Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
temperature   water   day length
THE PRINCIPLE OF    CROSS-DATING      THE PRINCIPLE OFAGGREGATE TREE GROWTH      THE PRINCIPLE OF     REPLICATION  STANDAR...
White pine 1714Photograph: Kurt Kipfmueller
C L I M AT E F R O M T R E E SPhotograph: RawheaD Rex
empirical Information gained by means ofobservation, experience or experiment.
Photograph: Minyoung Choi
h p://sokar.geo.umn.edu/weather/
Single-site reconstruction
A time series is a set of observationsordered in time.
time span                               resolution       10                           last century                        ...
variance a statistical measure that describes how a         set of numbers vary around their mean.         The second mome...
variance         observation                           sample                            mean        sample          size ...
10        5PDSI        0        -5       -10             1900   1920   1940    1960   1980   2000                         ...
empirical comparisons
thermometers                              tree ringsSource: Hughes et al., 1999
rain gauges                                           tree ringsSource: Hughes and Funkhouser, 1998
correlation The Pearson product-momentcorrelation coefficient is probably the singlemost widely used statistic for summarizi...
covariance           product of both standard deviationsCorrelation Pearson’s product-moment correlation
variable ‘Y’                              r = +1.0               variable ‘X’
variable ‘Y’                              r = -1.0               variable ‘X’
variable ‘Y’                          r = +0.85               variable ‘X’
Ring-width  index
“SHARED”VARIANCE
10                                                                         3                                              ...
r = 0.62r2   =   0.62 2r2   = 0.38
38% shared variance         10                                                                            3               ...
covariance           product of both standard deviationsCorrelation Pearson’s product-moment correlation
r = 0.816Source: Wikipedia
Single-site reconstruction
CORRELATION FUNCTION
Source: Kipfmueller, 2008
LINEARREGRESSION
yt = axt + b + ε
the climate variableof interest (at year t)              yt = axt + b + ε
yt = axt + b + ε     the tree-ring  variable (at year t)
regression weightfor the tree-ring     variable         yt = axt + b + ε
constantyt = axt + b + ε
yt = axt + b + ε error of the residual
yt = axt + b + ε
Ring-width  index
CLIMATERECONSTRUCTION
never trust    one tree
Multiple-site reconstruction
‘multiple’ linear regressonyt = a1x1t + a2x2t + a3x3t ... + b + ε
Network reconstruction
yt = axt + b + ε  average tree-ring width at many sites      (in year t)
‘SHARED’ VARIANCECORRELATION FUNCTION  LINEAR REGRESSIONCLIMATE RECONSTRUCTION
Tree rings can provide extra-ordinarily good estimates (sometimes)Source: Woodhouse et al., 2006
White pine 1714Photograph: Kurt Kipfmueller
GEOG3839.9: Climate from trees
GEOG3839.9: Climate from trees
GEOG3839.9: Climate from trees
GEOG3839.9: Climate from trees
GEOG3839.9: Climate from trees
Upcoming SlideShare
Loading in …5
×

GEOG3839.9: Climate from trees

568 views

Published on

Published in: Education, Technology, Business
  • Be the first to comment

  • Be the first to like this

GEOG3839.9: Climate from trees

  1. 1. temperature water day length
  2. 2. THE PRINCIPLE OF CROSS-DATING THE PRINCIPLE OFAGGREGATE TREE GROWTH THE PRINCIPLE OF REPLICATION STANDARDIZATION THE PRINCIPLE OFECOLOGICAL AMPLITUDE THE PRINCIPLE OF SITE SELECTION
  3. 3. White pine 1714Photograph: Kurt Kipfmueller
  4. 4. C L I M AT E F R O M T R E E SPhotograph: RawheaD Rex
  5. 5. empirical Information gained by means ofobservation, experience or experiment.
  6. 6. Photograph: Minyoung Choi
  7. 7. h p://sokar.geo.umn.edu/weather/
  8. 8. Single-site reconstruction
  9. 9. A time series is a set of observationsordered in time.
  10. 10. time span resolution 10 last century annual 5PDSI 0 chronological uncertainty -5 sub-annual -10 1900 1920 1940 1960 1980 2000 Year (A.D.)
  11. 11. variance a statistical measure that describes how a set of numbers vary around their mean. The second moment of a distribution.
  12. 12. variance observation sample mean sample size Variance
  13. 13. 10 5PDSI 0 -5 -10 1900 1920 1940 1960 1980 2000 Year (A.D.)
  14. 14. empirical comparisons
  15. 15. thermometers tree ringsSource: Hughes et al., 1999
  16. 16. rain gauges tree ringsSource: Hughes and Funkhouser, 1998
  17. 17. correlation The Pearson product-momentcorrelation coefficient is probably the singlemost widely used statistic for summarizingthe relationship between two variables.
  18. 18. covariance product of both standard deviationsCorrelation Pearson’s product-moment correlation
  19. 19. variable ‘Y’ r = +1.0 variable ‘X’
  20. 20. variable ‘Y’ r = -1.0 variable ‘X’
  21. 21. variable ‘Y’ r = +0.85 variable ‘X’
  22. 22. Ring-width index
  23. 23. “SHARED”VARIANCE
  24. 24. 10 3 2 5 Ringwidth 1PDSI 0 0 -1 -5 -2 -10 -3 1900 1920 1940 1960 1980 2000 Year (A.D.)St. George et al., (2009), Journal of Climate
  25. 25. r = 0.62r2 = 0.62 2r2 = 0.38
  26. 26. 38% shared variance 10 3 2 5 Ringwidth 1PDSI 0 0 -1 -5 -2 -10 -3 1900 1920 1940 1960 1980 2000 Year (A.D.)St. George et al., (2009), Journal of Climate
  27. 27. covariance product of both standard deviationsCorrelation Pearson’s product-moment correlation
  28. 28. r = 0.816Source: Wikipedia
  29. 29. Single-site reconstruction
  30. 30. CORRELATION FUNCTION
  31. 31. Source: Kipfmueller, 2008
  32. 32. LINEARREGRESSION
  33. 33. yt = axt + b + ε
  34. 34. the climate variableof interest (at year t) yt = axt + b + ε
  35. 35. yt = axt + b + ε the tree-ring variable (at year t)
  36. 36. regression weightfor the tree-ring variable yt = axt + b + ε
  37. 37. constantyt = axt + b + ε
  38. 38. yt = axt + b + ε error of the residual
  39. 39. yt = axt + b + ε
  40. 40. Ring-width index
  41. 41. CLIMATERECONSTRUCTION
  42. 42. never trust one tree
  43. 43. Multiple-site reconstruction
  44. 44. ‘multiple’ linear regressonyt = a1x1t + a2x2t + a3x3t ... + b + ε
  45. 45. Network reconstruction
  46. 46. yt = axt + b + ε average tree-ring width at many sites (in year t)
  47. 47. ‘SHARED’ VARIANCECORRELATION FUNCTION LINEAR REGRESSIONCLIMATE RECONSTRUCTION
  48. 48. Tree rings can provide extra-ordinarily good estimates (sometimes)Source: Woodhouse et al., 2006
  49. 49. White pine 1714Photograph: Kurt Kipfmueller

×