1. October 18 the ‘detrended’
ring-width
The linear aggregate model of tree growth
index

2. Ed Cook Lamont-Doherty Earth Observatory

3. h p://www.ldeo.columbia.edu/tree-ring-laboratory/

4. THE PRINCIPLE OF
AGGREGATE TREE GROWTH
Any individual tree-growth series can be "decomposed" into a
set of environmental signals that affected the tree’s growth
through its lifespan.

5. Tree-ring width data
tree age
or size pith
climate landscape
change bark
forest dynamics
ecology

6. SIGNAL vs. NOISE

7. the environmental factor
of interest
SIGNAL vs. NOISE

8. SIGNAL vs. NOISE
everything else

9. THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et

10. helps us THINK about
signals in tree rings
a conceptual model of tree growth
NOT used for
CALCULATIONS

12. Earlywood
Latewood
Total ring-width
Eastern hemlock
Tsuga canadensis

13. THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et
=
tree growth in year ‘t’

14. THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et
size-related growth trend
caused by physiological aging

16. Artist: Giuseppe Penone

17. Ring width
Tree age

20. At
does not have a universal or predictable shape.

21. “ At should be thought of as a nonstationary,
stochastic process which may, as a special
case, be modeled as a determinstic process.
”
Ed Cook
Tree-Ring Bulletin 1987

22. 10.0
7.5
At = a × exp-bt +k
5.0
2.5
0
0 25 50 75 100

23. THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et
climate during year ‘t’

24. THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et

25. Source: United States Forest Service

26. Source: Eli Sagor

27. A disturbance is a temporary event that causes a
major change in the structure of an ecosystem.

28. THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et
disturbance within the forest

31. THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et
disturbance from outside
the forest

33. δD1t + δD2t
Both disturbance terms include a value for
‘delta’, which can be either ‘0’ (no
disturbance) or ‘1’ (disturbance).

34. THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et
random processes
not accounted by other sources

35. Rt = At + Ct + δD1t + δD2t + Et

36. SIGNAL vs. NOISE

38. Rt = At + Ct + δD1t + δD2t + Et

39. never trust
one tree

40. ation replication replication replication replic
ation replication replication replication replic
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ation replication replication replication replic
ation replication replication replication replic
ation replication replication replication replic
ation replication replication replication replic
ation replication replication replication replic
ation replication replication replication replic

41. THE PRINCIPLE OF
REPLICATION
Making measurements from (i) more than one radius per
tree and (ii) more than one tree per site maximizes the
environmental signal and minimizes the amount of
environmental ‘noise’.

43. mean of
all trees

44. Et
can be assumed to be uncorrelated within
and between trees in a stand.

45. δD1t
Endogenous (‘originating within’) disturbances will be random events
in both space and time (if the stand of trees is large enough).

46. δD2t
o en is shared by most or all trees within a stand, but
may not be shared by all forest stands within a region.

47. Source: St. George et al.,
Quaternary Research, 2008

48. 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

49. Rt = At + Ct + δD1t + δD2t + Et

50. At
is the tough one.

52. STANDARDIZATION
“Standardization” describes a suite of mathematical methods
that a empt to remove long-term trends in ringwidth caused
by normal physiological aging processes and changes in the
surrounding forest community.

53. “ 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

54. one of the simplest cases

55. ays!
a lw
,not
im es
et
som
At = a × exp -bt +k
Changes in ringwidth due to tree age (or size)
can sometimes be approximated as
a negative exponential function.

56. 10.0
7.5
At = a × exp-bt +k
5.0
2.5
0
0 25 50 75 100

57. (A) the ‘raw’
ring-width data

58. (B) the ‘detrending’ curve

59. DIVIDE
(A) the raw ring-width data
by (B) the ‘detrending’ curve

60. the ‘detrended’
ring-width
index

61. removing At

62. “ 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

63. At
does not have a universal or predictable shape.

65. THE ‘SEGMENT-LENGTH’
CURSE

67. THE PRINCIPLE OF
CROSS-DATING
THE PRINCIPLE OF
AGGREGATE TREE GROWTH
THE PRINCIPLE OF
REPLICATION
STANDARDIZATION
THE PRINCIPLE OF
ECOLOGICAL AMPLITUDE
THE PRINCIPLE OF
SITE SELECTION

68. GEOG5839
XT C L AS S
NE
Source: Danny Margoles