SUMMARY OF EXPLAINED VARIANCE

 For each principal component region, variances are calculated in this script. The maximum available period is the period in which all the MBH98 sites are available as summarized here. The overlap period is the common period between the available period and the MBH period.  Total variance is calculated for both periods. In the Texas-Oklahoma case, the overlap period and the maximum available period are close and there is little difference in this quantity.  The "recalculated" principal components and eigenvectors are calculated using a standard R-algorithm; these are expanded and the unexplained variance calculated.  For MBH, the eigenvectors are calculated to maximize explained variance using the qr-function in R. The explained variance using MBH principal components is then calculated.  The extremely low explained variance for the MBH Texas-Mexico principal components - 5% for 9 principal components and only 20 sites - was the stimulus for the present analysis.  If the collation errors are fixed in this series, the explained variance increases to 41%, but in no case is the MBH calculation correct. 

  Maximum Available Period Overlap Period
  Total Variance Unexplained Variance Total Variance Unexplained Variance
  Recalculated MBH   Recalculated MBH
Texas-Oklahoma                    3,949                     1,526                  1,914                 3,916            1,510         1,898
Texas-Mexico                    4,341                        745                  4,107                 4,341               745         4,107
ITRDB US                  81,313                   48,147                67,647               52,019          28,790        44,542
South America                    7,273                     4,050                  4,965                 3,912            1,983         2,517
Australia                    5,585                     2,715                  3,085                 3,808            1,776         2,044
           
  Explained Variance (%)   Explained Variance (%)
  Recalculated MBH   Recalculated MBH
Texas-Oklahoma   61% 52%   61% 52%
Texas-Mexico   83% 5%   83% 5%
ITRDB US   41% 17%   45% 14%
South America   44% 32%   49% 36%
Australia   51% 45%   53% 46%