  A Model Intercomparison Project (MIP) consists of teams who each estimate the
same underlying quantity (e.g., temperature projections to the year 2070), and
the spread of the estimates indicates their uncertainty. It recognizes that a
community of scientists will not agree completely but that there is value in
looking for a consensus and information in the range of disagreement. A simple
average of the teams' outputs gives a consensus estimate, but it does not
recognize that some outputs are more variable than others. Statistical analysis
of variance (ANOVA) models offer a way to obtain a weighted consensus estimate
of outputs with a variance that is the smallest possible and hence the tightest
possible 'one-sigma' and 'two-sigma' intervals. Modulo dependence between MIP
outputs, the ANOVA approach weights a team's output inversely proportional to
its variation. When external verification data are available for evaluating the
fidelity of each MIP output, ANOVA weights can also provide a prior
distribution for Bayesian Model Averaging to yield a consensus estimate. We use
a MIP of carbon dioxide flux inversions to illustrate the ANOVA-based weighting
and subsequent consensus inferences.
