Methods
Data Sources
Following analyses required tree ring widths as an indicator of growth, and a climate moisture indicator to be used to determine drought. Two separate tree ring databases were used: a version of the International Tree Ring Database (ITRDB) revised by Manvailer and Hamann in 2022, and another database for Spruce tree rings in Alberta received from the Canadian Forest Service and used by Hynes and Hamann in a 2020 study. The databases were filtered to time series with values between 1980 and 2010 within the Yukon, Northwest Territories, British Columbia, Alberta, and Saskatchewan. Climate data were retrieved from ClimateNA for each tree location (Wang, Hamann, Spittlehouse, & Carroll, 2016), (ClimateNA, 2022). Additionally, a shapefile filtered to the relevant provinces and territories was used to limit the analyses to the study area and outline provincial borders (Statistics Canada, 2016).
Detrending
Tree ring widths were detrended using the Friedman method for each time series (Friedman, 2001). Figure 3 displays an example of detrending and how the values are adjusted. A line, referred to as a spline, is calculated as a representation of average growth for each year of the tree's lifespan. This spline can be adjusted depending on the targeted degree of variation. In this case the spline is fairly loose since the desired variation is on an annual scale to highlight annual effects of drought. The values are then recalculated so that the spline is equal to one and ring widths are relative to this line (e.g. if the spline value for a year was 2mm and the ring width was 2.5mm, then the Ring Width Index (RWI) would be 1.5). This removes the effect of longer term trends so annual variations can be highlighted.
Figure 2. Example of ring width detrending. The ring widths are shown in the top graph with the spline drawn throughout. This spline can be seen again in the bottom graph, re-projected as a flat line throughout the time series. The ring widths can be seen adjusted to a Ring Width Index (RWI) in relation to that line.
Climate Moisture Index
Monthly Climate Moisture Index (CMI) was selected as the indicator for environmental moisture to find droughts. CMI is calculated as the difference between precipitation and potential evapotranspiration derived from Thornthwaite’s equation (Pereira & Paes De Camargo, 1989) and can be used as a proxy for relative moisture levels (Hogg, Barr, & Black, 2013). These monthly values were converted to periodic values by summing the CMI for June to August for each year. The average geographic distribution of annual CMI values between 1981 and 2010 can be seen in figure 2, which illustrates the relative moisture levels of each part of the study area (Wang, Hamann, Spittlehouse, & Carroll, 2016).
Figure 3. A map showing the distribution of the normal annual Climate Moisture Index (CMI) from 1981-2010 throughout Canada.
Clustering and Drought Determination
Trees were grouped using k-means clustering of a principle component analysis (PCA) based on CMI and RWI. Both RWI and CMI were converted into a wide format, standardized, negated, and joined to the same table so that each year of each factor would be represented by a variable. The CMI and RWI for each tree were then used to generate a PCA ordination so locations with similar variations were plotted closer to each other. K-means clustering created groupings based on these similarities or differences in variation.
The RWI and CMI of each year were plotted as vectors on the PCA ordination. If the vector for a year of CMI or RWI pointed towards particular plots, that indicated a significantly lower value for that vector in that year. CMI vectors with years marginally preceding (i.e. same or 1-2 years) RWI vectors pointing towards the same trees were used to indicate a relationship between low CMI and RWI, which indicated periods of drought in each cluster. These indicated events were compared to CMI and RWI patterns in the affected clusters for verification.
Resilience
Figure 4. A graph displaying Resistance (Rt), Recovery (Rc), and Resilience (Rs) in relation to the aspects they represent during drought (Lloret, Keeling, & Sala, 2011) .
Rt = Dr/PreDr
Rc = PostDr/Dr
Rs = PostDr/PreDr
Resistance(Rt), recovery(Rc), and resilience(Rs) were calculated for each instance of drought found through the cluster and drought analysis. Pre- and post-drought growth (PreDr, PostDr) were calculated as the average RWI over 2 years respectively before or after each drought event for each tree. Drought growth (Dr) was the RWI during the year(s) where growth was reduced by the drought. Resilience indices were calculated with the formulae beside figure 4 for each event and tree and then averaged by chronology.
The average of each resilience index for each species by cluster was then estimated using a regression that considered the interaction between species and cluster using the chronology averages.
Resistance represents the loss in growth during a drought event, recovery signifies the increase in growth when a tree approaches normal levels after a drought, and resistance demonstrates the relative change from pre-drought levels following an event. A graphical representation of each index and how they relate to drought timing and growth can be seen in figure 4. Representing these aspects as ratios allows for responses between different sites, trees, and events to be compared more directly (Lloret, Keeling, & Sala, 2011).