Data and Methods

We identify representative large-scale atmospheric patterns over the northeast Pacific Ocean/North American sector using a neural-network-based tool called Self-Organizing Maps (SOMs; Skific and Francis, 2012). The SOM algorithm ingests large, two-dimensional data sets and groups the fields into clusters or nodes of representative patterns found in the data. The patterns are arranged in a variable-size matrix according to their similarity with each other, with most similar patterns positioned near each other and most dissimilar patterns farthest apart. For this application we use daily fields of anomalies in the 500-hPa geopotential heights from 1948-2019 (~26,000 days) obtained from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) Reanalysis (Kalnay et al., 1996). The spatial domain extends from 30oN-80oN and 180-60oW. Daily anomalies were calculated by subtracting the 72-year mean value for each gridpoint for that calendar day. We note that 500hPa height fields from other reanalyses are very similar (e.g., Archer and Caldeira 2008).
For this application, we chose a 4x3 SOM matrix, which balances sufficient representation of the atmosphere’s dominant patterns with ease of displaying of results (Fig. 1 ). The algorithm places each daily field into the node with the most similar pattern. Once this so-called master SOM has been created, other fields of data can be mapped to the patterns, which is especially powerful for variables that are spatially and/or temporally discontinuous (e.g., cloud cover, precipitation, or extreme events). We take advantage of this tool to explore extreme temperatures and precipitation associated with each pattern. Changing frequencies of occurrence of the SOM nodes allow an assessment of trends in extreme conditions associated with each large-scale pattern. Air temperature at 925 hPa and precipitation data are also obtained from the NCEP/NCAR Reanalysis, which at the grid-box scale (2.5o) should reasonably represent patterns of precipitation and changes over time.
In this study, we develop a novel metric for the detection of WWEs. We begin by identifying long-duration events (LDEs) during winter (January-March) and summer (July-September), defined as cases when the large-scale atmospheric pattern remains in one node of the SOM for four or more consecutive days (Francis et al., 2018; Vihma et al., 2019; Francis et al., 2020). The relatively small matrix was selected to ensure that adjacent patterns would be sufficiently distinct from each other and so consecutive days would be less apt to jump between nearby, similar patterns that typically characterize larger matrices. We then identify the node associated with the second day after each LDE and determine the Euclidean distance between the LDE node and the one containing the atmospheric pattern two days later as a measure of dissimilarity between the patterns. Based on examination of several actual WWEs (such as the example shown in Figs. S1-S3 for 2-9 March 2019), the two-day time interval appears to be typical for a new pattern to become established after an LDE (conclusions are similar, however, for 1 and 3 days later). The LDE presented in Figs. S1-S3 began on 27 February 2019, when a strong positive height anomaly persisted for 7 days across much of northern North America along with a negative anomaly over the central continent (Fig. S1 ). Two-meter air temperature anomalies associated with this weather regime exhibit a broad area of much-above-normal values across the Arctic along with much-below-normal temperatures from the Pacific Northwest extending across the continent to the southeastern U.S. (Fig. S2 ). Anomalies in precipitable water are generally positive across the southern states, while the northern tier and southern Canada are drier than normal (Fig. S3 ). Beginning on March 6th, this pattern began to break down, and over a two-day period, shifted to a substantially different one in which low height anomalies invaded the northwest part of the continent as well as a large portion of the western U.S. This new regime ended the prolonged cold spell in the central and eastern states and marked the beginning of a period of intense and prolonged precipitation in the Midwest that caused record-breaking floods in eastern Nebraska and the surrounding region. The surge of moisture into the Upper Midwest is evident on March 8 and 9 in Fig. S3 . In practical terms, a WWE is experienced when a persistent weather pattern ends abruptly and it is replaced by weather conditions that differ markedly from those in the prior persistent pattern, such as in this example and those described in the introduction.
We compiled the distribution of Euclidean distances from each LDE (about 2,015 of them from 1948 to 2019) to the node containing the pattern two days later and determined that the 50th percentile distance value establishes a suitable threshold for identifying a WWE. As shown in Table S1 , which displays results for winter, this value corresponds to a mean Euclidean distance of 1440 (a unitless metric internal to the SOM algorithm). This distance is approximately the same as between two non-adjacent nodes, such as nodes #1 and #3 (Table S2 ), thereby constituting a major pattern shift. For summer months, this threshold is 889, indicative of the reduced pattern contrasts in the warm season when the jet stream is farther poleward and the north-south temperature gradient is smaller. We then identify a WWE when the distance from the LDE node to the node two days later exceeds the seasonal threshold, which also enables us to quantify the WWE magnitude by the exceedance amount. The logic of this methodology is also illustrated in Figs. 2, S4 and S5 . The histograms inFig. 2 display the node number containing the sample that occurs two days after an LDE during winter originating in each node in the matrix (the corresponding plot for summer months (not shown) is very similar). For example, the top left histogram indicates that the samples two days after LDEs occurring in node #1 fall most frequently into nodes #3 and #9. If a sample two days later falls in nodes other than #2 or #5 (the two nodes within the distance threshold from #1), a WWE is identified. Note that when the same node number as that of the initiating LDE appears in the histogram – e.g., the histogram for node #1 has a bar in the node #1 location – the pattern shifts away from node #1 on the first day then returns to node #1 on the 2nd day. A similar set of histograms is shown inFig. S4 , but instead of displaying the node numbers for the sample two days later, the x-axis represents the Euclidean distance between the LDE node and the node containing the field 2 days later. One additional visualization of the Euclidean distances between nodes is presented in Fig. S5 , a so-called Sammon map of the SOM matrix. The uneven distribution of distances between nodes is clearly evident, and this mapping shows that nodes #1 (warm Arctic) and #12 (cold Arctic) constitute the largest difference among the circulation patterns, while nodes #4 and #9 (cold or warm North Pacific) in the other two opposing corners also differ substantially.
Our analysis produces a total of 948 (annual), 239 (winter), and 228 (summer) WWEs over the 72-year record, which translates to an annual- or seasonal-mean frequency of 13.2, 3.3, and 3.2. These events are relatively rare because LDEs themselves occur infrequently (Fig. S6 , and also see Francis et al., 2018; 2020).
The same WWE metric is applied to output from climate model simulations. We analyze ten ensemble members from the NCAR Community Earth System Model Large Ensemble (CESM1) that span the historical period (1979–2005) as well as into the future (2006–2100) (Kay et al., 2015). Daily 500 hPa height fields were obtained fromhttps://www.cesm.ucar.edu/projects/community-projects/MMLEA/ . Historical runs incorporate observed natural and anthropogenic forcings, while future projections assume conditions defined by the RCP8.5 scenario (Riahi et al., 2011). Anomalies in future projections were calculated relative to the mean from 2006 to 2100.