Methods
The following steps were taken to determine which populations of white spruce and lodgepole pine are the most susceptible to ongoing climate warming: 1) data collection; 2) standardizing raw tree-ring data and building chronologies; 3) correlating annual chronology ring-width values to historical monthly climate variables using a bootstrapped response function analysis; 4) using a cluster analysis to map tree populations across North America that could be the most at risk of future climate warming based on the climatic variables that are currently limiting both species.
1. Climate Data
Annual climate data according to normal (1961-1990) values as well as historical monthly data (1901-2010) were downloaded using the software ClimateWNA v4.62 (Hamann et al., 2013). These data were then sorted, standardized, and built into a master table for further analysis in ArcMap 10.5.1. and R Programming Environment (ESRI, 2011; R Core Team, 2018).
The climate variables included in this analysis are:
Directly calculated annual variables:
Mean Annual Temperature (°C)(MAT); Mean Warmest Month Temperature (°C)(MWMT); Mean Coldest Month Temperature (°C)(MCMT); Mean Annual Precipitation (mm)(MAP); Total Difference between MCMT and MWMT (°C)(TD); Mean Summer Precipitation (mm)(MSP); Annual Heat-Moisture Index (MAT+10)/(MAP/1000)(AHM); Summer Heat-Moisture Index (MWMT)/(MSP/1000)(SHM).
Derived annual variables:
Degree Days below 0°C (DD<0); Degree Days above 5°C (DD>5); Frost-Free Period (FFP); Beginning of the Frost-Free Period (bFFP); End of the Frost-Free Period (eFFP); Extreme Minimum Temperature (EMT); Precipitation as Snow (PAS); Number of Frost-Free Days (NFFD).
2. Tree-ring Data
1. Climate Data
Annual climate data according to normal (1961-1990) values as well as historical monthly data (1901-2010) were downloaded using the software ClimateWNA v4.62 (Hamann et al., 2013). These data were then sorted, standardized, and built into a master table for further analysis in ArcMap 10.5.1. and R Programming Environment (ESRI, 2011; R Core Team, 2018).
The climate variables included in this analysis are:
Directly calculated annual variables:
Mean Annual Temperature (°C)(MAT); Mean Warmest Month Temperature (°C)(MWMT); Mean Coldest Month Temperature (°C)(MCMT); Mean Annual Precipitation (mm)(MAP); Total Difference between MCMT and MWMT (°C)(TD); Mean Summer Precipitation (mm)(MSP); Annual Heat-Moisture Index (MAT+10)/(MAP/1000)(AHM); Summer Heat-Moisture Index (MWMT)/(MSP/1000)(SHM).
Derived annual variables:
Degree Days below 0°C (DD<0); Degree Days above 5°C (DD>5); Frost-Free Period (FFP); Beginning of the Frost-Free Period (bFFP); End of the Frost-Free Period (eFFP); Extreme Minimum Temperature (EMT); Precipitation as Snow (PAS); Number of Frost-Free Days (NFFD).
2. Tree-ring Data
Tree-ring data for white spruce across North America was accessed from the work of Zhao et al. (2018) where raw tree-ring data was collected and corrected from the International Tree-Ring Database (ITRDB). Using the dplR package in the R Programming Environment, tree-ring data was examined and stored in a Tucson format for 191 white spruce and lodgepole pine sites across North America (Figure 2). These sites occupy 8 broad ecozones, including the Great Plains, the Hudson Plain, the Marine West Coast Forest, North American Deserts, Northern Forests, Northwestern Forested Mountains, the Taiga, and the Tundra.
Figure 2. A map showing the location of each tree-ring chronology collected from Zhao et al. (2018) across North America according to which ecozone it occupies.
The tree-ring data for each site required data transformation to create master chronology files and emphasize inter-annual growth variations. Each raw .rwl (ring-width length) file was detrended and standardized to create tree-ring indices with a mean of 1.00 and a variance independent of age and other biological factors (Fritts, 1966). This was acheived by fitting a smoothing spline to each ring-width series and dividing the actual ringwidth by each yearly value of the fitted growth curve (Fritts, 1966). These dimensionless ring-wdith indices are then cross-dated with other trees from the same stand to build a master chronology for each white spruce and lodgepole pine site (Figure 3)(Cook & Peters, 1997). These chronologies were then used for further analysis.
Figure 3. A graph of a master chronology for white spruce at a site in northern Alaska (ak031). This graph shows the annual variation in growth according to ring-width (RWI) and sample depth (the number of trees sampled in a stand) on the y-axis as a function of time (x-axis). The red line is an example of a smoothing spline with a 50% frequency-response cut-off that captures the overall growth trend while minimizing some of the variability.
