The Annals of Applied Statistics

Spatio-temporal assimilation of modelled catchment loads with monitoring data in the Great Barrier Reef

Daniel W. Gladish, Petra M. Kuhnert, Daniel E. Pagendam, Christopher K. Wikle, Rebecca Bartley, Ross D. Searle, Robin J. Ellis, Cameron Dougall, Ryan D. R. Turner, Stephen E. Lewis, Zoë T. Bainbridge, and Jon E. Brodie

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Soil erosion and sediment transport into waterways and the ocean can adversely affect water clarity, leading to the deterioration of marine ecosystems such as the iconic Great Barrier Reef (GBR) in Australia. Quantifying a sediment load and its associated uncertainty is an important task in delineating how changes in management practices can contribute to improvements in water quality, and therefore continued sustainability of the GBR. However, monitoring data are spatially (and often temporally) sparse, making load estimation complicated, particularly when there are lengthy periods between sampling or during peak flow periods of major events when samples cannot be safely taken.

We develop a spatio-temporal statistical model that is mechanistically motivated by a process-based deterministic model called Dynamic SedNet. The model is developed within a Bayesian hierarchical modelling framework that uses dimension reduction to accommodate seasonal and spatial patterns to assimilate monitored sediment concentration and flow data with output from Dynamic SedNet. The approach is applied in the Upper Burdekin catchment in Queensland, Australia, where we obtain daily estimates of sediment concentrations, stream discharge volumes and sediment loads at 411 spatial locations across 20 years. Our approach provides a method for assimilating both monitoring data and modelled output, providing a statistically rigorous method for quantifying uncertainty through space and time that was previously unavailable through process-based models.

Article information

Ann. Appl. Stat., Volume 10, Number 3 (2016), 1590-1618.

Received: June 2015
Revised: June 2016
First available in Project Euclid: 28 September 2016

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Zentralblatt MATH identifier

Water quality Bayesian hierarchical model SedNet catchment modelling spatio-temporal


Gladish, Daniel W.; Kuhnert, Petra M.; Pagendam, Daniel E.; Wikle, Christopher K.; Bartley, Rebecca; Searle, Ross D.; Ellis, Robin J.; Dougall, Cameron; Turner, Ryan D. R.; Lewis, Stephen E.; Bainbridge, Zoë T.; Brodie, Jon E. Spatio-temporal assimilation of modelled catchment loads with monitoring data in the Great Barrier Reef. Ann. Appl. Stat. 10 (2016), no. 3, 1590--1618. doi:10.1214/16-AOAS950.

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Supplemental materials

  • Supplement to “Spatio-temporal assimilation of modelled catchment loads with monitoring data in the Great Barrier Reef”. The supplementary material contains additional information related to the development and results of our model. We present figures for the available monitoring data described in Section 2. Additional posterior results not discussed in Section 4 are shown, including results for the dynamic parameters and covariate coefficients. Lastly, the details of the Markov Chain Monte Carlo algorithm are included.