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READING
     Dendroclimatology
             Brian Luckman

Encyclopedia of Quaternary Sciences, 2006
READING
A conceptual linear aggregate model
          for tree rings
                   Ed Cook

       Methods of Dendrochronology, 1990
“   We’re all restless teens when some authority figure
    with an overhead projector starts yammering.             ”
                                              Noel Murray
                                             The A.V. Club
observation
The Central England Temperature record is
                  the longest instrumental record of temperature in the world.
      Degrees celsius relative to the long-term mean




Source: Parker et al., Journal of Climate, 1992
Source: Goddard Institute for Space Studies, NASA
The number of climate stations recording air temperature
                                 falls off rapidly prior to AD 1900.

       Number of stations in the Northern Hemisphere




Source: Jones et al., Journal of Geophysical Research, 2012
anecdote   <   observations   <<
CLIMATE HISTORY OF NORTH AMERICA

                    Younger              Demise of Laurentide
                     Dryas                    Ice Sheet

    20         16     12             8                4              0

                                                                         THOUSANDS OF
                                                                         YEARS AGO




                              Final Drainage
                              of Lake Agassiz
LAST GLACIAL                                                      MODERN
  MAXIMUM                                                       OBSERVATIONS
CLIMATE PROXIES
               ice cores
              tree rings
        lake sediments
          speleothems
                  corals
PALEOCLIMATOLOGY
the study of climate prior to the period of instrumental measurement
Source: Tim Shanahan, University of Texas at Austin
Source: Geological Survey of Canada
Source: LACCORE, University of Minnesota
OBSERVATIONS   PROXIES   MODELS
READING
       Holocene perspectives
      on future climate change
                    Ray Bradley

Natural Climate Variability and Global Warming, 2008
“   Tree-ring analysis is one of the most powerful tools
    available for the study of environmental change
    and the identification of fundamental relationships
                                                                    ”
    between tree growth and climate.

                                       Ed Cook and Neil Pederson
                                 Lamont-Doherty Earth Observatory
“   RINGS
                     ”
    IN THE BRANCHES OF
    SAWED TREES SHOW
THE NUMBER OF YEARS
  AND, ACCORDING TO THEIR
     THICKNESS,
   THE YEARS WHICH WERE
        MORE OR LESS
          DRY.
      Leonardo da Vinci
“   The trees composing the forest rejoice and
    lament with its successes and failures and
    carry year by year something of its story in
                                                   ”
    their annual rings.

    A. E. Douglass
    University of Arizona
755 m3/s

847 m 3/s

809 m 3/s

770 m 3/s

823 m 3/s

787 m 3/s

901 m3/s
      3
5
COMPONENTS
OF DENDROCLIMATOLOGY
ACTIVITY TIMELINE
ACTIVITY TIMELINE
Obtaining tree-ring data
ACTIVITY TIMELINE


 Understanding COFECHA
ACTIVITY TIMELINE
     The physical basis for dendroclimatology
ACTIVITY TIMELINE


        Using ARSTAN
ACTIVITY TIMELINE
               Assessing chronology quality
Source: Baillie (1982)
?1
Where (and how) can we obtain
       tree-ring data?
DOWNLOAD THESE DATA


   Bear Canyon West (NM586)        Rito de los Frijoles (NM501)

Fenton Lake Recollection (NM587)         Baca (NM558)

      Los Alamos (NM044)           Abouselman Spring (NM555)

      Los Alamos (NM046)               Cat Mesa (NM556)
h p://www.ldeo.columbia.edu/tree-ring-laboratory/resources/so ware
www.twi er.com/sco stgeorge
?2
    How can we tell if publicly-available
ringwidth measurements are good quality?
COFECHA
“   The main purpose of Program COFECHA
    is the identification of [tree-ring] data
    that should be reexamined for possible error.
                                                            ”
                                         Richard Holmes
                                  Tree-Ring Bulletin 1983
READING
 Computer-assisted quality control
in tree-ring dating and measurement
             Richard Holmes