3. Analysis of Climate-Growth Associations
Using the treeclim package in R Programming Environment, static bootstrapped response functions were calculated for each chronology using historical monthly climate variables to test the significance of climate variables on annual radial tree growth (Figure 4)(Zang & Biondi, 2015). This package incorporates the monthly climate variables TAVE (average temperature) and PPT (precipitation) from June of the previous year to September of the current year as model parameters to compare to each annual growth measurement. This is important to incorporate into the model because legacy growing conditions from the previous season can influence tree growth the following year. By sub-sampling the inputted data, a calibration dataset is then applied to a verification dataset to create regression (response) coefficients and test their significance according to a 95% confidence interval.
Using the treeclim package in R Programming Environment, static bootstrapped response functions were calculated for each chronology using historical monthly climate variables to test the significance of climate variables on annual radial tree growth (Figure 4)(Zang & Biondi, 2015). This package incorporates the monthly climate variables TAVE (average temperature) and PPT (precipitation) from June of the previous year to September of the current year as model parameters to compare to each annual growth measurement. This is important to incorporate into the model because legacy growing conditions from the previous season can influence tree growth the following year. By sub-sampling the inputted data, a calibration dataset is then applied to a verification dataset to create regression (response) coefficients and test their significance according to a 95% confidence interval.
Figure 4. An output from the treeclim package showing whether average temperature or precipitation limits the growth of white spruce during different times of year at a northern Alaska site (ak031). The months that are in lower case are those of the previous year, while the months that are in upper case letters include the current year. From this graph, we can see that radial growth in this white spruce stand is positively influenced by precipitation in September and negatively influenced by temperature during July of the previous year.
4. Cluster Analysis
Using the R package cluster, an initial cluster analysis was completed using the PAM (partitioning around mediods) function to establish 6 groups based on raw annual radial growth measurements and 16 historical monthly climate variables. The climate variables used for this cluster analysis were MAT, MWMT, MCMT, TD, MAP, MSP, AHM, SHM, PAS, DD5, DD0, NFFD, bFFP, eFFP, FFP, and EMT. As seen in Figure 5, Climate Group 6 covers the largest geographical area and contains a significant overlap with Climate Group 4.
For final results, a second cluster analysis was conducted using the PAM function to cluster similar response coefficients from the response function analysis and external baseline climate variables (1961-1990 normals). This would ultimately show which populations of white spruce group together based on how their growth has been limited by the same climate variables over the last 100 years.
Using the R package cluster, an initial cluster analysis was completed using the PAM (partitioning around mediods) function to establish 6 groups based on raw annual radial growth measurements and 16 historical monthly climate variables. The climate variables used for this cluster analysis were MAT, MWMT, MCMT, TD, MAP, MSP, AHM, SHM, PAS, DD5, DD0, NFFD, bFFP, eFFP, FFP, and EMT. As seen in Figure 5, Climate Group 6 covers the largest geographical area and contains a significant overlap with Climate Group 4.
For final results, a second cluster analysis was conducted using the PAM function to cluster similar response coefficients from the response function analysis and external baseline climate variables (1961-1990 normals). This would ultimately show which populations of white spruce group together based on how their growth has been limited by the same climate variables over the last 100 years.
Figure 5. The results of a white spruce climate cluster analysis using the PAM function in the R package cluster, where 6 climate groups were created across North America based on annual radial tree growth measurements and 16 historical monthly climate variables. The two principal components account for 99.89% of the variance.
To further understand these climate-growth relationships, Walter and Lieth climate graphs were created to graphically display the relationship between temperature and precipitation for the new white spruce climate groups (Figure 6).
Figure 6. The relationships between average annual precipitation and temperature for each of the 6 white spruce climate groups. Walter and Lieth climate graphs were created to correspond to each climate group. The x-axis displays each month of the year starting from January to December. The left y-axis displays the average temperature each month in red and includes the average annual maximum and minimum temperatures. The right y-axis indicates the average precipitation received per month.
As shown above, Climate Group 2 and Climate Group 5 approach a moisture deficit period in the spring. Climate Group 6 has longest growing season overall as indicated by the positive temperatures from May to September. The shortest frost-free growing seasons exist in Climate Groups 1, 3, and 4, where only three months of the year remain consistently above 0°C.
As shown above, Climate Group 2 and Climate Group 5 approach a moisture deficit period in the spring. Climate Group 6 has longest growing season overall as indicated by the positive temperatures from May to September. The shortest frost-free growing seasons exist in Climate Groups 1, 3, and 4, where only three months of the year remain consistently above 0°C.