On the Statistical Estimation of Asymmetrical Relationship Between Two Climate Variables

• Published in: Geophysical research letters Vol. 49; no. 20
• Main Authors: Frankignoul, Claude, Kwon, Young‐Oh
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 28.10.2022; American Geophysical Union
• Subjects: Asymmetry; asymmetry and composite analysis; Climate; Climate change; Climate variability; Climatic analysis; Dependent variables; El Nino; El Nino phenomena; ENSO asymmetry; Environmental Sciences; Estimates; Independent variables; La Nina; Mathematical analysis; ocean/atmosphere interactions; Regression; Sea level; Sea level pressure; Sea surface; Sea surface temperature; Statistical analysis; Surface temperature; Winter
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2022GL100777

Two simple methods commonly used to detect asymmetry in climate research, composite analysis, and asymmetric linear regression, are discussed and compared using mathematical derivation and synthetic data. Asymmetric regression is shown to provide unbiased estimates only when the respective mean of positive and negative events is removed from both independent and dependent variables (i.e., non‐zero y‐intercepts). Composite analysis always provides biased results and strongly underestimates the asymmetry, albeit less so for very larger thresholds, which cannot be used with limited observational data. Hence, the unbiased asymmetric regression should be used, even though uncertainties can be large for small samples. Differences in estimated asymmetry are illustrated for the sea surface temperature and winter sea level pressure signals associated with El Niño and La Niña. Plain Language Summary There is increasing evidence of asymmetry in climate variability so that the response to a positive event may not always be opposite to that of a negative event. The most common method to estimate such asymmetry is by compositing sufficiently large positive and negative events. We demonstrate that composites are always biased and underestimate asymmetry, albeit less so for large threshold. Unbiased estimates can be obtained by separate regressions on positive and negative events provided their respective mean is removed. This is illustrated with synthetic data and an application to El Niño and La Niña sea surface temperature signals and winter sea level pressure teleconnections to extratropical latitudes. Key Points Composite analysis is biased and always underestimates climate variable asymmetry Asymmetric linear regression provides unbiased estimates if the mean of positive and negative events are removed (non‐zero intercepts)