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.

Shallow groundwater thermal sensitivity to climate change and land cover disturbances: derivation of analytical expressions and implications for stream temperature modeling

“…where λ is the bulk thermal conductivity of the soil-water matrix (W m −1 • C −1 ), T is the temperature at any point in space or time ( • C), z is the depth below the surface (m; down is positive and the land surface occurs at z = 0), q is the vertical Darcy flux (m s −1 ; down is positive), c w ρ w is the volumetric heat capacity of pure water (4.18 × 10 6 J m −3 • C −1 ; Bonan, 2008), t is time (s), and cρ is the bulk volumetric heat capacity of the soil-water matrix (J m −3 • C −1 ). The first term on the left of Eq.…”

“…In fact, small streams are generally very dependent on groundwater inputs and temperatures, and their low thermal capacity (shallow depth and volume) makes them very vulnerable to any surface or subsurface-energy flux modifications (e.g., Matheswaran et al, 2014). This has been shown in many timber harvesting studies, where the smallest streams have experienced the greatest increase in stream temperature following forest removal (e.g., Brown and Krygier, 1970). Thus, quantifying future changes in shallow groundwater flow and temperatures is essential for a better understanding of the future thermal regimes of groundwater-dominated rivers and associated impacts to aquatic organisms (Kanno et al, 2014).…”

Effect of food shortage and temperature on age 0+ salmonids: a contribution to predict the effects of climate change

“…In the context of climate change, an increase of 3·2° C in air temperature will produce a moderate but sensible increase in stream water temperature from 1 to 2° C (Bal et al, ). Present results suggest that this may cause higher mortality rates during the critical period of emergence, especially when in conjunction with food shortage which is not a rare event in the wild (Kennedy et al, ).…”

Advantages and insights from a hierarchical Bayesian growth and dynamics model based on salmonid electrofishing removal data

“…The approach we used has the advantage of telling about the direction of the poor fits (under-and over-estimates) while the χ 2 statistic allows to measure the fit at different scales (by summing the χ 2 statistics, e.g., over size classes to get a measure at the survey level). A χ 2 type statistic can also be used to measure model fit for a wider range of models (Gelman et al, 2004;Ntzoufras, 2009;Bal et al, 2014). We did not use the deviance statistic as a metric for model fit (Ntzoufras, 2009) either, due to the externalized computations it requires in the case of a model with multiple error terms in the survey layer (in our case: Poisson and binomial).…”