33. THE PRINCIPLE OF REPLICATIONMaking measurements from (i) more than one radius pertree and (ii) more than one tree per site maximizes theenvironmental signal and minimizes the amount ofenvironmental ‘noise’.
34. mean ofall trees
35. Etcan be assumed to be uncorrelated within and between trees in a stand.
36. δD1tEndogenous (‘originating within’) disturbances will be random events in both space and time (if the stand of trees is large enough).
37. δD2to en is shared by most or all trees within a stand, butmay not be shared by all forest stands within a region.
38. Source: St. George et al.,Quaternary Research, 2008
39. The global network of public tree-ring width data includes measurements of nearly 20 million tree rings at more than 3,000 locations.Source: St. George et al., unpublished
40. Rt = At + Ct + δD1t + δD2t + Et
41. Atis the tough one.
42. STANDARDIZATION“Standardization” describes a suite of mathematical methodsthat a empt to remove long-term trends in ringwidth causedby normal physiological aging processes and changes in thesurrounding forest community.
43. “ Growth functions are removed by ﬁ ing a curve to the data and dividing each measured ring-width value by the "expected" value on the growth curve. ” Ray Bradley Paleoclimatology 1999
44. one of the simplest cases
45. ays! a lw ,not im es etsom At = a × exp -bt +k Changes in ringwidth due to tree age (or size) can sometimes be approximated as a negative exponential function.
46. 10.0 7.5 At = a × exp-bt +k5.0 2.5 0 0 25 50 75 100
47. (A) the ‘raw’ring-width data
48. (B) the ‘detrending’ curve
49. DIVIDE(A) the raw ring-width databy (B) the ‘detrending’ curve
50. the ‘detrended’ ring-width index
51. removing At
52. “ Standardization transforms the non-stationary ring-widths in a new series of stationary, relative tree-ring indices that have a deﬁned mean of 1.0 and a constant variance. ” Ed Cook Tree-Ring Bulletin 1987
53. Atdoes not have a universal or predictable shape.
54. THE ‘SEGMENT-LENGTH’CURSE
55. THE PRINCIPLE OF CROSS-DATING THE PRINCIPLE OFAGGREGATE TREE GROWTH THE PRINCIPLE OF REPLICATION STANDARDIZATION THE PRINCIPLE OFECOLOGICAL AMPLITUDE THE PRINCIPLE OF SITE SELECTION