Multi-decadal records of hourly observations of wind were obtained from a publicly available Canadian Weather Energy and Engineering Dataset (CWEEDS) representing the period from 1953 to 2003 [24]. All 235 CWEEDS stations were ranked according to the relative length of the maximum gap in each station’s annual record. The trade-off between the record quality and a representative continent-wide coverage was achieved with a sub-set of 149 stations, where the largest temporal data gap did not exceed 12%. On average 3% of the hourly data was missing.

The 149 stations selected comprised of 131 Weather-Bureau-Army-Navy (WBAN) stations and 18 other stations recently added to CWEEDS. Gap-filling methods for sporadic temporal omissions in the surface wind data for the 149 Canadian meteostations and for calms (where no actual wind direction was identified) were based on the work of Fernandes and colleagues [25]—small data gaps in wind direction were filled by interpolation and longer data gaps (outages, etc.) were taken from the similar period of the highest quality year on the record. The wind rose data documented for 1953 to 1980 in the Canadian Weather Atlas [26] was used for quality control, as it conveniently matched part of the time period covered by data from the selected CWEEDS stations.

Full rotations completed by the vane anemometer are absent in the standard record of wind direction due to discontinuity when crossing the compass bearings from 360° to 0°. The traditional compass-based CWEEDS data was therefore reconstructed to accommodate directional continuity by adding 360° to the wind direction angle if the indication was that the wind direction passed through 360°/0°. For example, if five consecutive anticyclonic readings were 270°, 290°, 5°, 10°, and 30°, then this data was reconstituted as 270°, 290°, 365°, 370°, and 390°. Readings indicating a cyclonic rotation were treated in a similar fashion (i.e., 30°, 10°, 5°, 290°, and 270° could have been reconstituted as 750°, 730°, 725°, 650°, and 630°).

Therefore, reconstruction of full rotation counts at the 360°/0° crossing appears a generally straightforward task even when taking into account infrequent occurrences of large shifts in wind direction. Large wind shifts in the standard compass-based record of say +270° were substituted by the smaller and thus more likely shifts in the opposite direction, i.e., −90°, complemented by a full rotation count being added to the reconstructed record (in this case the count was −1 as 360° was subtracted from +270° and not added). Ambiguity as to whether the rotation was cyclonic or anticyclonic could, however, occur for two consecutive wind directions that had a difference angle approaching 180°, indicating a near reversal in direction. According to Mahrt [27], detailed reconstruction of wind direction change requires the comparison of winds averaged over various time window widths. In this study, for simplicity, a limiting threshold difference angle was used in the reconstruction of the wind direction data to reduce the ambiguity that is most pronounced for 180° changes. Instead of a 180° threshold, a more conservative threshold angle of 120° was employed to differentiate the directional shift from discontinuity and to calculate long-term direction drift, as this threshold angle results in a tolerable error of 9% in the rotation rate. In this way, only direction shifts of larger than 240° were interpreted as artifacts of the discontinuity crossings and were accommodated as an indication of the subsequent complete rotations (which were added as multiples of 360° to the traditional wind direction angle, so that a trend in the continuous record of historic wind direction angle was reconstructed). The reconstruction error of ±9% corresponds to missing counts of complete rotations that occur (in both directions of rotation) at discontinuities not distinguished among shifts in the range from 120° to 240°, which were all considered as simple shifts and thus were left intact.

In the present study, the trend in wind direction drift (specifically, the net anticyclonic drift) is termed SWR, instead of the more broadly defined term LFV. The long-term average of SWR was assigned a positive value if anticyclonic (i.e., clockwise in the NH) and a negative value if cyclonic (i.e., anticlockwise in the NH) [14,15].

Wind direction drift (trend) was established and analyzed for all 149 selected CWEEDS stations. The degree of long-term stationarity of rotation was assessed by linear correlations of the continuous SWR record to time (i.e., to the linear trend). The robustness of the established SWR effect was assessed on the basis of wind rotary spectra analysis [28,29].

