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 environmentalforcings              Similar      growth pa erns
Earlywood        LatewoodTotal ring-width                   Eastern hemlock                   Tsuga canadensis
Same environmentalforcings              Similar      growth pa erns
Same environmental              forcingsSimilargrowth pa erns
TREE-RING WIDTH DATApith                        bark
how do we interpret tree-ring width measurements?
THE PRINCIPLE OF      LIMITING FACTORSThe rates of biological processes in trees, including theformation of woody cells, a...
temperature   water   day length
THELIMITING FACTOR          IS NOT THE ONLY FACTOR THAT INFLUENCES TREE GROWTH.
Photograph: Andy Frasse o
Photograph: kevmann16
tree age or size                   climate             landscape                                         change forest dyn...
TREE-RING WIDTH DATA
SIGNAL vs. NOISE
the environmental factor       of interest          SIGNAL vs. NOISE
SIGNAL vs. NOISE         everything else
SIGNAL vs. NOISE
SIGNAL vs. NOISE
THE PRINCIPLE OFAGGREGATE TREE GROWTHAny individual tree-growth series can be "decomposed" into aset of environmental sign...
a conceptual model of tree growth
helps us THINK about       signals in tree ringsa conceptual model of tree growth
helps us THINK about       signals in tree ringsa conceptual model of tree growth          NOT used for          CALCULATI...
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et         tree growth in year ‘t’
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et                =
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et                 size-related growth trend           ...
Ring width             Tree age
10.0 7.5                At = a ×   exp-bt   +k5.0 2.5  0       0   25      50           75       100
Atdoes 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 s...
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et                         climate during year ‘t’
temperature   water   day length
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et                       disturbance within the forest
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et                       disturbance from outside      ...
δD1t + δD2t  Both disturbance terms include a value for‘delta’, which can be either ‘0’ (no disturbance)               or ...
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et                         random processes            ...
SIGNAL  vs.  NOISE
Rt = At + Ct + δD1t + δD2t + Et
ation   replication   replication   replication   replication   replication   replication   replication   replication   re...
THE PRINCIPLE OF             REPLICATIONMaking measurements from (i) more than one radius per treeand (ii) more than one t...
never trust    one tree
mean ofall trees
Etcan be assumed to be uncorrelated within      and between trees in a stand.
δD1tEndogenous (‘originating within’) disturbances will be random events   in both space and time, if the stand of trees i...
δD2to en is shared by most or all trees within a stand, butmay not be shared by all forest stands within a region.
never trust    one tree
Source: St. George et al.,Quaternary Research, 2008
Source: Cook et al., Earth Science Reviews, 2007
Atis the tough one.
STANDARDIZATION“Standardization” describes a suite of mathematical methodsthat a empt to remove long-term trends in ringwi...
one of the simplest cases
ays!                a   lw           ,not      im es om ets           At = a ×      exp -bt     +k    Changes in ringwidth...
(A) the ‘raw’ring-width data
(B) the ‘detrending’ curve
DIVIDE(A) the raw ring-width databy (B) the ‘detrending’ curve
the ‘detrended’  ring-width     index
removing   At
THE PRINCIPLE OFAGGREGATE TREE GROWTH      THE PRINCIPLE OF     REPLICATION  STANDARDIZATION
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings
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Class 7, Extracting signal from tree rings

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Class 7, Extracting signal from tree rings

  1. 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. 2. Same environmentalforcings Similar growth pa erns
  3. 3. Earlywood LatewoodTotal ring-width Eastern hemlock Tsuga canadensis
  4. 4. Same environmentalforcings Similar growth pa erns
  5. 5. Same environmental forcingsSimilargrowth pa erns
  6. 6. TREE-RING WIDTH DATApith bark
  7. 7. how do we interpret tree-ring width measurements?
  8. 8. THE PRINCIPLE OF LIMITING FACTORSThe rates of biological processes in trees, including theformation of woody cells, are constrained by the primaryenvironmental variable that is most limiting.
  9. 9. temperature water day length
  10. 10. THELIMITING FACTOR IS NOT THE ONLY FACTOR THAT INFLUENCES TREE GROWTH.
  11. 11. Photograph: Andy Frasse o
  12. 12. Photograph: kevmann16
  13. 13. tree age or size climate landscape change forest dynamics c ecology
  14. 14. TREE-RING WIDTH DATA
  15. 15. SIGNAL vs. NOISE
  16. 16. the environmental factor of interest SIGNAL vs. NOISE
  17. 17. SIGNAL vs. NOISE everything else
  18. 18. SIGNAL vs. NOISE
  19. 19. SIGNAL vs. NOISE
  20. 20. THE PRINCIPLE OFAGGREGATE TREE GROWTHAny individual tree-growth series can be "decomposed" into aset of environmental signals that affected the tree’s growththrough its lifespan.
  21. 21. a conceptual model of tree growth
  22. 22. helps us THINK about signals in tree ringsa conceptual model of tree growth
  23. 23. helps us THINK about signals in tree ringsa conceptual model of tree growth NOT used for CALCULATIONS
  24. 24. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et
  25. 25. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et tree growth in year ‘t’
  26. 26. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et =
  27. 27. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et size-related growth trend caused by physiological aging
  28. 28. Ring width Tree age
  29. 29. 10.0 7.5 At = a × exp-bt +k5.0 2.5 0 0 25 50 75 100
  30. 30. Atdoes not have a universal or predictable shape.
  31. 31. 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.
  32. 32. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et climate during year ‘t’
  33. 33. temperature water day length
  34. 34. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et disturbance within the forest
  35. 35. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et disturbance from outside the forest
  36. 36. δD1t + δD2t Both disturbance terms include a value for‘delta’, which can be either ‘0’ (no disturbance) or ‘1’ (disturbance).
  37. 37. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et random processes not accounted by other sources
  38. 38. SIGNAL vs. NOISE
  39. 39. Rt = At + Ct + δD1t + δD2t + Et
  40. 40. ation replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replication replic
  41. 41. THE PRINCIPLE OF REPLICATIONMaking measurements from (i) more than one radius per treeand (ii) more than one tree per site maximizes theenvironmental signal and minimizes the amount ofenvironmental ‘noise’.
  42. 42. never trust one tree
  43. 43. mean ofall trees
  44. 44. Etcan be assumed to be uncorrelated within and between trees in a stand.
  45. 45. δD1tEndogenous (‘originating within’) disturbances will be random events in both space and time, if the stand of trees is large enough.
  46. 46. δD2to en is shared by most or all trees within a stand, butmay not be shared by all forest stands within a region.
  47. 47. never trust one tree
  48. 48. Source: St. George et al.,Quaternary Research, 2008
  49. 49. Source: Cook et al., Earth Science Reviews, 2007
  50. 50. Atis the tough one.
  51. 51. 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.
  52. 52. one of the simplest cases
  53. 53. ays! a lw ,not im es om ets At = a × exp -bt +k Changes in ringwidth due to tree age (or size) can sometimes be approximated as a negative exponential function.
  54. 54. (A) the ‘raw’ring-width data
  55. 55. (B) the ‘detrending’ curve
  56. 56. DIVIDE(A) the raw ring-width databy (B) the ‘detrending’ curve
  57. 57. the ‘detrended’ ring-width index
  58. 58. removing At
  59. 59. THE PRINCIPLE OFAGGREGATE TREE GROWTH THE PRINCIPLE OF REPLICATION STANDARDIZATION

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