We first establish the contextual long-term climatology of the wind power resource, the solar power resource, and heating/cooling degree days (experienced by land) prior to investigating their most extreme weeks.
Spatial long-term climatology
Most of the wind power supply is located on the lee side (i.e., to the east) of the Rocky Mountains in the U.S.’s “wind corridor” (Fig. 1a–c). There is little seasonal spatial shift in the location of the maximum wind supply and instead the stationary pattern intensifies in winter and weakens in summer (c.f. Fig. 1a, b).
The surface solar power resource is concentrated in the southwest corner of the land in the domain but is more homogeneous than the wind power resource because topography exerts a smaller influence on cloud cover than it does on near surface atmospheric flow. Near the summer solstice, the meridional gradient of top-of-atmosphere daily mean incoming solar radiation is very small so most of the spatial variation in surface solar radiation is due to cloud cover (Fig. 1e). Because of this, summer zonal gradients in incident solar radiation can be as large as meridional gradients. Near the winter solstice, on the contrary, the meridional gradient of incident daily mean incoming solar radiation is dominant (Fig. 1d).
The seasonal cycle in HDDs and CDDs is as would be expected. Most of the domain has a long-term daily mean temperature colder than 18 °C so there are more HDDs than CDDs (c.f. Fig. 1l, i). Seasonally, this affect is most pronounced in the winter when there is nearly zero land experiencing CDDs (Fig. 1g) but substantial HDDs (over 30 HDDs per day over most of the higher latitudes and elevations; Fig. 1j). Even in the summer there are only slightly more CDDs than HDDs when averaged over the domain (c.f. Fig. 1h, k). Despite this, because of the larger use of electricity for cooling than for heating and because of the tendency for people to live in warmer climates, electricity demand over the Western Interconnection tends to peak in the late summer . This pattern of a dual peak in demand (one corresponding to the winter peak in HDDs and one corresponding to the summer peak in CDDs) is observed in actual load data for the United States.
Seasonal long-term climatology
The right side of Fig. 1 shows the mean and standard deviation of the seasonal cycle for the solar power resource, the wind power resource, HDDs and CDDs averaged over the entire WNA domain. All values are expressed as a fraction of their long-term mean value.
The solar power resource runs from ~ 40% of its annual mean near the winter solstice to ~ 160% of its annual mean near the summer solstice (Fig. 1m). Variability in solar power is dominated by the seasonal cycle. This suggests that solar droughts (as defined here using absolute minimum weeks over the entire period) will occur during the weeks near the winter solstice (squares in Fig. 1m, n).
The seasonal cycle in wind power is slightly anticorrelated with the seasonal cycle in solar power but its phase lags that of solar power by about five weeks (Fig. 1m). The amplitude of the seasonal cycle in wind power is much less than the amplitude of the seasonal cycle in solar power. Wind power supply is about 110% above its annual mean for much of the cooler portion of the year and it dips to about 60% of its annual mean in mid to late summer when the Northern Hemisphere meridional temperature gradient, and thus upper-level geostrophic wind, is at an annual minimum. However, wind power variability is dominated by synoptic weather conditions rather than the seasonal cycle. This implies that a wind drought can plausibly occur at any time of the year but that they are most-likely in the late summer in July and August (circles in Fig. 1m, n).
Overall, weekly solar power has 167% of the variability of weekly wind power and weekly solar variability is dominated by the seasonal cycle (99% of weekly solar variability is linearly explained by the week-of-the-year) while wind power variability is dictated more by atmospheric circulation variability (only 42% of weekly wind variability is linearly explained by the week-of-the-year).
Weekly wind and solar values
Figure 2 shows the domain mean for each week in the dataset plotted in a two-dimensional wind power and solar power space with CDDs displayed as colors (Fig. S5 shows the corresponding figure with HDDs). Wind droughts are shown as circles with black outlines, solar droughts as squares with black outlines and compound wind and solar droughts as diamonds with black outlines (same as in Fig. 1m, n).
Wind droughts tended to occur in astronomical summer (Fig. 1m and Quadrant II in Fig. 2). During wind droughts, solar power averaged ~ 135% of its long-term mean (large dark circle in Fig. 2), with a tendency towards increased CDDs and decreased HDDs.
