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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
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
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
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
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
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

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  • 1. October 18 the ‘detrended’ ring-widthThe 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 OFAGGREGATE TREE GROWTHAny individual tree-growth series can be "decomposed" into aset of environmental signals that affected the tree’s growththrough its lifespan.
  • 5. Tree-ring width datatree 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 GROWTHRt = At + Ct + δD1t + δD2t + Et
  • 10. helps us THINK about signals in tree ringsa conceptual model of tree growth NOT used for CALCULATIONS
  • 11. Earlywood LatewoodTotal ring-width Eastern hemlock Tsuga canadensis
  • 12. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et = tree growth in year ‘t’
  • 13. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et size-related growth trend caused by physiological aging
  • 14. Artist: Giuseppe Penone
  • 15. Ring width Tree age
  • 16. Atdoes not have a universal or predictable shape.
  • 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. 10.0 7.5 At = a × exp-bt +k5.0 2.5 0 0 25 50 75 100
  • 19. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et climate during year ‘t’
  • 20. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et
  • 21. Source: United States Forest Service
  • 22. Source: Eli Sagor
  • 23. A disturbance is a temporary event that causes amajor change in the structure of an ecosystem.
  • 24. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et disturbance within the forest
  • 25. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et disturbance from outside the forest
  • 26. δD1t + δD2tBoth disturbance terms include a value for ‘delta’, which can be either ‘0’ (no disturbance) or ‘1’ (disturbance).
  • 27. THE PRINCIPLE OF AGGREGATE TREE GROWTHRt = At + Ct + δD1t + δD2t + Et random processes not accounted by other sources
  • 28. Rt = At + Ct + δD1t + δD2t + Et
  • 29. SIGNAL vs. NOISE
  • 30. Rt = At + Ct + δD1t + δD2t + Et
  • 31. never trust one tree
  • 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. 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
  • 56. GEOG5839 XT C L AS S NESource: Danny Margoles

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