment quality model parameters.