          Tree-Ring Bulletin, 1983
COFECHA ‘master’ chronology
CAT011



COFECHA ‘master’ chronology
CAT011



COFECHA ‘master’ chronology
CAT011



COFECHA ‘master’ chronology
CAT011



COFECHA ‘master’ chronology
EXERCISE
  Use COFECHA to confirm that our sets of
ringwidth measurements are dated correctly.
QUALITY CONTROL THESE DATA


   Bear Canyon West (NM586)        Rito de los Frijoles (NM501)

Fenton Lake Recollection (NM587)         Baca (NM558)

      Los Alamos (NM044)           Abouselman Spring (NM555)

      Los Alamos (NM046)               Cat Mesa (NM556)
755 m3/s

847 m 3/s

809 m 3/s

770 m 3/s

823 m 3/s

787 m 3/s

901 m3/s
      3
?3
Why should tree-ring variables
 be connected to climate?
Pinus spp.

Source: Paul Schulte
TEMPERATURE

high growth




low growth
              cold          hot
TEMPERATURE

high growth
                        frozen water
              low photosynthetic rate
              shorter growing season




low growth
                  cold                  hot
TEMPERATURE

high growth
                            low photosynthetic rate
                            higher evaporation




low growth
              cold                     hot
“
The growth of trees is undoubtably controlled more by
the movement of water than by the movement of any
other single substance.”
                               Hal Fri s
                               Tree Rings and Climate
WATER

high growth




low growth
              dry           wet
WATER

high growth
                reduced cell division
              reduced cell expansion
                      C02 starvation




low growth
                 dry                    wet
WATER

high growth
                            flooding
                            anoxic conditions




low growth
              dry                         wet
Climate acts to synchronize growth rates
at the level of the cell, the tree, the forest and beyond.
READING
How well understood are the processes
 that create dendroclimatic records?
   Eugene Vaganov, Kevin Anchukaitis and Michael Evans

                 Dendroclimatology, 2012
EARLYWOOD AND LATEWOOD WIDTH

  MAXIMUM LATEWOOD DENSITY

  VESSEL SIZE AND DISTRIBUTION

      WOOD BIOCHEMISTRY

        STABLE ISOTOPES

       TOTAL RING WIDTH
Tree-ring display at elementary school




                                    Photograph:Tom Swetnam
?4
How do we extract climate information
      from a (complex) set of
     tree-ring measurements?
TREE-RING WIDTH DATA
pith




                        bark
“ THERMOMETERS ”
 TREES ARE NOT
 OR RAIN GAUGES.
    Keith Briffa and colleagues
Ed Cook Lamont-Doherty Earth Observatory
THE PRINCIPLE OF
AGGREGATE TREE GROWTH
READING
The decomposition of tree-ring series
     for environmental studies
                  Ed Cook

           Tree-Ring Bulletin, 1987
THE PRINCIPLE OF AGGREGATE TREE GROWTH




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




Rt = At + Ct + δD1t + δD2t + Et

                         random processes
                   not accounted by other sources
SIGNAL vs. NOISE
THE PRINCIPLE OF AGGREGATE TREE GROWTH




Rt = At + Ct + δD1t + δD2t + Et
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
never trust
   one tree
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.
THE PRINCIPLE OF AGGREGATE TREE GROWTH




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




             Tree age
At
does 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 determinstic process.
                                                          ”
                                              Ed Cook
                                Tree-Ring Bulletin 1987
STANDARDIZATION
READING
Standardization of tree-ring data
              Ray Bradley

         Paleoclimatology, 1999
“   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
(A) the ‘raw’
ring-width data
(B) the ‘detrending’ curve
DIVIDE
(A) the raw ring-width data
by (B) the ‘detrending’ curve
the ‘detrended’
  ring-width
     index
“   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
ARSTAN
  autoregressive
  standardization
PROGRAM ARSTAN

