Objective Probabilistic Forecasts of Future Climate Based on Jeffreys' Prior: the Case of Correlated Observables

TL;DR

This paper extends the use of Jeffreys' Prior for probabilistic climate forecasting to correlated observations, simplifying prior calculations for complex models by leveraging multivariate normal distributions.

Contribution

It derives explicit expressions for Jeffreys' Prior with correlated Gaussian observations, enabling easier incorporation of parameter uncertainty in climate forecasts.

Findings

Derived formulas for Jeffreys' Prior with correlated data

Simplified prior calculation reduces to mean differences

Applicable to complex climate models

Abstract

To include parameter uncertainty into probabilistic climate forecasts one must first specify a prior. We advocate the use of objective priors, and, in particular, the Jeffreys' Prior. In previous work we have derived expressions for the Jeffreys' Prior for the case in which the observations are independent and normally distributed. These expressions make the calculation of the prior much simpler than evaluation directly from the definition. In this paper, we now relax the independence assumption and derive expressions for the Jeffreys' Prior for the case in which the observations are distributed with a multivariate normal distribution with constant covariances. Again, these expressions simplify the calculation of the prior: in this case they reduce it to the calculation of the differences between the ensemble means of climate model ensembles based on different parameter settings. These calculations are simple enough to be applied to even the most complex climate models.