Bayesian analysis for uncertainty estimation of a canopy transpiration model

Abstract

A Bayesian approach was used to fit a conceptual transpiration model to half‐hourly transpiration rates for a sugar maple (Acer saccharum) stand collected over a 5‐month period and probabilistically estimate its parameter and prediction uncertainties. The model used the Penman‐Monteith equation with the Jarvis model for canopy conductance. This deterministic model was extended by adding a normally distributed error term. This extension enabled using Markov chain Monte Carlo simulations to sample the posterior parameter distributions. The residuals revealed approximate conformance to the assumption of normally distributed errors. However, minor systematic structures in the residuals at fine timescales suggested model changes that would potentially improve the modeling of transpiration. Results also indicated considerable uncertainties in the parameter and transpiration estimates. This simple methodology of uncertainty analysis would facilitate the deductive step during the development cycle of deterministic conceptual models by accounting for these uncertainties while drawing inferences from data.