  Remote sensing data products often include quality flags that inform users
whether the associated observations are of good, acceptable or unreliable
qualities. However, such information on data fidelity is not considered in
remote sensing data analyses. Motivated by observations from the Atmospheric
Infrared Sounder (AIRS) instrument on board NASA's Aqua satellite, we propose a
latent variable co-kriging model with separable Gaussian processes to analyze
large quality-flagged remote sensing data sets together with their associated
quality information. We augment the posterior distribution by an imputation
mechanism to decompose large covariance matrices into separate computationally
efficient components taking advantage of their input structure. Within the
augmented posterior, we develop a Markov chain Monte Carlo (MCMC) procedure
that mostly consists of direct simulations from conditional distributions. In
addition, we propose a computationally efficient recursive prediction
procedure. We apply the proposed method to air temperature data from the AIRS
instrument. We show that incorporating quality flag information in our proposed
model substantially improves the prediction performance compared to models that
do not account for quality flags.
