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A Hierarchical Bayesian Model to Quantify Uncertainty of Stream Water Temperature Forecasts

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  • Guillaume Bal
  • Etienne Rivot
  • Jean-Luc Baglinière
  • Jonathan White
  • Etienne Prévost

Abstract

Providing generic and cost effective modelling approaches to reconstruct and forecast freshwater temperature using predictors as air temperature and water discharge is a prerequisite to understanding ecological processes underlying the impact of water temperature and of global warming on continental aquatic ecosystems. Using air temperature as a simple linear predictor of water temperature can lead to significant bias in forecasts as it does not disentangle seasonality and long term trends in the signal. Here, we develop an alternative approach based on hierarchical Bayesian statistical time series modelling of water temperature, air temperature and water discharge using seasonal sinusoidal periodic signals and time varying means and amplitudes. Fitting and forecasting performances of this approach are compared with that of simple linear regression between water and air temperatures using i) an emotive simulated example, ii) application to three French coastal streams with contrasting bio-geographical conditions and sizes. The time series modelling approach better fit data and does not exhibit forecasting bias in long term trends contrary to the linear regression. This new model also allows for more accurate forecasts of water temperature than linear regression together with a fair assessment of the uncertainty around forecasting. Warming of water temperature forecast by our hierarchical Bayesian model was slower and more uncertain than that expected with the classical regression approach. These new forecasts are in a form that is readily usable in further ecological analyses and will allow weighting of outcomes from different scenarios to manage climate change impacts on freshwater wildlife.

Suggested Citation

  • Guillaume Bal & Etienne Rivot & Jean-Luc Baglinière & Jonathan White & Etienne Prévost, 2014. "A Hierarchical Bayesian Model to Quantify Uncertainty of Stream Water Temperature Forecasts," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-24, December.
  • Handle: RePEc:plo:pone00:0115659
    DOI: 10.1371/journal.pone.0115659
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    References listed on IDEAS

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    1. Camille Parmesan & Gary Yohe, 2003. "A globally coherent fingerprint of climate change impacts across natural systems," Nature, Nature, vol. 421(6918), pages 37-42, January.
    2. Gian-Reto Walther & Eric Post & Peter Convey & Annette Menzel & Camille Parmesan & Trevor J. C. Beebee & Jean-Marc Fromentin & Ove Hoegh-Guldberg & Franz Bairlein, 2002. "Ecological responses to recent climate change," Nature, Nature, vol. 416(6879), pages 389-395, March.
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    Cited by:

    1. Laplanche, Christophe & Leunda, Pedro M. & Boithias, Laurie & Ardaíz, José & Juanes, Francis, 2019. "Advantages and insights from a hierarchical Bayesian growth and dynamics model based on salmonid electrofishing removal data," Ecological Modelling, Elsevier, vol. 392(C), pages 8-21.
    2. Puwasala Gamakumara & Edgar Santos-Fernandez & Priyanga Dilini Talagala & Rob J Hyndman & Kerrie Mengersen & Catherine Leigh, 2023. "Conditional Normalization in Time Series Analysis," Monash Econometrics and Business Statistics Working Papers 10/23, Monash University, Department of Econometrics and Business Statistics.
    3. Santos-Fernandez, Edgar & Ver Hoef, Jay M. & Peterson, Erin E. & McGree, James & Isaak, Daniel J. & Mengersen, Kerrie, 2022. "Bayesian spatio-temporal models for stream networks," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).

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