 PRODUCES CHRONOLOGIES
    FROM TREE-RING MEASUREMENT SERIES

BY DETRENDING AND INDEXING
       (STANDARDIZING) THE SERIES,
             THEN APPLYING

    A ROBUST ESTIMATION
OF THE MEAN VALUE FUNCTION
         TO REMOVE EFFECTS OF
    ENDOGENOUS STAND DISTURBANCES.
DIVIDE
(A) the raw ring-width data
by (B) the ‘detrending’ curve
ARSTAN OUTPUT
CHRONOLOGY
EXERCISE
    Use several different detrending methods
to standardize our set of ring-width chronologies
                   and let’s see what happens!
STANDARDIZE THESE DATA


   Bear Canyon West (NM586)        Rito de los Frijoles (NM501)

Fenton Lake Recollection (NM587)         Baca (NM558)

      Los Alamos (NM044)           Abouselman Spring (NM555)

      Los Alamos (NM046)               Cat Mesa (NM556)
USE FOUR DIFFERENT APPROACHES
      TO STANDARDIZATION
             Horizontal line
       Negative exponential curve
           20-yr flexible spline
Flexible spline set to 67% of series length
How should we plot our results?
DPL : YUX
WHO WILL FIND THE FIRST

                     “DIRTY DOG”?
Source: Terry Bain
USE FOUR DIFFERENT APPROACHES
      TO STANDARDIZATION
             Horizontal line
       Negative exponential curve
           20-yr flexible spline
Flexible spline set to 67% of series length
Pinus longaeva in western North America show a recent increase in
                growth even without any standardization to remove age-effects.




Source: Saltzer et al., Proceedings of the National Academy of Sciences, 2009
READING
   Recent unprecedented tree-ring
   growth in bristlecone pine at the
highest elevations and possible causes
  Ma hew Salzer, Malcolm Hughes, Andy Bunn and Kurt
                     Kipfmeuller

  Proceedings of the National Academy of Sciences, 2009
THE ‘SEGMENT-LENGTH’


CURSE
READING
  The ‘segment-length curse’ in long
tree-ring chronology development for
    palaeoclimatic reconstruction
Ed Cook, Keith Briffa, David Meko, Donald Graybill and Gary
                       Funkhouser

                   The Holocene, 1995
The maximum wavelength of recoverable climatic information
  is related to the lengths of the individual tree-ring series
       used to construct the millennia-long chronology.
LOWEST RESOLVABLE FREQUENCY




3/n when n represents the average lengths of
     segments that make up the chronology
the ‘detrended’
  ring-width
     index
Autocorrelation describes the correlation of a
time series with its own past and future values.
Ringwidth
       lag-0 autocorrelation                        3

                                                    2

                                                    1

                                                    0

                                                    -1

                                                    -2

                                                    -3
1900        1920     1940      1960   1980   2000
                       Year (A.D.)
Ringwidth
       lag-1 autocorrelation                        3

                                                    2

                                                    1

                                                    0

                                                    -1

                                                    -2

                                                    -3
1900        1920     1940      1960   1980   2000
                       Year (A.D.)
Ringwidth
       lag-2 autocorrelation                        3

                                                    2

                                                    1

                                                    0

                                                    -1

                                                    -2

                                                    -3
1900         1920    1940      1960   1980   2000
                       Year (A.D.)
Ringwidth
   lag-3 autocorrelation                        3

                                                2

                                                1

                                                0

                                                -1

                                                -2

                                                -3
1900     1920    1940      1960   1980   2000
                   Year (A.D.)
covariance




                        product of
                  the standard deviation

Autocorrelation
The spectrum of a time series describes
the distribution of variance of the series
as a function of frequency.
yellow
violet   blue   green      orange   red
yellow
 violet   blue   green      orange     red




   short                                long
wavelengths                          wavelengths
yellow
violet    blue   green      orange   red




  Fast                                 slow
changes                              changes
4
            example of a ‘white’ time series
3


