final_program_abstracts[1]

11 IMSC Session Program
A relaxes Bayesian approach to climate projection and
attribution
Thursday - Parallel Session 6
Stephen S. Leroy, Yi Huang and Richard M. Goody
We will present an approach to climate projection and climate signal detection and
attribution that is based in Bayesian statistics. It is derived in the same fashion as the
equations of optimal detection but without the assumptions of a prior separable in
signal shape and signal trend and of uninformed signal trend. In it, a probability
density function is formed in the space of observed variables and predicted variables
from an ensemble of runs of a climate model that spans both a historical period and a
future period. Every model is equally weighted, and only a single realization of each
model is included. This way, the joint PDF includes the uncertainties introduced by
natural variability and model uncertainty. Then, by inserting data into the data
variables in the PDF, the section in the space of the prediction variables is the
posterior PDF for climate projection. The normalization constant for the posterior
PDF is the joint probability of the ensemble of climate models used to formulate the
PDF and the data, a quantity that can be used to test the ensemble of climate models.
A hypothesis testing approach to attribution is obtained when the joint probabilities of
ensemble and data are determined using (1) an ensemble of “all” climate forcings is
generated for the historical variables, and (2) and ensemble of “natural” climate
forcings is generated for the historical variables.
We apply the method to 20 th century surface air temperature using the CMIP3
ensemble. The data vector contains historical trends in eight different regions. The
prediction vector contains the evolution of temperature change for a particular region
over the coming century. Because of the limited number of independent models that
contributed to CMIP3, it is valid to approximate the joint prior distribution as normal.
The resulting equations require the inversion of the covariance matrix in the space of
the data variables only, and this matrix is ill-determined because of the paucity of
models used to construct it. Consequently, only two eigenmodes are permitted in
decomposition according to the North criterion, and four are permitted using a
statistical F-test on the post-fit residuals. Our effort points toward the need to use a
perturbed physics ensemble of runs of a climate model because they typically provide
far more independent runs, historical and prediction, than an ensemble of bestjudgment
climate model runs.
Abstracts 262