Solar droughts all occurred around the winter solstice (Fig. 1m and Quadrant III and Quadrant IV in Fig. 2). During solar droughts, wind power had a mean of ~ 111% of its long-term mean (large dark square in Fig. 2), with a tendency towards decreased CDDs and increased HDDs.
Simultaneously considering the proxies for energy supply (Fig. 1m and axes of Fig. 2) and energy demand (Fig. 1n and colors of Fig. 2 and Fig. S5), the least stress on the energy system would be experienced in the astronomical spring when both wind and solar power tend to be above their long-term mean and both HDDs and CDDs are near their long-term mean. Conversely, the most stress on the energy system would tend to occur in the astronomical autumn (Quadrant III of Fig. 2), when there tends to be low solar power and still the substantial possibility for low wind power. HDDs are also high at this time (Fig. S5), potentially adding stress on the demand side of an underlying energy system if that system uses electricity for heating.
There are 23 weeks in the 71 year time period where CDDs were above their long term mean while both wind and solar resources were below their long term mean (pink and red circles in Quadrant III of Fig. 2). None of these weeks reach the wind/solar drought threshold so we will not focus on them here but they nevertheless indicate potentially large stress on an underlying energy system and may merit study in future research.
Compound wind and solar droughts all occur near the winter solstice (Fig. 1m and Quadrant III in Fig. 2). This is because the dominance of the seasonal cycle in solar power confines the compound wind and solar droughts to this time of the year. During compound wind and solar droughts, solar power tends to be ~ 43% of its long-term mean and wind power tends to be ~ 56% of its long-term mean (dark diamond in Fig. 2), with a tendency towards decreased CDDs and increased HDDs (Fig. S5). Thus heating demand is more of a concern than cooling demand with regard to electricity demand increases exacerbating compound wind and solar droughts.
Synoptic meteorology of wind and solar droughts
Here we assess the first-order, proximate, synoptic-dynamic mechanisms associated with wind and solar droughts. From this perspective, our expectation is that surface high pressure systems will be associated with subsidence, clear skies (enhanced surface solar radiation) and calm conditions. On the other hand, surface low pressure systems will be associated with ascent, clouds (reduced surface solar radiation) and enhanced wind. As mentioned above, one of our central questions is to see if the empirical data conforms to this first order expectation.
We connect surface high and low pressure systems to dynamic “forcing” aloft by invoking Quasi-Geostrophic (QG) Theory [44, 45]. QG theory states that under a number of assumptions that are plausible at synoptic spatiotemporal scales, vertical motion in the atmosphere is related to non-geostrophic circulations that restore thermal wind balance: Positive (negative) differential vorticity advection by the geostrophic wind is associated with divergence (convergence) aloft, ascent (subsidence) and low (high) surface pressure. Also, relatively warm (cold) temperature advection by the geostrophic wind implies upward (downward) vertical motion over the lower half of the atmosphere which is associated with surface low (high) pressure. We use a standard meteorological convention of investigating vorticity advection via the relative vorticity at 500mb (Fig. 5d–f) and temperature advection at the 700mb level temperature (Fig. 5g–i.).
Figure 3 shows the average normalized spatial anomalies of wind power, solar power, and temperature variables during drought events. During a typical wind drought, the entire WNA domain tends to experience reduced wind with respect to the mean for that week of the year (spatial average of 43% of typical wind power, Fig. 3a). During a wind drought, solar power tends to be both above-average seasonally (135% long-term mean) and slightly above average with respect to the mean for that week of the year (102%, Fig. 3d). Thus, wind droughts tend to be accompanied by slightly enhanced solar availability. However, wind droughts are consistently associated with slightly less solar power than average over the climatologically sunniest region (indicated by the stippling on the bottom half of the WNA domain in Fig. 3d).
During wind droughts, it tends to be warmer than average to the north where climatological temperatures are below 18 °C and colder than average to the south where climatological temperatures are above 18 °C (Fig. 3g). This is indicative of a simultaneous reduction in HDDs and CDDs potentially reducing stress on the demand side of a hypothetical underlying energy system.
