Alberta wildfire 2016: Apt contribution from anomalous planetary wave dynamics

In May-June 2016 the Canadian Province of Alberta suffered one of the most devastating wildfires in its history. Here we show that in mid-April to early May 2016 the large-scale circulation in the mid- and high troposphere of the middle and sub-polar latitudes of the northern hemisphere featured a persistent high-amplitude planetary wave structure dominated by the non-dimensional zonal wave number 4. The strongest anticyclonic wing of this structure was located over western Canada. In combination with a very strong El Niño event in winter 2015/2016 this favored highly anomalous, tinder-dry and high-temperature conditions at the surface in that area, entailing an increased fire hazard there. This critically contributed to the ignition of the Alberta Wildfire in May 2016, appearing to be the costliest disaster in Canadian history thus far.

strongly amplifying large-scale planetary waves on 10-day-to-monthly time scale should be gradually introduced into the practice of the wildfire managers and forecasters, because the low-frequency nature of these waves favors their detection at relatively long lead-times (i.e. beyond 10 days) which could potentially improve wildfire forecasts, and because the spatial structure of these resonant waves can dictate locations of very strong anticyclonic circulations associated with them, which support noticeable downward vertical motions, inhibiting middle and high cloudiness, suppressing precipitation and supporting warm and dry conditions at the surface, favoring the wildfire ignition. We discuss this issue at length in Results. Several informative parameters in this context of the large-scale planetary waves are discussed in Results.

