Box 3.4: Defining the Circulation Indices A teleconnection is made up of a fixed spatial pattern with an associated index time series showing the evolution of its amplitude and phase. Teleconnections are best defined by values over a grid but it is often convenient to devise simplified indices based on key station values. A classic example is the Southern Oscillation (SO), encompassing the entire tropical Pacific, yet encapsulated by a simple SO Index (SOI), based on differences between Tahiti (eastern Pacific) and Darwin (western Pacific) MSLP anomalies. A number of teleconnections have historically been defined from either station data (SOI, NAO) or from gridded fields (NAM, SAM, PDO/NPI and PNA): Southern Oscillation Index (SOI). The MSLP anomaly difference of Tahiti minus Darwin, normalised by the long-term mean and standard deviation of the MSLP difference (Troup, 1965; Können et al., 1998). Available from the 1860s. Darwin can be used alone, as its data are more consistent than Tahiti prior to 1935. North Atlantic Oscillation (NAO) Index. The difference of normalised MSLP anomalies between Lisbon, Portugal and Stykkisholmur, Iceland has become the most widely used NAO index and extends back in time to 1864 (Hurrell, 1995), and to 1821 if Reykjavik is used instead of Stykkisholmur and Gibraltar instead of Lisbon (Jones et al., 1997). Northern Annular Mode (NAM) Index. The amplitude of the pattern defined by the leading empirical orthogonal function of winter monthly mean NH MSLP anomalies poleward of 20°N (Thompson and Wallace, 1998, 2000). The NAM has also been known as the Arctic Oscillation (AO), and is closely related to the NAO. Southern Annular Mode (SAM) Index. The difference in average MSLP between SH middle and high latitudes (usually 45°S and 65°S), from gridded or station data (Gong and Wang, 1999; Marshall, 2003), or the amplitude of the leading empirical orthogonal function of monthly mean SH 850 hPa height poleward of 20°S (Thompson and Wallace, 2000). Formerly known as the Antarctic Oscillation (AAO) or High Latitude Mode (HLM). Pacific-North American pattern (PNA) Index. The mean of normalised 500 hPa height anomalies at 20°N, 160°W and 55°N, 115°W minus those at 45°N, 165°W and 30°N, 85°W (Wallace and Gutzler, 1981). Pacific Decadal Oscillation (PDO) Index and North Pacific Index (NPI). The NPI is the average MSLP anomaly in the Aleutian Low over the Gulf of Alaska (30°N–65°N, 160°E–140°W; Trenberth and Hurrell, 1994) and is an index of the PDO, which is also defined as the pattern and time series of the first empirical orthogonal function of SST over the North Pacific north of 20°N (Mantua et al., 1997; Deser et al., 2004). The PDO broadened to cover the whole Pacific Basin is known as the Inter-decadal Pacific Oscillation (IPO: Power et al., 1999b). The PDO and IPO exhibit virtually identical temporal evolution (Folland et al., 2002).