Class 7, Extracting signal from tree rings

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Scott St. George

Formation Technologie Business

E XT R AC T I N G S I G N A L F R O M T R E E R I N G S

Same environmental
forcings

Similar
growth pa erns

Earlywood

Latewood

Total ring-width

Eastern hemlock
Tsuga canadensis

how do we interpret tree-ring width measurements?

THE PRINCIPLE OF
LIMITING FACTORS
The rates of biological processes in trees, including the
formation of woody cells, are constrained by the primary
environmental variable that is most limiting.

THE

LIMITING FACTOR
IS NOT THE

ONLY FACTOR
THAT INFLUENCES TREE GROWTH.

tree age
or size
climate landscape
change
forest dynamics
c
ecology

the environmental factor
of interest

SIGNAL vs. NOISE

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.

helps us THINK about
signals in tree rings

a conceptual model of tree growth

helps us THINK about
signals in tree rings

a conceptual model of tree growth

NOT used for
CALCULATIONS

THE PRINCIPLE OF AGGREGATE TREE GROWTH

Rt = At + Ct + δD1t + δD2t + Et

THE PRINCIPLE OF AGGREGATE TREE GROWTH

Rt = At + Ct + δD1t + δD2t + Et
tree growth in year ‘t’

THE PRINCIPLE OF AGGREGATE TREE GROWTH

Rt = At + Ct + δD1t + δD2t + Et
size-related growth trend
caused by physiological aging

10.0

7.5

At = a × exp-bt +k
5.0

2.5

0
0 25 50 75 100

At
does not have a universal or predictable shape.

growth trend in year ‘t’

Gt = At + δD1t + δD2t + Et
You’ll notice that your reading deﬁnes another term, Gt,
which is the sum of all growth factors OTHER than climate.

THE PRINCIPLE OF AGGREGATE TREE GROWTH

Rt = At + Ct + δD1t + δD2t + Et
climate during year ‘t’

THE PRINCIPLE OF AGGREGATE TREE GROWTH

Rt = At + Ct + δD1t + δD2t + Et

disturbance within the forest

THE PRINCIPLE OF AGGREGATE TREE GROWTH

Rt = At + Ct + δD1t + δD2t + Et

disturbance from outside
the forest

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

THE PRINCIPLE OF AGGREGATE TREE GROWTH

Rt = At + Ct + δD1t + δD2t + Et

random processes
not accounted by other sources

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
ation replication replication replication replic
ation replication replication replication replic
ation replication replication replication replic
ation replication replication replication replic

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’.

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

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

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.

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

Source: Cook et al., Earth Science Reviews, 2007

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.

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

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

THE PRINCIPLE OF
AGGREGATE TREE GROWTH

THE PRINCIPLE OF
REPLICATION

STANDARDIZATION

Class 7, Extracting signal from tree rings

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A good talk can open the doors to new collaborations, increase your chances of funding success, and make it more likely other people will respond to your ideas. But scientific presentations are too often confusing, boring, and overstuffed. Here are some suggestions, based on our experience as speakers, audience members, and presentation trainers, that we hope will make your next conference talk or seminar more enjoyable, engaging and effective.

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How long do we need to watch a river before its behavior holds no more surprises? In this country, instrumental measurements of river stage and discharge stretch back a century or more, but this observed history still provides only a rough guide to the risks of future extreme floods. In this lecture, I’ll outline how paleoflood hydrology expands our perspective on river history by combining historical, botanical, and geological evidence of earlier (and ofttimes unknown) floods. And I’ll explain how we can interpret those physical clues left behind by ancient floods to improve hazard assessments for at-risk communities, support decisions about flood infrastructure, and investigate the long-term effects of climate or land-use changes on flooding. Because what has happened before can happen again, most everyone near a river would profit by keeping a longer memory of old floods.

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Even after more than a century of coordinated monitoring, instrumental weather observations are still too short to adequately constrain decadal or multidecadal behavior in the Earth’s climate system. Leading climatologists and climate modelers have called for the wider application of high-resolution proxy records to decadal variability and prediction studies, and our community has responded by producing new paleoclimate products that specifically target this type of ‘intermediate-term’ behavior. But we now also know our medium changes that message: the biological and geological systems that encode climate information into natural archives often also alter the original ‘input’, usually due to either seasonal filtering or non-climatic persistence. In this talk, we’ll discuss some of the challenges inherent to the use of high-resolution proxies to study decadal or multi-decadal climate variability, and suggest strategies that might clarify how climate acts on those timescales. And we’ll also present a new theoretical framework that could help paleo-scientists evaluate competing ideas about the causes of decadal- or multi-decadal events known to have occurred during the past one or two millennia.

