A synthesis of the time-scale variability of commonly used climate indices using continuous wavelet transform

Climate indices are commonly used as indicators of climate variations and very often compared to those of environmental processes (geophysical, hydrological, ecological, etc.) in order to understand them in terms of regional- to global-scale fluctuations. Through their use in many research fields and published works, it appears that (sometimes not so) slight differences may exist in the identification of the characteristic time-scales governing the temporal variations of those indices from one work to another, and one eventually may experience difficulties in finding a “unified” referencing of these typical scales of variability. For this purpose, we propose a synthetic description and quantification of the time-scale variability of some of the most commonly used climate indices: the Atlantic Multidecadal Oscillation (AMO), the North Atlantic Oscillation (NAO), the Northern Annular Mode (NAM), the Pacific Decadal Oscillation (PDO), the Southern Oscillation Index (SOI) and the Pacific–North-America teleconnection (PNA); which was performed using a single unified methodology, i.e. continuous wavelet analysis, adapted to the study of stochastic processes that exhibit time-varying statistical characteristics.Each climate index presents its own characteristic time-scales, from inter-annual to multi-decadal scales. However, some energy bands present common characteristics in terms of frequency (or time-scale) ranges and/or temporal occurrence, from inter-annual scale (a group of 2–4 y, 3–6 y and 4–8 y fluctuations), to (pluri-)decadal scale (a group of 5–12 y, 8–16 y, 12–20 y and 17–30 y fluctuations) and in the long term (a group of 20–50 y, 40–60 y and 50–80 y fluctuations). Moreover, a common structuration for all climate indices seems to appear in the form of an inter-annual scale structuration in 1930, and a global shift in the frequency structuration of all climate indices in 1970 affecting decadal and pluri-decadal scales.Analysis of the distribution of the total variance of climate indices over time highlights different periods of high/low variability according to each index. However, a common distribution could also be observed for all climate indices, suggesting a more or less “connected” evolution (i.e. shared by all indices) of the total variance over time. At a global scale (i.e. averaging of the AMO, PDO, SOI and NAO), evolution of the total variance was evaluated for the 1900–2009 period and indicates the same periods of high/low variability: the 1930–1960 and 1980–2000 periods correspond to the periods of maximum variance, with maxima observed around 1940 and in particular in 1990; and the 1960–1980 period corresponds to a period of lower variance, centered around 1970. These 1970's changes, both in the total variance (which marks a notable increase of total variability) and in frequency changes observed in all climate indices, definitely constitute a major and global shift in the climate system observed in several other indicators over the world.

► We propose a synthetic description of the time-scale variability of the most used climate indices.
► Description of these time-scales was performed using a single unified methodology, i.e. continuous wavelets analysis.
► Although each climate index presents its own characteristic time-scales, some energy bands present common characteristics.
► A common distribution of the total variance (periods of high/low variability) is observed for all climate indices.
► A global shift in the frequency structuration and total variance of all climate indices is detected in 1970.