title: A hierarchical bayesian model to quantify uncertainty of stream water temperature forecasts.
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.
authors.affiliation: INRA, UMR 0985 ESE Ecologie et Santé des Ecosystèmes, Rennes, France; Marine Institute, Oranmore, Ireland.
authors.forename: Guillaume
authors.initials: G
authors.lastname: Bal
authors.affiliation: Agrocampus Ouest, UMR 0985 ESE Ecologie et Santé des Ecosystèmes, Rennes, France.
authors.forename: Etienne
authors.initials: E
authors.lastname: Rivot
authors.affiliation: INRA, UMR 0985 ESE Ecologie et Santé des Ecosystèmes, Rennes, France.
authors.forename: Jean-Luc
authors.initials: JL
authors.lastname: Baglinière
authors.affiliation: Marine Institute, Oranmore, Ireland.
authors.forename: Jonathan
authors.initials: J
authors.lastname: White
authors.affiliation: INRA, UMR 1224 Ecobiop Ecologie Comportementale et Biologie des Populations de Poissons, Saint Pée sur Nivelle, France; Université de Pau et des Pays de l'Adour, UMR 1224 Ecobiop Ecologie Comportementale et Biologie des Populations de Poissons, Anglet, France.
authors.forename: Etienne
authors.initials: E
authors.lastname: Prévost
mesh_terms: D001499:Bayes Theorem; D055904:Meteorology / Q000379:methods; D012621:Seasons; D013696:Temperature; D035501:Uncertainty; D014872:Water Movements