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We know from tree rings and other natural drought records that the western United States has been affected by several 'megadroughts' during the past millennium. But are these exceptionally long-lasting droughts due to unusual external forcings, or are they inevitable given a sufficiently long period of time? Here we present a statistical model that combines sea surface temperature records and drought severity statistics from the western USA, and use that tool to set out an expectation for megadrought, given no other changes in the climate system. Even though this model was trained using only modern climate data (and incorporates no information from tree rings or other proxies), it still produced megadroughts. Moreover, those simulated megadroughts were just as long-lasting, covered as large an area, and were just as severe as real megadroughts estimated from tree rings. That result means that megadroughts can occur in the western United States even if nothing else changes in the climate -- they really are just a matter of time. On the other hand, the only aspect of real-world megadroughts that the model cannot duplicate was the high number of these events during the so-called Medieval Climate Anomaly (800 to 1300 CE). So that cluster of megadroughts may have been caused by some sort of unusual climate circumstances that have not been observed by us during the past few decades. The proxy record tells us that many different kinds of exceptional or unusual climate events happened in the past. But it is often difficult to determine what caused those exceptional events because even, within a period of a thousand years, we still have very few cases. So besides being an aid to understand the causes of past megadroughts, we hope this approach can be applied to other paleoclimate records to distinguish between real interrelations between separate components of the climate system and simple coincidences.

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Class 7, Extracting signal from tree rings

1. E XT R AC T I N G S I G N A L F R O M T R E E R I N G S

2. Same environmental forcings Similar growth pa erns

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

5. Same environmental forcings Similar growth pa erns

6. Same environmental forcings Similar growth pa erns

10. TREE-RING WIDTH DATA pith bark

11. how do we interpret tree-ring width measurements?

12. THE PRINCIPLE OF LIMITING FACTORS The rates of biological processes in trees, including the formation of woody cells, are constrained by the primary environmental variable that is most limiting.

13. temperature water day length

14. THE LIMITING FACTOR IS NOT THE ONLY FACTOR THAT INFLUENCES TREE GROWTH.

15. Photograph: Andy Frasse o

16. Photograph: kevmann16

17.

18.

19.

20.

21. tree age or size climate landscape change forest dynamics c ecology

22. TREE-RING WIDTH DATA

23. SIGNAL vs. NOISE

24. the environmental factor of interest SIGNAL vs. NOISE

25. SIGNAL vs. NOISE everything else

26. SIGNAL vs. NOISE

27. SIGNAL vs. NOISE

28. 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.

29. a conceptual model of tree growth

30. helps us THINK about signals in tree rings a conceptual model of tree growth

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

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

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

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

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

36.

37. Ring width Tree age

38.

39.

40.

41. 10.0 7.5 At = a × exp-bt +k 5.0 2.5 0 0 25 50 75 100

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

43. growth trend in year ‘t’ Gt = At + δD1t + δD2t + Et You’ll notice that your reading deﬁnes another term, Gt, which is the sum of all growth factors OTHER than climate.

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

45. temperature water day length

46.

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

48.

49.

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

51.

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

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

54.

55. SIGNAL vs. NOISE

56.

57. Rt = At + Ct + δD1t + δD2t + Et

58. 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 ation replication replication replication replic ation replication replication replication replic ation replication replication replication replic ation replication replication replication replic

59. 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’.

60. never trust one tree

61.

62. mean of all trees

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

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

65. 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.

66. never trust one tree

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

68. Source: Cook et al., Earth Science Reviews, 2007

69. At is the tough one.

70.

71. 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.

72. one of the simplest cases

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

74. (A) the ‘raw’ ring-width data

75. (B) the ‘detrending’ curve

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

77. the ‘detrended’ ring-width index

78. removing At

79. THE PRINCIPLE OF AGGREGATE TREE GROWTH THE PRINCIPLE OF REPLICATION STANDARDIZATION