Wind droughts tend to be associated with a warm core (dynamic) high over British Columbia flanked by cold core lows on either side (Figs. 4d and 5g). This is reminiscent of a positive Pacific North American (PNA) pattern that accentuates the typical meridional deviations in the large-scale atmospheric flow, making it wavier than normal and possibly generating more persistent conditions.
At mid-levels, we see convergence over most of the WNA domain (Fig. 5a) associated with subsidence and high sea level pressure (Fig. 4g). One reason for this is likely the negative vorticity advection on the downstream side of ridge (Fig. 5d) and the negative vorticity advection associated with the left entrance region of a jet streak at 250mb (Fig. 4a). Additionally, cold air advection over some of the eastern side of the domain promotes subsidence (Fig. 5g). Some positive vorticity advection and divergence is also observed near the southwest U.S. (Fig. 5a, d) which would typically be associated with upward vertical motion and thus is consistent with the region experiencing anomalously cloudy conditions (Fig. 3d).
Sea surface temperature anomalies show a pattern reminiscent of a western Pacific El Niño occurring during an enhanced Aleutian low  and a positive phase of the Pacific Decadal Oscillation (PDO, [47,48,49]) (Fig. 4j). However, the lack of widespread stippling indicates that this is not a necessary condition for a wind drought and that they can easily occur under a diverse set of sea surface temperature patterns (Fig. S13).
During a typical solar drought, almost the entire WNA domain consistently experiences reduced solar power with respect to the week-of-the-year (spatial average of 93% of typical values, Fig. 3e). Also, during a solar drought, there tends to be more wind power than average overall (111% of long-term mean, Fig. 3b) and it tends to be windier than average with respect to the mean for that week of the year (101%, Fig. 3b). This is further evidence of an inverse relationship between wind and solar power. This anomalously high wind power is centered over the southwest U.S. but a lack of stippling indicates that the spatial manifestation of this feature is not consistent across solar drought events.
During a typical solar drought, the surface over most of the domain tends to be warmer than average for that week of the year (Fig. 3h). Since the entire domain is typically below 18 °C during the winter (Fig. 1j), this reduces HDDs. Thus, the stress-inducing impact of solar droughts on a hypothetical underlying energy system may be partially mitigated by their co-occurrence with reduced HDDs.
Solar droughts tend to be associated with cold core (dynamic) lows occurring on the west coast of the U.S. (Fig. 4e, h). This damps the typical meridional deviations in the large-scale flow, making it more zonal than normal and possibly contributes to the shorter duration of solar droughts compared to wind droughts.
At mid-levels, we see divergence off the west coast of WNA (Fig. 5b), which in turn is associated with ascent, low sea level pressure (Fig. 4h), high winds (Fig. 3b) and cloudier than normal conditions (Fig. 3e). One reason for this is likely the positive shear vorticity advection off the west coast of WNA (Fig. 5e) and the positive vorticity advection associated with the left exit region of a jet streak on the northwest side of the WNA domain at 250 mb (Fig. 4b). Additionally, some slight warm air advection is seen off the west coast of WNA which also is associated with ascent (Fig. 5h).
We see some evidence that solar droughts are associated with the positive state of the North Atlantic Oscillation [50, 51] (Fig. 4h, k), and are slightly associated with the negative phase of Atlantic Multidecadal Variability ( AMV, Fig. 4k) but with little consistency across events (see the diversity of patterns in Fig. S14). There is some evidence of an association with El Niño and this becomes stronger when more extreme solar droughts are considered (using a half percentile threshold, c.f. Fig. 4k with Fig. S17k).
Compound wind and solar droughts
Compound wind and solar drought events tend to be similar in character to wind drought events in terms of their surface manifestation (c.f. the right and left columns of Fig. 3), and their circulations (c.f. the right and left columns of Figs. 3 and 4). There is relatively little atmospheric circulation influence on surface solar radiation (relative to the influence of the seasonal cycle) and thus it is the atmospheric influence on the wind that dictates the occurrence of compound wind and solar droughts.
Compound wind and solar drought events tend to be characterized by warm air advection (Fig. 5i), which would typically be associated with ascent, enhanced winds and storms. However, the negative vorticity advection (Fig. 5f) appears to cancel this effect, resulting in convergence aloft over the climatological windiest region (Fig. 5c).