Preprints
https://doi.org/10.5194/hess-2021-296
https://doi.org/10.5194/hess-2021-296

  02 Jun 2021

02 Jun 2021

Review status: this preprint is currently under review for the journal HESS.

Spatially Referenced Bayesian State-Space Model of Total Phosphorus in western Lake Erie

Timothy Maguire1, Craig Stow2, and Casey Godwin1 Timothy Maguire et al.
  • 1Cooperative Institute for Great Lakes Research, School for Environment and Sustainability, University of Michigan, Ann Arbor, Michigan 48109, United States
  • 2NOAA Great Lakes Environmental Research Laboratory, Ann Arbor, Michigan, 48108, United States

Abstract. Collecting water quality data across large lakes is often done under regulatory mandate, however it is difficult to connect nutrient concentration observations to sources of those nutrients and to quantify this relationship. This difficulty arises from the spatial and temporal separation between observations, the impact of hydrodynamic forces, and the cost involved in discrete samples collected aboard vessels. These challenges are typified in Lake Erie, where binational agreements regulate riverine loads of total phosphorus (TP) to address the impacts from annual harmful algal blooms (HABs). While it is known that the Maumee River supplies 50 % of the nutrient load to Lake Erie, the details of how the Maumee River TP load changes Lake Erie TP concentration have not been demonstrated. We developed a hierarchical spatially referenced Bayesian state-space model with an adjacency matrix defined by surface currents. This was applied to a 2 km-by-2 km grid of nodes, to which observed lake and river TP concentrations were joined. The model generated posterior samples describing the unobserved nodes and observed nodes on unobserved days. We quantified the impact plume of the Maumee River by experimentally changing concentration data and tracking the change of in-lake predictions. Our impact plume represents the spatial and temporal variation of how river concentrations correlate with lake concentrations. We used the impact plume to scale the Maumee River spring TP load to an effective Maumee River TP spring load for each node in the lake. By assigning an effective load to each node the relationship between load and concentration is consistent throughout our sampling locations. A linear model of annual lake node mean TP concentration and effective Maumee River load estimated that in the absence of the Maumee River load lake concentrations at the sampled nodes would be 23.1 µg l−1 (±1.75, 95 % credible interval, CI) and that for each 100 tons of spring TP effective load delivered to Lake Erie, mean TP concentrations increase by 11 µg l−1 (±1, 95 % CI). Our proposed modelling technique allowed us to establish these quantitative connections between Maumee TP load and Lake Erie TP concentrations which otherwise would be masked by the movement of water through space and time.

Timothy Maguire et al.

Status: open (until 28 Jul 2021)

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Timothy Maguire et al.

Model code and software

Spatially Referenced Bayesian State-Space Model of Total Phosphorus in western Lake Erie Maguire, Timothy; Stow, Craig; Godwin, Casey https://doi.org/10.5281/zenodo.4884997

Video supplement

Impact of the Maumee River through Time Maguire, Timothy; Stow, Craig; Godwin, Casey https://doi.org/10.5446/53429

Timothy Maguire et al.

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Short summary
Water within large waterbodies is constantly moving. Consequently, water movement masks causal relationships that exist between rivers and lakes. Incorporating water movement in models of nutrient concentration allows us to predict concentrations at unobserved locations and at observed locations on days not sampled. Our modelling approach does this while accommodating nutrient concentration data from multiple sources and provides a way to experimentally define the impact of rivers on lakes.