Spatial analysis consisted of investigating the zonal structure of SWR by assessing the correlation of SWR with longitude within the whole dataset and in moderately narrow (i.e., ~10°-wide) E-W transects. Meridional dependence was investigated by comparison of SWR with an analytical expression based on latitude rather than with the latitude per se. The analytical meridional structure of SWR (and SWR latitudinal dependence) was identified by least-squares fit to the SWR latitudinal distribution in a mid-continental (80°W–90°W) N-S transect. This mid-continental analytical latitudinal dependence was further evaluated in all other transects, using the Kendall non-parametric test [30,31] on correlation with each station’s average SWR. The whole dataset has also been evaluated using the Kendall test: the arbitrary Kendall-tau (dispersion threshold) divided the dataset into the core subset with clear latitudinal dependence and a subset of exceptions.

The net anticyclonic drift, or SWR, subsequently represents the net asymmetry between cyclones and anticyclones. Observations of much longer than a month are required to clearly identify consistent anticyclonic SWR and to subsequently measure SWR frequency (Figure 1). The last five decades documented in CWEEDS (1953–2003) thus provide a convenient framework for identification of SWR and analysis of its frequency.

Most of the Canadian landmass (144 out of 149 meteostations), including the High Arctic, appears to be marked by anticyclonic SWR (Figure 2). The mean period of observed anticyclonic rotation ranged from 7 days (52 rotations, or cycles per annum, cpa) at Medicine Hat (50°N, 110°W) to 25 days (15 cpa) at Resolute (75°N, 95°W), in the latter case—well beyond the synoptic range.

In addition to the analysis of the continuous SWR (completed by vane anemometer), the rotary spectra of wind were calculated at 15 random locations in order to assess the robustness of the observed SWR effect. The frequency corresponding to SWR was clearly seen in each analyzed case; this is illustrated in Figure 3 depicting 6 locations. The net anticyclonic rotation follows from generally larger magnitude of the corresponding clockwise rotational component. However, the unambiguous identification of the SWR frequency based solely on the rotary spectra would have been difficult.

Most of the Canadian landmass, including the High Arctic, exhibits anticyclonic and steady SWR, which also appears directly correlated with latitude (as seen in Figure 4, Table 1 and explained in Section 3.3). Clear examples of SWR steadiness are provided in Figure 5, as shown by inserted plots for nine stations showing wind direction angle drift over several decades. Table 1 presents a test on steadiness of rotation, based on a linear least squares fit to constant rotation (i.e., to time).

In Table 1, eight stations, where negative cyclonic rotation occurs either permanently (at five stations in British Columbia and Yukon) or persistently over a year or longer (Whitehorse in Yukon, and Kuujuaq and Bagotville in Quebec), were set aside and grouped as “outliers”. For each N-S transect listed in Table 1, the significance level (α_max) of maximum tolerance of a linear relationship between each transect station’s SWR rate versus time was recorded.

Table 1 also provides the coefficient of determination (R²) of SWR with time for all stations in each transect. Dispersion is mostly attributed to seasonal SWR variability accompanied by a much smaller interannual variability. Long-term stationarity appears strong across Canada (including the set of 8 outliers) because the least squares fit to constant rotation is consistently significant at level α_max ≤ 0.1 (and mostly at level α ≤ 0.01), with dispersion characterized by R² ≥ 0.8.

No significant association was found at the level of α ≤ 0.1 for SWR correlation with longitude, either for the continent-wide data set (n = 149) or within the 10°-wide E-W transects. Therefore, no zonal dependency in SWR was established.