2


 1


0


-1


-2


-3

200   250       300        350       400       450   500
4
            example of a ‘red’ time series
3


2


 1


0


-1


-2


-3

200   250      300        350       400      450   500
4
            example of a ‘blue’ time series
3


2


 1


0


-1


-2


-3

200   250      300        350        400      450   500
“White”
“Red”
“Blue”
IF a time series (of length N) is
significantly autocorrelated, then:

    The series is not random in time
    Each observation is not independent
    from other observations
    The number of independant
    observations is fewer than N
STANDARD


RESIDUAL
CAT MESA, NEW MEXICO

‘Standard’ chronology




‘Residual’ chronology
?YEAH, BUT
WHICH CHRONOLOGY
    SHOULD I USE?
PDO index                              Mexican PDSI
3                                                      10

2
                                                       5
 1

0                                                      0

-1
                                                       -5
-2

-3                                                     -10
     1900   1920   1940   1960   1980        2000
The “effective sample size” is an estimate of
the “real” number of observations a er
adjusting for the effects of autocorrelation.
sample
                         size



  effective
   sample
    size
                                    first-order
                                autocorrelation

Effective sample size
?5
How can we determine if the common signal
             embedded within
     a set of tree-ring measurements
            is strong or weak?
?
To what degree does the chronology represent
   the hypothetical population chronology?
r      bt
The mean inter-series correlation calculated
between all possible pairs of indexed series
       drawn from different trees.
How self-similar is this set of detrended ring-width measurements?
How self-similar is this set of detrended ring-width measurements?




                           r = 0.51
                             bt
EPS
quantifies the degree to which this particular chronology
    portrays the hypothetically perfect chronology.
EPS = f(rbt, t)
CAT MESA, NEW MEXICO

‘Standard’ chronology




‘Residual’ chronology
READING
 On the average value of correlated time
       series, with applications in
dendroclimatology and hydrometeorology
          Tom Wigley, Keith Briffa and Phil Jones

     Journal of Climate and Applied Meteorology, 1984
READING
Millennial precipitation reconstruction
for the Jemez Mountains, New Mexico,
    reveals changing drought signal
Ramzi Touchan, Connie Woodhouse, Dave Meko and Craig Allen

          International Journal of Climatology, 2011
PRODUCE CHRONOLOGIES
              FOR THESE DATA

   Bear Canyon West (NM586)        Rito de los Frijoles (NM501)

Fenton Lake Recollection (NM587)         Baca (NM558)

      Los Alamos (NM044)           Abouselman Spring (NM555)

      Los Alamos (NM046)               Cat Mesa (NM556)
Building tree-ring chronologies and Program ARSTAN

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Building tree-ring chronologies and Program ARSTAN

