San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

A Cyclic Pattern in the North Atlantic
Oscillation Index and Its Correspondence
With Average Global Temperature

Elsewhere there was found a correspondence between a cyclic pattern in the Pacific (Multi)Decadal Oscillation Index and the Average Global Temperature, shown below. It is natural therefore to look for a similar correspondence of the cycle in average global temperature with the North Atlantic Oscillation.

The North Atlantic Oscillation

The weather pattern called the North Atlantic Oscillation was identified by Sir Gilbert Walker in the 1920's. The theory asserts, at least in the way it is usually presented and explained, that there are two meteorological states for the North Atlantic. These states are a bit persistent once in place but eventually the condition switches. The primary characteristics of the states are the sea surface temperature (SST) and the magnitude of the pressure difference between the Azores area and the Iceland area. These states can be referred to as warmer and cooler.

In the cooler phase, often denoted as NAO+, there is a high pressure system located near the Azores Islands and a low pressure system over Iceland. The low pressure system over Iceland has winds flowing counterclockwise around it. The high pressure system over the Azores has winds flowing clockwise. Thus the wind coming into the North Atlantic from the west gets accelerated by the pair of rollers situated over Iceland and the Azores. According to the theory, when this state prevails the wind from the west blows strongly directly across the Atlantic Ocean. This state is one of cooler SST's and a higher differential pressure.

The winds pick up heat even from the ocean in its cooler state and carry it across northern Europe and Asia. Continental temperatures to the east are raised as a consequence. This makes for milder, wetter winters there. To the west in northern Canada and Greenland the winters are colder and drier. To the south in the eastern United States the winters are mild and wet.

In the summers for the NAO+ the strong westerlies are cooled by their passage over the Atlantic and thus summers in northern Europe are cooler.

When SST's are warmer and the pressure is not so high in the south and/or not so low over Iceland the winds from the west are not constrained from continuing on their natural trajectory to the southeast. Their movement toward the equator results in their slowing down due to the Coriolis Effect. In this meteorological configuration the winds are not bringing heat and moisture to northern Europe and Asia. The winters are then colder and drier and the summers hotter. In their southeasterly trajectory the winds from the west then bring warmer temperatures and more rain to the Mediterranean Basin and the Middle East.

The Index of the North Atlantic Oscillation

The North Atlantic Oscillation Index is the difference between the normalized sea level pressures at the Ponta Delgada station in the Azores Islands and the station at Stykkisholmur at Reykjavik, Iceland. The monthly values of the index are available from January of 1865. The data set used in the following analysis is limited to the end of 2002.

The values of the annual average of the monthly values are given in the graph below.

There is so much variation between years that it is difficult to see any pattern at all. Taking a three-year moving average helps somewhat in identifying a cyclicity.

An eight-year moving average reveals something of a cyclic pattern.

A bent line fits the eight-year moving average data reasonably well, as shown below.

The coefficient of determination for this regression is 0.75. All of the regression coefficients are statistically significant at the 95 percent level of confidence; i.e., the t-ratios are greater than 2 in magnitude. (They range from 3.4 to 9.6.)

The bend-points, the years in which the index switches direction, were chosen to maximize the coefficient of determination for the regression. These years were: 1876, 1921, 1954, 1966 and 1993. This means the first full episode of an increasing NAO index lasted from 1876 to 1921, a period of 45 years. The episode of decreasing indices was from 1921 to 1966, a period of 45 years. The next period of increasing indices lasted only from 1966 to 1993, a period of only 27 years. This suggests that the turning point for 1993 is probably not valid.

The episodes of an increasing NAO index have approximately the same slopes. The episodes of downwards slopes are more difficult to compare because of the bend in the middle of the major episode of a declining index. A regression without the bend in the declining index was fitted and the result is below.

The coefficient of determination for this regression is 0.67, a significant drop from the 0.75 of the previous regression.

The equality of the slopes is close enough to make it worthwhile to estimate a bent-line regression in which the corresponding slopes are constrained to be equal. The result is:

The coefficient of determination drops a bit for this constrained regression; it is 0.645. The t-ratios for the coefficients are high; -11.6 for the downslopes and 14.1 for the upslopes.

A comparison of the regression line for a cycle of the moving average of the index with the annual values of the index is of interest.

The Trend and Cycle in Global Average Temperature

The turning point years for the cyclic pattern in global average temperature were 1916, 1937, 1971 and 2005. There was probably a turning point year in 1884 which was missed because the data set from the National Oceanic and Atmospheric Administration (NOAA) started only in 1880. The dates were chosen to maximize the coefficient of determination (R²) for the regression function shown below.

The value of the coefficient of determination for this regression is 0.88.

The period of the upswings and the period of the downswings for global average temperature are both about thirty years. The corresponding period for the North Atlantic Oscillation appears to be about 45 years. Generally the two cycles do not correspond but when the turning points are close together the turning point for the NAO is later than the turning point for global temperature. Thus if there were to be a causal relationship between the two phenomena it would be that the turning of the NAO cycle was an effect of the turning of the temperature cycle. However the purpose of the analysis was to find other phenomena which would account for the fact that the average global temperature cycle does not exactly correspond to the Pacific (Multi)Decadal Oscillation. The North Atlantic Oscillation could well be an influence that perturbs the pattern which the North Pacific has on global temperature. The El Niño Southern (Pacific) Oscillation (ENSO) is clearly one such perturbation.


The North Atlantic Decadal Oscillation appears to have a weak cyclic pattern but with so much unexplainable variation that it is difficult to perceive this cycle. The cycle shows up in terms of a moving average. The timing of the turning points in comparison to the turning points for the global average temperature indicates that the North Atlantic Oscillation could be an effect of the cycle in global temperatures rather than a cause of it. On the other hand, the NAO could be lesser influence modifying the effect of the Pacific (Multi)Decadal Oscillation just as the El Niño Southern Oscillation is.

HOME PAGE OF applet-magic
HOME PAGE OF Thayer Watkins