A Bayesian approach to integrate satellite-estimated instantaneous photosynthetically active radiation product for daily value calculation

Abstract

Most terrestrial ecology models need daily incident photosynthetically active radiation (PAR) values, but only instantaneous PAR values are directly derivable from remotely sensed data. The conventional interpolation/integration method for estimating daily PAR from instantaneous values is not an optimal choice when only sparsely spaced instantaneous PAR is available. In this study, a method of ratio (MOR) is developed as an alternative, which is proved to provide a more accurate PAR estimation than the interpolation/integration method when the time interval between adjacent instantaneous PAR increases to 3-4 h. Furthermore, a Bayesian MOR is developed to combine the information from instantaneous PAR and existing knowledge of a given location to provide probabilistic estimation of daily PAR based on posterior distribution. The Bayesian MOR models a day's full set of actual-to-maximum instantaneous PAR ratios as a population from a normal process, and it is configured to estimate the joint posterior distribution of the population's mean and variance. The inference of daily PAR is carried out through Monte Carlo simulations based on the joint posterior distribution. Applications to both synthesized ground measurement data and MODIS (Moderate Resolution Imaging Spectroradiometer) derived instantaneous PAR at six Surface Radiation network (SURFRAD) sites demonstrate that the 90% confidence interval inferred from Bayesian MOR successfully includes the actual daily PAR values. Furthermore, sensitivity study demonstrates that sensible changes in prior distribution only have insignificant impacts on the estimation accuracy of daily PAR based on posterior distribution. Copyright 2011 by the American Geophysical Union.