  • 1. READING Dendroclimatology Brian Luckman Encyclopedia of Quaternary Sciences, 2006
  • 2. READING A conceptual linear aggregate model for tree rings Ed Cook Methods of Dendrochronology, 1990
  • 3.
  • 4. We’re all restless teens when some authority figure with an overhead projector starts yammering. ” Noel Murray The A.V. Club
  • 5.
  • 7.
  • 8. The Central England Temperature record is the longest instrumental record of temperature in the world. Degrees celsius relative to the long-term mean Source: Parker et al., Journal of Climate, 1992
  • 9. Source: Goddard Institute for Space Studies, NASA
  • 10. The number of climate stations recording air temperature falls off rapidly prior to AD 1900. Number of stations in the Northern Hemisphere Source: Jones et al., Journal of Geophysical Research, 2012
  • 11. anecdote < observations <<
  • 12. CLIMATE HISTORY OF NORTH AMERICA Younger Demise of Laurentide Dryas Ice Sheet 20 16 12 8 4 0 THOUSANDS OF YEARS AGO Final Drainage of Lake Agassiz LAST GLACIAL MODERN MAXIMUM OBSERVATIONS
  • 13.
  • 14. CLIMATE PROXIES ice cores tree rings lake sediments speleothems corals
  • 15. PALEOCLIMATOLOGY the study of climate prior to the period of instrumental measurement
  • 16. Source: Tim Shanahan, University of Texas at Austin
  • 19. OBSERVATIONS PROXIES MODELS
  • 20.
  • 21. READING Holocene perspectives on future climate change Ray Bradley Natural Climate Variability and Global Warming, 2008
  • 22.
  • 23.
  • 24. Tree-ring analysis is one of the most powerful tools available for the study of environmental change and the identification of fundamental relationships ” between tree growth and climate. Ed Cook and Neil Pederson Lamont-Doherty Earth Observatory
  • 25. RINGS ” IN THE BRANCHES OF SAWED TREES SHOW THE NUMBER OF YEARS AND, ACCORDING TO THEIR THICKNESS, THE YEARS WHICH WERE MORE OR LESS DRY. Leonardo da Vinci
  • 26. The trees composing the forest rejoice and lament with its successes and failures and carry year by year something of its story in ” their annual rings. A. E. Douglass University of Arizona
  • 27. 755 m3/s 847 m 3/s 809 m 3/s 770 m 3/s 823 m 3/s 787 m 3/s 901 m3/s 3
  • 32. ACTIVITY TIMELINE The physical basis for dendroclimatology
  • 33. ACTIVITY TIMELINE Using ARSTAN
  • 34. ACTIVITY TIMELINE Assessing chronology quality
  • 35.
  • 36.
  • 38.
  • 39. ?1 Where (and how) can we obtain tree-ring data?
  • 40.
  • 41.
  • 42.
  • 43. DOWNLOAD THESE DATA Bear Canyon West (NM586) Rito de los Frijoles (NM501) Fenton Lake Recollection (NM587) Baca (NM558) Los Alamos (NM044) Abouselman Spring (NM555) Los Alamos (NM046) Cat Mesa (NM556)
  • 44.
  • 45.
  • 48.
  • 49. ?2 How can we tell if publicly-available ringwidth measurements are good quality?
  • 50.
  • 51.
  • 52.
  • 54. The main purpose of Program COFECHA is the identification of [tree-ring] data that should be reexamined for possible error. ” Richard Holmes Tree-Ring Bulletin 1983
  • 55. READING Computer-assisted quality control in tree-ring dating and measurement Richard Holmes Tree-Ring Bulletin, 1983
  • 56.
  • 57.
  • 58.
  • 59.
  • 60.
  • 66.
  • 67. EXERCISE Use COFECHA to confirm that our sets of ringwidth measurements are dated correctly.
  • 68. QUALITY CONTROL THESE DATA Bear Canyon West (NM586) Rito de los Frijoles (NM501) Fenton Lake Recollection (NM587) Baca (NM558) Los Alamos (NM044) Abouselman Spring (NM555) Los Alamos (NM046) Cat Mesa (NM556)
  • 69.
  • 70. 755 m3/s 847 m 3/s 809 m 3/s 770 m 3/s 823 m 3/s 787 m 3/s 901 m3/s 3
  • 71. ?3 Why should tree-ring variables be connected to climate?
  • 72.
  • 73.
  • 76. TEMPERATURE high growth frozen water low photosynthetic rate shorter growing season low growth cold hot
  • 77. TEMPERATURE high growth low photosynthetic rate higher evaporation low growth cold hot