Results
Surface Conditions (Temperature, Soil Moisture). Figure 2 shows the evolution of the surface temperature T s (Fig. 2a) and soil moisture S w (Fig. 2b) over Alberta (110°W-120°W, 50°N-60°N), through April-May 2016. The figure is plotted using time series of the 15-day running means of these variables that we calculated based on daily NCEP-NCAR reanalysis data 13 . As seen in Fig. 2, both variables experienced pronounced trendspositive for T s and negative for S w -in late April/early May over Alberta, having been strongly anomalous for that period (beyond 1.5 SD relative to 2003-2015 climatology), and pointing out at unusually warm and tinder-dry conditions in Alberta. A low reliability of the reanalysis data on S w before the year 2000 14  time range over Alberta in April, with high positive and negative anomaly at the equivalent barotropic level (EBL) 300 hPa, respectively, for geopotential height H 300 (Fig. 3a) and RV 300 (Fig. 3b)    and increasing the danger of wildfires over Alberta in April of those two years. 2016 also enters a set of four years (1980,1983,2012 and 2016) that feature in April, according to monthly NCEP-NCAR reanalysis data 13 , the highest amplitudes of monthly wave-4 Fourier component of the meridional velocity at 300 hPa among all Aprils 1980-2016, exceeding 1.5 SD of the 1980-2015 climatology (Fig. 3c).
Moreover, in those four years monthly wave-4 for April was the dominant one in the mid-and sub-polar latitudes of the NH. This conclusion is supported by Fig. 4 that pictures the amplitudes of the Fourier components, up to n = 24, of monthly meridional velocity at 300 hPa ((a) and (b)) and longitudinal distribution of monthly H 300 ((c) and (d)), averaged over the 50N-60N ((a) and (c)) and 45N-70N ((b) and (d)). Figure 4a,c indicates that in all four years wave-4 Fourier component had the highest amplitude among the total planetary wave field, both in mid-and sub-polar latitudes of the NH, with four high ridges of H 300 (see Fig. 4c,d) accompanying four strong anticyclonic circulations with highly negative RV 300 in the wave-4AS shown in Fig. 1a. Furthermore, Fig. 4c,d attest that in all four Aprils western Canada was located just within one of these anticyclonic circulations. This was caused by the occurrence of an active thermal source of negative RV in the considered region, due to a sharp longitudinal gradient of the surface temperature between oceanic and land masses across a narrow strip of the eastern Pacific coast. In combination with a strong orographic source of RV of the same sign caused by steep Rocky Mountains massive located in the region, the above-mentioned active thermal source of RV appeared to be the most powerful one within the considered two latitudinal belts at that time, dictating in this way a position of the governing zero phase at ca. 120°W for the wave-4 longitudinal distribution along both latitudinal circles, fully in line with Haurwitz theory 16 of atmospheric sources of RV. It is instructive to plot a total monthly mean  ). This is due to the dominant contribution of wave-4 to the total spectrum of V 300 shown in Fig. 4a.
On the other hand, a comparison of Figs 4c and 5a,b attests that the positions of the zero phase in the wave V 300 and wave-4 longitudinal distributions over western Canada at ca. 120°W correspond well to the location of the crest (maximum) in the longitude distribution of the geopotential height H 300 . This can be explained by a strong dynamical coupling of V 300 and H 300 fields, on the strength of hydrostatic balance and quasi-geostrophic relations (see equation (1)) below). This results, in turn, in the anomalously high pressure over Alberta throughout the total depth of the mid and lower troposphere in April 2016 13 , due to a very strong anticyclonic branch of RV (Fig. 3a,b), which entailed a strong downward vertical motion in the mid-and lower troposphere. These could favor a pronounced adiabatic warming of the mid-and lower troposphere air, accompanied by a decrease in high/mid cloud amount and drying/warming of the surface 17 . This led to a rather high wildfire hazard situation over Alberta in April 2016. Let us note that we discuss here persistent (with 10-day to monthly time scales), resonant-type planetary waves, which anticyclonic wings operate in the situations of nearly absence of cumulonimbus clouds, with lightning strikes as rare events.
Conditions that lead to amplified planetary wave-4 (resonance). The anomalously high amplitudes of wave-4 and wave V 300 shown in Fig. 5 are due to the mechanism of quasi-resonant amplification (QRA) of quasi-stationary planetary waves first proposed in 18 and developed further in [19][20][21] . This mechanism is considered here on a particular example of quasi-stationary planetary wave-4. Given the quasi-geostrophic coupling between V 300 and H 300 , QRA led also to a high amplitude of the respective H 300 wave. The essence of the QRA mechanism is trapping (locking) and corresponding strong (resonant) amplification of the energy of the mid/high troposphere quasi-stationary planetary waves with non-dimensional zonal wave numbers m = 4-8 within specific mid-latitude and sub-polar waveguides. This happens due to drastically diminished exchange of the trapped wave action (energy) between mid-and tropical, and sub-polar and polar latitudes caused by a strong reflection of these waves at the lateral (meridional) boundaries of the waveguides 18 . The occurrence of the above-mentioned waveguides is strictly regulated by a set of certain necessary conditions, which the latitudinal distribution of the zonally averaged zonal winds should meet [18][19][20][21] . We have previously implemented and documented an automated QRA-detection-scheme developed in 20,21 which identifies the presence of the QRA resonance in the mid-and/or sub-polar latitude ranges. As we noted earlier, the frequency of the QRA events and associated weather extremes noticeably increased over recent decades, possibly due to anthropogenic forcing 22 .
When we applied the QRA-detection-scheme to the NH extra-tropics for March-April-May (MAM) 2016, we found that QRA resonance conditions for wave-4 were present in MAM 2016 in the 35°N-70°N belt and the scheme predicted its high amplitudes within this time range (see Fig. 6). We analyzed 15-day running means of the meridional velocity in the mid-and sub-polar latitudes of the NH at 300 hPa for the 15-day time periods with central dates from 24 March 2016 to 7 May 2016 (see Fig. 6). Here, slowly moving, quasi-stationary components of wave-4 had significantly higher amplitudes during QRA events, while fast-moving components demonstrated the opposite tendency. In accordance with this finding, the probability density function distribution for the wave-4 amplitudes is narrower and steeper, and has higher maximum during QRA days, as compared to non-resonance periods. According to the results of our calculations, the QRA quasi-stationary wave-4 developed  within the corresponding waveguides (cf. 18,20,21 ) in early April at latitudes 35°N-55°N, and then again in the second half of April around latitudes 40°N, 55°N and 65°N (see Fig. 6a). Both detected events are associated with low phase speed and very high amplitude (higher than 1.5 SD from 1980-2016 climatology) of this wave.
In agreement with what we discussed in the beginning of this section of Results the meridional exchange of atmospheric planetary wave action (energy) between tropics and the extra-tropical latitudes was small during the periods of occurrence (marked in black in Fig. 6b) of high-amplitude quasi-stationary QRA wave-4 in MAM 2016. Fig. S2 in SI shows the example of such situation that emerged on the eve of the Fire. In this figure, locking of the resonant QRA wave-4 is traced by close to zero values of the meridional velocity at 300 hPa over subtropical belt at ca. 25°N-35°N. Under these circumstances, the above-mentioned wave-4AS system of four high-amplitude anticyclones began to drive -in concert with a very strong El Niño 2015-16 -highly fire-hazardous, tinder-dry and warm temperature conditions over respective regions of the NH marked by labels in Fig. 1a so unusually early, already in April (see Fig. 2 and Fig. S1). This just favored the ignition of strong wildfires at the onset of May not only over Canada, but also over a broad 45N-70N belt of the NH. Indeed, May-June of 2016 featured outbreaks of simultaneous, closely linked (concatenated) forest and steppe wildfires favored by wave-4AS (see, e.g., 23,24 ).

