Appendix D. Sensitivity analyses of Eq. 1 to input variables.
Over the central and eastern boreal forest, drought severity exhibits strong regional coherence, that is, drought in one region is related to drought in other regions, largely due to the common influence of the large-scale features of atmospheric circulation (Girardin et al. 2006). Therefore, it is appropriate to summarize the dominant information contained within the seven drought reconstructions into a new set of uncorrelated variables. The variability within the reconstructions may be analyzed using Principal Component Analysis (PCA) (Legendre and Legendre 1998). In this procedure, the amount of variability is described using the same number of variables, but the first principal component (PC1) accounts for the maximum possible proportion of the total variance. Succeeding PCs, in turn, account for as much of the residual variance as possible. The loading of each reconstruction on each component gives the spatial representation of the PCs.
In the current application, the leading principal component (PC1) of all seven drought records (tree-ring reconstruction + ECHAM4 A2 simulations; 1768–2100) accounts for 42.2% of the variance in the dataset. The loading of each reconstruction on PC1 is as follows:
Records | |
Boreal Plains (BP) = | |
Lac Seul Upland and Lake of the Woods (LS) = | |
Lake Nipigon (LN) = | |
Abitibi Plains west (APw) = | |
Abitibi Plains east (APe) = | |
Southern Laurentians (SL) = | |
Central Laurentians (CL) = |
Note: A correlation matrix was used for the PCA. The variance in PC1 is hence essentially centered on the Ontario regions.
The equation linking PC1 (current year and previous year lag) to FireOcc is:
(D.1) |
A total of 40.7% of the variance in FireOcc observations over the period 1959–1998 is accounted for by estimates obtained from this equation. FireOcc estimates obtained from Eq. D1 over the period 1769–2100 closely resemble those obtained from the regional drought records (see Fig. D1). The FireOcc estimates obtained from PC1 have the caveat of containing much greater serial persistence (AR1 = 0.63 as opposed to 0.30 in the original model, period 1769–2100). The same is true for FireOcc estimates obtained from the leading principal component of the July mean of the daily Drought Code indices computed from meteorological station data from 1913 to 1998.
FIG. D1. Sensitivity analyses in which calibration of Eq. 1 (see paper) was conducted on the leading principal component (PC1) of the seven drought records. FireOcc estimates account for 40.7% of the variance in FireOcc observations (verification RE = 0.36 and 0.19 and r = 0.76 and 0.58). Adjustments to the mean and variance were made so that reconstruction and simulation data had equal mean and variance over their common period 1961–1998. A similar model computed from the leading principal component of Drought Code indices calculated from meteorological station data accounted for 28.4% of the variance in FireOcc observations (verification RE = 0.07 and -0.01 and r = 0.65 and 0.53). The FireOcc estimates obtained from meteorological station data share 48% of common variance with the original FireOcc estimates (obtained from Eq. 5, see paper) over their common period 1913–1998. |
LITERATURE CITED
Legendre, P., and l. Legendre. 1998. Numerical ecology. Elsevier, New York, New York, USA.
Girardin, M. P., J. C. Tardif, M. D. Flannigan, and Y. Bergeron. 2006. Synoptic-scale atmospheric circulation and boreal Canada summer drought variability of the past three centuries. Journal of Climate 19:1922–1947.