  • 78. “ The growth of trees is undoubtably controlled more by the movement of water than by the movement of any other single substance.” Hal Fri s Tree Rings and Climate
  • 80. WATER high growth reduced cell division reduced cell expansion C02 starvation low growth dry wet
  • 81. WATER high growth flooding anoxic conditions low growth dry wet
  • 82.
  • 83. Climate acts to synchronize growth rates at the level of the cell, the tree, the forest and beyond.
  • 84.
  • 85. READING How well understood are the processes that create dendroclimatic records? Eugene Vaganov, Kevin Anchukaitis and Michael Evans Dendroclimatology, 2012
  • 86. EARLYWOOD AND LATEWOOD WIDTH MAXIMUM LATEWOOD DENSITY VESSEL SIZE AND DISTRIBUTION WOOD BIOCHEMISTRY STABLE ISOTOPES TOTAL RING WIDTH
  • 87. Tree-ring display at elementary school Photograph:Tom Swetnam
  • 88. ?4 How do we extract climate information from a (complex) set of tree-ring measurements?
  • 90. “ THERMOMETERS ” TREES ARE NOT OR RAIN GAUGES. Keith Briffa and colleagues
  • 91. Ed Cook Lamont-Doherty Earth Observatory
  • 93. READING The decomposition of tree-ring series for environmental studies Ed Cook Tree-Ring Bulletin, 1987
  • 94. THE PRINCIPLE OF AGGREGATE TREE GROWTH Rt = At + Ct + δD1t + δD2t + Et
  • 95. THE PRINCIPLE OF AGGREGATE TREE GROWTH Rt = At + Ct + δD1t + δD2t + Et disturbance within the forest
  • 96.
  • 97. THE PRINCIPLE OF AGGREGATE TREE GROWTH Rt = At + Ct + δD1t + δD2t + Et disturbance from outside the forest
  • 98.
  • 99. THE PRINCIPLE OF AGGREGATE TREE GROWTH Rt = At + Ct + δD1t + δD2t + Et random processes not accounted by other sources
  • 101. THE PRINCIPLE OF AGGREGATE TREE GROWTH Rt = At + Ct + δD1t + δD2t + Et
  • 102. 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
  • 103. never trust one tree
  • 104. 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’.
  • 105. Et can be assumed to be uncorrelated within and between trees in a stand.
  • 106. δD1t Endogenous (‘originating within’) disturbances will be random events in both space and time, if the stand of trees is large enough.
  • 107. 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.
  • 108. THE PRINCIPLE OF AGGREGATE TREE GROWTH Rt = At + Ct + δD1t + δD2t + Et size-related growth trend caused by physiological aging
  • 109. Ring width Tree age
  • 110.
  • 111. At does not have a universal or predictable shape.
  • 112. 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
  • 114. READING Standardization of tree-ring data Ray Bradley Paleoclimatology, 1999
  • 115. 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
  • 118. DIVIDE (A) the raw ring-width data by (B) the ‘detrending’ curve
  • 119. the ‘detrended’ ring-width index
  • 120. 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
  • 121. ARSTAN autoregressive standardization
  • 122.
  • 123. PROGRAM ARSTAN PRODUCES CHRONOLOGIES FROM TREE-RING MEASUREMENT SERIES BY DETRENDING AND INDEXING (STANDARDIZING) THE SERIES, THEN APPLYING A ROBUST ESTIMATION OF THE MEAN VALUE FUNCTION TO REMOVE EFFECTS OF ENDOGENOUS STAND DISTURBANCES.
  • 124. DIVIDE (A) the raw ring-width data by (B) the ‘detrending’ curve
  • 125.
  • 126.
  • 127.
  • 128.
  • 129.
  • 131.
  • 132.
  • 134.
  • 135.
  • 136. EXERCISE Use several different detrending methods to standardize our set of ring-width chronologies and let’s see what happens!
  • 137. STANDARDIZE THESE DATA Bear Canyon West (NM586) Rito de los Frijoles (NM501) Fenton Lake Recollection (NM587) Baca (NM558) Los Alamos (NM044) Abouselman Spring (NM555) Los Alamos (NM046) Cat Mesa (NM556)
  • 138. USE FOUR DIFFERENT APPROACHES TO STANDARDIZATION Horizontal line Negative exponential curve 20-yr flexible spline Flexible spline set to 67% of series length
  • 139.
