3.1 Mean patterns and changing frequencies of occurrence
The characteristic patterns in 500 hPa height anomalies across the domain for all months are displayed in the master SOM matrix (Fig. 1 ). Adjacent nodes are most similar to each other while those farthest apart are most dissimilar. Nodes along the edges of the matrix, and especially in the corners, occur most frequently. The percentages of winter (JFM) and summer (JAS) days belonging in each node are indicated over each map in the matrix. Winter days are more likely to exhibit patterns with large height contrasts, while summer days are fairly evenly distributed across the SOM.
Patterns in the upper-left part of the matrix feature positive height anomalies (ridging) in northern and western areas of the domain along with negative anomalies (troughing) in the east. The total number of days belonging in node #1 has increased during recent years (Figs. 3, S7 ), though not in winter (Fig. 3b ). Anomalous temperature and precipitation patterns associated with each node can be used to ascertain weather conditions associated with each node. Figure 4a displays the number of days at each gridpoint in which anomalously high (> 1.5 σ) temperatures occurred, and Fig. 4b indicates the occurrence of extremely low (< -1.5 σ) temperatures associated with each pattern. The weather associated with node #1, for example, favors relatively dry, warm conditions in California, below-average snowpacks in western mountain ranges, and prolonged cold, wet spells in the Midwest and East (Figs. 4, 5 ). Nodes in the bottom-right part of the matrix feature the opposite anomaly pattern, with negative (positive) values spanning much of the high (middle) latitudes. Western states tend to be relatively cool and wet in these patterns, while the east experiences abnormally warm conditions. The total number of days belonging in these nodes, especially node #12, has declined in recent decades, particularly during winter (Fig. 3 ). In the upper-right and lower-left corners are opposing patterns featuring a strong zonal anomaly gradient, indicative of an amplified ridge/trough in each half of the domain. In terms of weather conditions, the strong western trough depicted in node #4, for example, tends to bring anomalously cold temperatures to Alaska along with stormy weather to the U.S. west coast. The opposite pattern in node #9 produces abnormally warm conditions along the west coast, cold temperatures in much of the central and eastern continent, and unsettled conditions in the eastern states.
As high latitudes warm disproportionately faster than midlatitudes, we find that patterns exhibiting positive (negative) high-latitude height anomalies are occurring more (less) frequently, especially in the most recent decades (Fig. 3a and S7 ). During winter months, the pattern featuring anomalous troughing in the west and ridging in the east (#4) is the only one that has occurred significantly more frequently (Fig. 3b ), which is consistent with the region of strongest AAW during JFM presented in Fig. 1b of Francis and Vavrus (2012). During summer, nodes #1 and #3 are more common. Spring and fall also exhibit significant increases node #1 (not shown).