Anomaly time series

In the natural sciences, especially in atmospheric and Earth sciences involving applied statistics, an anomaly is the deviation in a quantity from its expected value, e.g., the difference between a measurement and a mean or a model prediction. Similarly, a standardized anomaly equals an anomaly divided by a standard deviation. A group of anomalies can be analyzed spatially, as a map, or temporally, as a time series. There are examples in atmospheric sciences and in geophysics.

The location and scale measures used in forming an anomaly time-series may either be constant or may themselves be a time series or a map. For example, if the original time series consisted of temperatures measured every hour, the effect of typical daily cycles of temperature might be remove by subtracting a time series containing mean temperature values for each hour of the day: clearly, this can be extended by including seasonal variations of temperature.

Robust statistics, resistant to the effects of outliers, are sometimes used as the basis of the transformation.

In the atmospheric sciences, the climatological annual cycle is often used as the mean value. Famous atmospheric anomalies are for instance the Southern Oscillation index (SOI) and the North Atlantic oscillation index. SOI is the atmospheric component of El Niño, while NAO plays an important role for European weather by modification of the exit of the Atlantic storm track.

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