Likelihood function construction and Bayesian data fusion for analyzing cloud fraction data

Poster PDF

Description

Bayesian data analysis methodology has become popular in various fields, including climate science, for analyzing observed and modeled data, because it allows relaxed assumptions on the data distribution compared to the least squares approach, and because it outputs a probability density function called the posterior distribution. The posterior distribution is calculated from a prior distribution of the objective parameter under analysis, and a likelihood function, which may be regarded as a conditional distribution based on known data. This paper will discuss the construction of a likelihood function for cloud fraction observations derived from different instruments. In particular, ARSCL (Active Remotely-Sensed Clouds Locations) and TSI (Total Sky Imager) data over the ARM Southern Great Plains (SGP) site from 2001–2007 will be considered. It will be shown that the likelihood function can be modeled by a linear regression procedure and hence is a normally distributed function. However, the prior distribution of the cloud fraction is modeled by a two-parameter Beta distribution, due to the high frequencies of either near-complete coverage (overcast) or near-zero coverage (clear sky) of the clouds over the SGP. The posterior distribution yields not only the median value of the cloud fraction, but also the confidence set that quantifies the errors of merged data from multiple observational sources. The procedure has been applied to revise the cloud fraction data from CAM3 and hence to produce an approximation of a global cloud fraction climatology based on the fusion of the modeled and observed data by the Bayesian approach.