A hierarchical bayesian model to quantify uncertainty of stream water temperature forecasts

PLoS One. 2014 Dec 26;9(12):e115659. doi: 10.1371/journal.pone.0115659. eCollection 2014.

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Bayes Theorem
  • Meteorology / methods
  • Seasons
  • Temperature*
  • Uncertainty*
  • Water Movements*

Grants and funding

This research was performed while Dr. Guillaume Bal was a Ph.D. student sponsored by the French Ministry of Education and Research. A grant from the French Ministry of Ecology and Sustainable Development ‘Programme GICC2: Gestion et Impact du Changement Climatique’ also supported this study. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.