October 18                       the ‘detrended’                                   ring-widthThe linear aggregate model of...
Ed Cook Lamont-Doherty Earth Observatory
h p://www.ldeo.columbia.edu/tree-ring-laboratory/
THE PRINCIPLE OFAGGREGATE TREE GROWTHAny individual tree-growth series can be "decomposed" into aset of environmental sign...
Tree-ring width datatree age or size    pith                       climate              landscape                         ...
SIGNAL vs. NOISE
the environmental factor       of interest          SIGNAL vs. NOISE
SIGNAL vs. NOISE         everything else
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et
helps us THINK about       signals in tree ringsa conceptual model of tree growth          NOT used for          CALCULATI...
Earlywood        LatewoodTotal ring-width                   Eastern hemlock                   Tsuga canadensis
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                size-related growth trend            ...
Artist: Giuseppe Penone
Ring width             Tree age
Atdoes not have a universal or predictable shape.
“   At should be thought of as a nonstationary,    stochastic process which may, as a special    case, be modeled as a det...
10.0 7.5                At = a ×   exp-bt   +k5.0 2.5  0       0   25       50          75       100
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et                         climate during year ‘t’
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et
Source: United States Forest Service
Source: Eli Sagor
A disturbance is a temporary event that causes amajor change in the structure of an ecosystem.
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 + δD2tBoth disturbance terms include a value for    ‘delta’, which can be either ‘0’ (no     disturbance) or ‘1’ (dis...
THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et                         random processes            ...
Rt = At + Ct + δD1t + δD2t + Et
SIGNAL vs. NOISE
Rt = At + Ct + δD1t + δD2t + Et
never trust   one tree
ation   replication   replication   replication   replication   replication   replication   replication   replication   re...
THE PRINCIPLE OF              REPLICATIONMaking measurements from (i) more than one radius pertree and (ii) more than one ...
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.
Source: St. George et al.,Quaternary Research, 2008
The global network of public tree-ring width data includes measurements                        of nearly 20 million tree r...
Rt = At + Ct + δD1t + δD2t + Et
Atis the tough one.
STANDARDIZATION“Standardization” describes a suite of mathematical methodsthat a empt to remove long-term trends in ringwi...
“   Growth functions are removed by fi ing a curve to    the data and dividing each measured ring-width    value by the "ex...
one of the simplest cases
ays!                a   lw           ,not      im es    etsom           At = a ×      exp -bt     +k    Changes in ringwid...
10.0 7.5                At = a ×   exp-bt   +k5.0 2.5  0       0   25       50          75       100
(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
“   Standardization transforms the non-stationary ring-widths    in a new series of stationary, relative tree-ring indices...
Atdoes not have a universal or predictable shape.
THE ‘SEGMENT-LENGTH’CURSE
THE PRINCIPLE OF    CROSS-DATING      THE PRINCIPLE OFAGGREGATE TREE GROWTH      THE PRINCIPLE OF     REPLICATION  STANDAR...
GEOG5839              XT C L AS S                         NESource: Danny Margoles
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
GEOG5839.12, the linear aggreate model of tree growth
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GEOG5839.12, the linear aggreate model of tree growth

  1. 1. October 18 the ‘detrended’ ring-widthThe linear aggregate model of tree growth index
  2. 2. Ed Cook Lamont-Doherty Earth Observatory
  3. 3. h p://www.ldeo.columbia.edu/tree-ring-laboratory/
  4. 4. 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.
  5. 5. Tree-ring width datatree age or size pith climate landscape change bark forest dynamics ecology
  6. 6. SIGNAL vs. NOISE
  7. 7. the environmental factor of interest SIGNAL vs. NOISE
  8. 8. SIGNAL vs. NOISE everything else
  9. 9. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et
  10. 10. helps us THINK about signals in tree ringsa conceptual model of tree growth NOT used for CALCULATIONS
  11. 11. Earlywood LatewoodTotal ring-width Eastern hemlock Tsuga canadensis
  12. 12. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et = tree growth in year ‘t’
  13. 13. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et size-related growth trend caused by physiological aging
  14. 14. Artist: Giuseppe Penone
  15. 15. Ring width Tree age
  16. 16. Atdoes not have a universal or predictable shape.
  17. 17. “ 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
  18. 18. 10.0 7.5 At = a × exp-bt +k5.0 2.5 0 0 25 50 75 100
  19. 19. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et climate during year ‘t’
  20. 20. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et
  21. 21. Source: United States Forest Service
  22. 22. Source: Eli Sagor
  23. 23. A disturbance is a temporary event that causes amajor change in the structure of an ecosystem.
  24. 24. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et disturbance within the forest
  25. 25. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et disturbance from outside the forest
  26. 26. δD1t + δD2tBoth disturbance terms include a value for ‘delta’, which can be either ‘0’ (no disturbance) or ‘1’ (disturbance).
  27. 27. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et random processes not accounted by other sources
  28. 28. Rt = At + Ct + δD1t + δD2t + Et
  29. 29. SIGNAL vs. NOISE
  30. 30. Rt = At + Ct + δD1t + δD2t + Et
  31. 31. never trust one tree
  32. 32. 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
  33. 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. 34. mean ofall trees
  35. 35. Etcan be assumed to be uncorrelated within and between trees in a stand.
  36. 36. δD1tEndogenous (‘originating within’) disturbances will be random events in both space and time (if the stand of trees is large enough).
  37. 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. 38. Source: St. George et al.,Quaternary Research, 2008
  39. 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. 40. Rt = At + Ct + δD1t + δD2t + Et
  41. 41. Atis the tough one.
  42. 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. 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. 44. one of the simplest cases
  45. 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. 46. 10.0 7.5 At = a × exp-bt +k5.0 2.5 0 0 25 50 75 100
  47. 47. (A) the ‘raw’ring-width data
  48. 48. (B) the ‘detrending’ curve
  49. 49. DIVIDE(A) the raw ring-width databy (B) the ‘detrending’ curve
  50. 50. the ‘detrended’ ring-width index
  51. 51. removing At
  52. 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. 53. Atdoes not have a universal or predictable shape.
  54. 54. THE ‘SEGMENT-LENGTH’CURSE
  55. 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
  56. 56. GEOG5839 XT C L AS S NESource: Danny Margoles

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