The latitudinal tendency is apparent in SWR rates shown in Figure 2, which results in a significant at the level α = 0.05 correlation with latitude. Latitudinal tendency in pan-Canadian data, nevertheless, appears subject to significant variability (R² = 0.2). This variability is caused by apparent outliers in Rocky Mountains and by the fact, that generally similar rotation rates are observed more to the North in Western Canada and more to the South in Eastern Canada, e.g., in the Prairies and in the Great Lakes region (which are located at different latitudes); similar pattern exists in Arctic Tundra (Figure 2). For this reason, it was decided to identify the meridional structure by limiting the continent-wide data to subsets from the 10°-wide N-S transects. A robust empirical relationship for the dependency of the SWR rate, ω*/2π, (cpa) on latitude, was derived from the least-squares fit to the data of the mid-continental N-S transect of 80.0°W–89.9°W (illustrated in Figure 4) and is given by: ω* = 2π k_a φ^−4.33(1) where φ is latitude (degrees) and k_a is a units conversion factor (k_a = 4.0 × 10⁸ cpa/degree). Further analysis of correlation between spatial distribution of SWR and empirical relationship (1) was based on the Kendall test (instead of least-squares fit), because of its robustness with respect to outliers, skewness and curtosis [32], since all of these complicating factors were encountered in our small transect data subsets. The nonparametric Kendall test returns a significance of fit to SWR at the level of α_K = 0.01 with corresponding dispersion estimated by Kendall-tau τ_K = 0.72 in the illustrated transect. Similar strength of correlation (with Equation (1) and the same empirical parameters) is also present in five other transects (Table 1). However, SWR latitudinal dependence is absent in the Maritimes and Pacific Coast/Rockies.

The existence of a certain number of exceptions to the general rule of steady latitudinal dependent SWR makes it more logical to use an arbitrarily chosen dispersion threshold τ_K and to have the whole dataset divided into a “core” clearly latitude-dependent subset and a subset of “subtle exceptions”, which could be later classified with respect to their climatic and orographic signatures and location.

A “core” subset of stations where SWR exhibited both strong latitudinal dependency and steadiness was identified. Steadiness in SWR is important, as it means a constant asymmetry between cyclones and anticyclones. Latitudinal dependence is perhaps the more important of the two features of SWR, because it defines the SWR frequency in each particular location. We started with a subset of stations exhibiting clear latitudinal dependence of SWR, and proceeded to reassess the stationarity within this subset. The number of stations within the identified core subset (n = 118) provides a clear measure of the strength of the latitudinal dependency and steadiness of SWR. Nine illustrations are presented as inserted plots in Figure 5.

Exceptions (subtle exceptions) to the whole dataset were identified on the basis of goodness of fit of SWR to Equation (1) provided by Kendall tau τ_K. It was suggested, that Kendall tau τ_K = 0.4 represents sufficient criterion to the goodness of fit of the core subset to Equation (1), as it is similar to the goodness of fit observed in the 100.0°W–109.9°W N-S transect. Exclusion of locations, which are characterized by SWR rates more than three times different from the value provided by Equation (1) resulted in τ_K = 0.4 and these locations were considered subtle exceptions to the rule set by Equation (1) and to the whole dataset. This arbitrary criterion (τ_K = 0.4, or conversely the factor of 3 anomaly to Equation (1)) resulted in the identification of 6 stations that were rotating faster, and 25 stations that were rotating slower, than expected (including 1 slowing down to no net rotation, and 5 rotating negatively). In other words, 31 of the 149 stations (or 21% of the analyzed dataset) did not show a strong latitudinal dependency. In this context, it is important to specify that cases of extreme violation of the Equation (1), as shown by the 5 cases of negative cyclonic rotation (3%), are rare and narrowly confined to the Pacific Coast and adjacent Rockies. Nine illustrations of exceptions to latitudinal tendency and to steadiness of SWR (subtle exceptions) are presented as inserts in Figure 6. It is worth noting, that in this pan-Canadian classification (differently from Table 1 transect-based results) many stations from the 50°W–60°W and 120°W–140°W transects appear included in the core subset and conversely, some of the stations from 60°W to 120°W region were discarded as subtle exceptions.

The analysis shows that the core subset of stations (n = 118) exhibits exemplary steadiness in terms of anticyclonic rotation, with an SWR inter-annual variability characterized by R² > 0.9. Therefore, as a general rule, we suggest that continental SWR is very steady, anticyclonic, and latitudinal dependent.