Using reliability diagrams to interpret the ‘signal-to-noise paradox’ in
seasonal forecasts of the winter North Atlantic Oscilation
Abstract
The ‘signal-to-noise paradox’ for seasonal forecasts of the winter NAO
is often described as an ‘underconfident’ forecast and measured using
the ratio-of-predictable components metric (RPC). However, comparison of
RPC with other measures of forecast confidence, such as spread-error
ratios, can give conflicting impressions, challenging this informal
description. We show, using a linear statistical model, that the
‘paradox’ is equivalent to a situation where the reliability diagram of
any percentile forecast has a slope exceeding 1. The relationship with
spread-error ratios is shown to be far less direct. We furthermore
compute reliability diagrams of winter NAO forecasts using seasonal
hindcasts from the European Centre for Medium-range Weather Forecasts
and the UK Meteorological Office. While these broadly exhibit slopes
exceeding 1, there is evidence of asymmetry between upper and lower
terciles, indicating a potential violation of linearity/Gaussianity. The
limitations and benefits of reliability diagrams as a diagnostic tool
are discussed.