Statistical correlations between Canadian wildfire activity and large-scale atmospheric weather/ climate characteristics.
To get an estimation of the depth of correlation between the Canadian wildfire activity in April with ENSO we show a table (hereafter, Table 1) of Pearson coefficients of correlation, r, of 3-monthly running means (ONI-NDJ to ONI-MAM) of the ONI ENSO Index 2,3 with monthly numbers of the Each column in Table 1 shows the values of r that we obtained with the use of respective 3-monthly moving average value of ONI, from November-December-January (ONI-NDJ column) of the previous year up to March-April-May (ONI-MAM column) of the current year.
As seen from Table 1 the maximum coefficient of correlation, r max , between ONI and MNWA is reached, when using in respective calculations ONI-DJF for the Alberta Province (r max ≈ 0.324), and ONI-JFM for Canada as a whole (r max ≈ 0.267). This indicates a rather low correlation between ONI and MNWA. The conclusion is supported by the analysis of the individual years. E.g., according to 25 the numbers of strong wildfires over Canada in Aprils of 1980Aprils of , 1987Aprils of , 1991Aprils of , 2006 and 2010 with weak and moderate El Niño 2,3 , as well as in April of 1988 with strong La Niña 2,3 , exceeded those in Aprils of 1982-1983 and 1997-1998 with very strong El Niño. This points to an important contribution to MNWA from specific hydrological and vegetation cover conditions over a given region in a particular year/month (see, e.g., 26 ), as well as the amount of snowfall in the previous winter and snow melting in the spring's eve. Here we show that one more important factor regulating MNWA can be the large-scale structure of the atmospheric circulations over the mid-and sub-polar latitudes of the NH.
In this context, our calculations reveal a significant correlation between MNWA and monthly H 300 averaged over Alberta and all-Canada for Aprils of 1980-2016, with r about 0.67 for all-Canada and 0.62 for Alberta. On the other hand, our calculations show that due to the quasi-geostrophic relation 27 (1) 300 300 and the hypsometric equation 27 where a is the Earth's radius. In our calculations, we put N = 9, as the number of the main components (cf. Fig. 4a,b) in the meridional velocity longitudinal Fourier decomposition. A significant Pearson correlation (with r about 0.6-0.7) is found between MNWA and 〈LC N (x, y)〉 A (with 〈X〉 A as the area average of X over the region). Importantly, Pearson correlation coefficients appear to be low (below 0.2) between MNWA and the amplitude of any individual wave from the above planetary wave set. This emphasizes the importance of taking into account, in the general case, not only the amplitudes but also the phases of the considered waves and the need for the full wave-ensemble description of the main waves when calculating the above correlation. Note, that the weighing factor n 2 in the first summand in the r.h.s. of equation (3) accounts for the application in our calculations of the geostrophic approximation (1). Omitting 1/n 2 weighing factor in equation (3) Fig. 6). Secondly, as far as the height H 300 of the 300 hPa surface over Canada in Aprils appeared to be rather closely correlated with the number of the Canadian wildfires (see above), we may assume that the abnormally high altitude of the 300 hPa surface in April 1980 over Alberta could be accompanied by a markedly high number of wildfires in the Province in that month. In this connection, according to 25  because of low values of both H 300 (x, y) and LC N (x, y) in Aprils 1983 and 2012 (noticeably below mean + 1.5 SD from the 1980-2016 climatology, see Fig. 3a), we can anticipate a rather low values of MNWA in Aprils of these two years. Indeed, MNWA was only 86 25 over Alberta in April 1983, and in April 2012 it was 122 25 , which is lower than 1980-2016 climatology (123, according to 25 ). This happened, despite very high values of the wave-4 amplitude in those two Aprils (see Fig. 3c). This fact indicates, again, that a full set of main planetary waves with phase positions and regional thermodynamical conditions should be accounted for when estimating correlations between MNWA and climate characteristics.
Statistical estimations of the numbers of wildfires do not always track the area burnt and strongly depends on the prescribed minimum size. In this connection, with ca. 590,000 hectares burnt the Fire is Canada's fourth largest fire on record 25 contributing to the ca. 634,000 ha burnt in Alberta in 2016 25 . April is usually the start of the fire season, where in the anomaly years 770 ha (2010; 5392 ha in May) or 3575 ha (2006; 3193 ha in May) forests were burnt in Alberta, whereas on average ca 800 ha (74000 ha) were burnt in April (May) in 1990-2015 25 . Burnt area is not only influenced by fire weather conditions, including wind, but also orography, fuel load, flammability of the dead and living biomass, and forest structure. Therefore, MWNA do not necessarily lead to maximum area burnt, with the exception of the Fire which contributed approximately 96% (42%) to the annual area burnt in Alberta (Canada) in 2016.

