The Atlantic Multi-decadal Oscillation (AMO) has been identified as a coherent mode of natural variability occurring in the North Atlantic Ocean with an estimated period of 60-80 years. It is based upon the average anomalies of sea surface temperatures (SST) in the North Atlantic basin, typically over 0-80N. To remove the climate change signal from the AMO index, users typically detrend the SST data at each gridpoint or detrend the spatially averaged timeseries. Trenberth and Shea (2006) recommend detrending each grid point based on the global mean SST timeseries, prior to taking the spatial average.
The following was contributed by Dr. Kevin Trenberth, August, 2015:
The increasing human influence on climate, mainly through changes in atmospheric composition, produce global warming. Many variables and climate indices are therefore influenced by associated climate changes and any analysis of variance can be dominated by the recent trends. It is therefore desirable to remove the trends to examine the underlying variability and associated patterns. One approach has been to fit a linear trend to a time series of an index, but this is a seriously flawed procedure because (i) it depends on the length of the time series; (ii) it implies the trend goes on indefinitely into the future and into the past; and (iii) there is no such trend evident in the earlier part of the 20th Century. A relatively simple approach instead is to use the global mean time series as a primary indicator of the non-stationary component, and remove that from each grid point prior to carrying out an analysis. This approach has been shown to work effectively by using model results, where the cause of the non-stationarity is known. A good example is the AMO, which is based on an index of area average SST over the North Atlantic from 0 to 60N (see Trenberth and Shea (2006)). The PDO is also derived from SSTs where the global mean has been removed, and a determination of the first mode of variability for 20-70N over the North Pacific (see Trenberth and Fasullo (2013)).##
Trenberth, Kevin & National Center for Atmospheric Research Staff (Eds). Last modified 06 Jan 2016. "The Climate Data Guide: Atlantic Multi-decadal Oscillation (AMO)." Retrieved from https://climatedataguide.ucar.edu/climate-data/atlantic-multi-decadal-oscillation-amo.