A mutual information criterion with applications to canonical correlation analysis and graphical models.

This paper derives a criterion for deciding conditional independence that is consistent with small-sample corrections of Akaike's information criterion but is easier to apply to such problems as selecting variables in canonical correlation analysis and selecting graphical models. The criterion reduces to mutual information when the assumed distribution equals the true distribution; hence, it is called mutual information criterion (MIC). Although small-sample Kullback-Leibler criteria for these selection problems have been proposed previously, some of which are not widely known, MIC is strikingly more direct to derive and apply.

Standard assessments of climate forecast skill can be misleading.

Assessments of climate forecast skill depend on choices made by the assessor. In this perspective, we use forecasts of the El Niño-Southern-Oscillation to outline the impact of bias-correction on skill. Many assessments of skill from hindcasts (past forecasts) are probably overestimates of attainable forecast skill because the hindcasts are informed by observations over the period assessed that would not be available to real forecasts. Differences between hindcast and forecast skill result from changes in model biases from the period used to form forecast anomalies to the period over which the forecast is made. The relative skill rankings of models can change between hindcast and forecast systems because different models have different changes in bias across periods.

Assessing probabilistic predictions of ENSO phase and intensity from the North American Multimodel Ensemble.

Here we examine the skill of three, five, and seven-category monthly ENSO probability forecasts (1982-2015) from single and multi-model ensemble integrations of the North American Multimodel Ensemble (NMME) project. Three-category forecasts are typical and provide probabilities for the ENSO phase (El Niño, La Niña or neutral). Additional forecast categories indicate the likelihood of ENSO conditions being weak, moderate or strong. The level of skill observed for differing numbers of forecast categories can help to determine the appropriate degree of forecast precision. However, the dependence of the skill score itself on the number of forecast categories must be taken into account. For reliable forecasts with same quality, the ranked probability skill score (RPSS) is fairly insensitive to the number of categories, while the logarithmic skill score (LSS) is an information measure and increases as categories are added. The ignorance skill score decreases to zero as forecast categories are added, regardless of skill level. For all models, forecast formats and skill scores, the northern spring predictability barrier explains much of the dependence of skill on target month and forecast lead. RPSS values for monthly ENSO forecasts show little dependence on the number of categories. However, the LSS of multimodel ensemble forecasts with five and seven categories show statistically significant advantages over the three-category forecasts for the targets and leads that are least affected by the spring predictability barrier. These findings indicate that current prediction systems are capable of providing more detailed probabilistic forecasts of ENSO phase and amplitude than are typically provided.

Decadal predictability without ocean dynamics.

This paper shows that the most predictable components of internal variability in coupled atmosphere-ocean models are remarkably similar to the most predictable components of climate models without interactive ocean dynamics (i.e., models whose ocean is represented by a 50-m-deep slab ocean mixed layer with no interactive currents). Furthermore, a linear regression model derived solely from dynamical model output can skillfully predict observed anomalies in these components at least a year or two in advance, indicating that these model-derived components and associated linear dynamics are realistic. These results suggest that interactive ocean circulation is not essential for the existence of multiyear predictability previously identified in coupled models and observations.