Discussion
In our analysis, we find that the anomalously high-amplitude quasi-stationary QRA wave-4 in April-May 2016 could be one of the factors favoring the ignition and geographic localization of the Fire in May-June 2016. This wave-4 could also trigger the occurrence of wave-4AS in April-June 2016, contributing to the generation of strong forest and steppe wildfires over the land masses in respective regions 23,24 and favoring the wavy structure of the extratropical jets in the NH.
The approach proposed here allows us to estimate a probability of the climate-forced trends of regional MNWA linked to the change of "global" parameters, T [ ] H 0 300 and 〈LC N (x, y)〉 A . Analogous estimations can be applied to other months and land areas susceptible to high wildfire activity. This might be especially useful in the studies on probability of strong wildfires and their trends under different future climate change scenarios.
Let us note that Lagerquist et al. (2017) developed recently a first machine-learning model for the goal of extreme fire weather prediction over Northern Alberta, using regional self-organizing maps (SOMs), with sea-level pressure and 500 hPa height as the predictors 28 . Employing the analogous weather predictors as in 28 , we use the information on the large-scale structure of dynamic and thermodynamic atmospheric fields in the NH middle and sub-polar latitudes.
We may speculate that recently observed slow-down of the NH mid-latitude zonal circulation due to Arctic amplification 29 could increase the occurrences of the enlarged 〈LC N (x, y)〉 A leading to the growing danger of extreme wildfires. This hypothesis is supported by the fire weather situation that was observed over the NH midand subpolar latitudes in August-September 2017. A very high-amplitude quasi-stationary (QRA) wave-4 reined there again in the middle and high troposphere 13 , being accompanied by the wave-4AS (see Fig. S6), with the fire weather situation featured in that case by the exceptional in number extreme wildfires in western Greenland 30 .
In the end let us note that tracking of strongly amplified QRA planetary waves on 10-day-to-monthly time scale using the QRA-detection-scheme developed in 20 , 21 , and applying equations (1)-(3) for the estimation of the correlations between 〈LC N (x, y)〉 A and MNWA suggested here, could be rather useful for and gradually be incorporated into the practical work of the wildfire forecasters. This is because the spatial structure of these resonant waves can dictate locations of very strong anticyclonic circulations, favoring high wildfire hazard in corresponding regions.

Methods
This section provides an overview of the basic methods used here to obtain the main results. The geographic maps of the azonal component of the relative vorticity and the vector field of the extratropical atmospheric jets at 300 hPa pressure level shown in Fig. 1a and b, respectively, as well as the graphs for the surface temperature and soil moisture over Alberta ( Fig. 2a and b) are created applying the appropriate time series of the 15-day running means of these variables calculated based on daily NCEP-NCAR reanalysis data for April-May 2016 13 . Figures 3c,  4a,b and 5a,b are plotted using a Fourier decomposition method to the respective longitudinal distributions of monthly meridional velocity at 300 hPa level in the NH based on daily NCEP-NCAR reanalysis data 13 for Aprils of different years over the 1980-2016 time range. Figure 6a-f demonstrate the results obtained here, applying the physical mechanism and the methodology of the Quasi-Resonant-Amplification (QRA) of the quasi-stationary atmospheric planetary waves proposed in 18 , to planetary wave-4 at 300 hPa for March-April-May of the years covering 1979-2016 with the usage of the automated QRA-detection scheme developed in 20,21 . In Results and Discussion we describe the results of our analysis, in terms of the Pearson correlation coefficients, of the statistical relationships between wildfire activity in the fire-susceptible NH regions and the parameters of the NH large-scale planetary-wave atmospheric circulation and the ENSO indices.

Conclusions
We showed noticeable contribution of the large-scale planetary wave circulations in the mid/high troposphere of the NH extra-tropics to the ignition of strong forest and steppe wildfires over Canada. We found that the anomalously high-amplitude QRA wave-4 was one of the important factors favoring the catastrophic wildfire in the Alberta Province of Canada in May-June 2016. This wave-4 also triggered the occurrence in April-June 2016 of the chain of strong anticyclonic circulations over western Canada, eastern North Atlantic/western Greenland/ British Islands, Siberia/Mongolia, and the Russian Far East. These, in turn, led to the ignition in respective land areas of synchronous strong wildfires encircling the NH and favored the observed wavy structure of the NH SCieNtifiC RePoRTS | (2018) 8:12375 | DOI:10.1038/s41598-018-30812-z extratropical jets. Generally, the results of our statistical analysis indicate that strong wildfires over Alberta and all-Canada appear to be noticeably linked to a set of large-scale quasi-stationary resonant planetary waves in the NH extra-tropics. Data availability. All data used for this research was downloaded from public sources, as referenced throughout the text. Data and processing scripts are stored in PIK's long-term archive, and will be made available to interested parties upon request. All plots and maps shown were created by the authors.