  • 140. How should we plot our results?
  • 142. WHO WILL FIND THE FIRST “DIRTY DOG”? Source: Terry Bain
  • 143. USE FOUR DIFFERENT APPROACHES TO STANDARDIZATION Horizontal line Negative exponential curve 20-yr flexible spline Flexible spline set to 67% of series length
  • 144. Pinus longaeva in western North America show a recent increase in growth even without any standardization to remove age-effects. Source: Saltzer et al., Proceedings of the National Academy of Sciences, 2009
  • 145. READING Recent unprecedented tree-ring growth in bristlecone pine at the highest elevations and possible causes Ma hew Salzer, Malcolm Hughes, Andy Bunn and Kurt Kipfmeuller Proceedings of the National Academy of Sciences, 2009
  • 146.
  • 148. READING The ‘segment-length curse’ in long tree-ring chronology development for palaeoclimatic reconstruction Ed Cook, Keith Briffa, David Meko, Donald Graybill and Gary Funkhouser The Holocene, 1995
  • 149. The maximum wavelength of recoverable climatic information is related to the lengths of the individual tree-ring series used to construct the millennia-long chronology.
  • 150. LOWEST RESOLVABLE FREQUENCY 3/n when n represents the average lengths of segments that make up the chronology
  • 151. the ‘detrended’ ring-width index
  • 152. Autocorrelation describes the correlation of a time series with its own past and future values.
  • 153. Ringwidth lag-0 autocorrelation 3 2 1 0 -1 -2 -3 1900 1920 1940 1960 1980 2000 Year (A.D.)
  • 154. Ringwidth lag-1 autocorrelation 3 2 1 0 -1 -2 -3 1900 1920 1940 1960 1980 2000 Year (A.D.)
  • 155. Ringwidth lag-2 autocorrelation 3 2 1 0 -1 -2 -3 1900 1920 1940 1960 1980 2000 Year (A.D.)
  • 156. Ringwidth lag-3 autocorrelation 3 2 1 0 -1 -2 -3 1900 1920 1940 1960 1980 2000 Year (A.D.)
  • 157. covariance product of the standard deviation Autocorrelation
  • 158.
  • 159. The spectrum of a time series describes the distribution of variance of the series as a function of frequency.
  • 160. yellow violet blue green orange red
  • 161. yellow violet blue green orange red short long wavelengths wavelengths
  • 162. yellow violet blue green orange red Fast slow changes changes
  • 163. 4 example of a ‘white’ time series 3 2 1 0 -1 -2 -3 200 250 300 350 400 450 500
  • 164. 4 example of a ‘red’ time series 3 2 1 0 -1 -2 -3 200 250 300 350 400 450 500
  • 165. 4 example of a ‘blue’ time series 3 2 1 0 -1 -2 -3 200 250 300 350 400 450 500
  • 169.
  • 170. IF a time series (of length N) is significantly autocorrelated, then: The series is not random in time Each observation is not independent from other observations The number of independant observations is fewer than N
  • 172. CAT MESA, NEW MEXICO ‘Standard’ chronology ‘Residual’ chronology
  • 173. ?YEAH, BUT WHICH CHRONOLOGY SHOULD I USE?
  • 174. PDO index Mexican PDSI 3 10 2 5 1 0 0 -1 -5 -2 -3 -10 1900 1920 1940 1960 1980 2000
  • 175. The “effective sample size” is an estimate of the “real” number of observations a er adjusting for the effects of autocorrelation.
  • 176. sample size effective sample size first-order autocorrelation Effective sample size
  • 177. ?5 How can we determine if the common signal embedded within a set of tree-ring measurements is strong or weak?
  • 178.
  • 179. ? To what degree does the chronology represent the hypothetical population chronology?
  • 180.
  • 181. r bt The mean inter-series correlation calculated between all possible pairs of indexed series drawn from different trees.
  • 182. How self-similar is this set of detrended ring-width measurements?
  • 183. How self-similar is this set of detrended ring-width measurements? r = 0.51 bt
  • 184. EPS quantifies the degree to which this particular chronology portrays the hypothetically perfect chronology.
  • 186.
  • 187. CAT MESA, NEW MEXICO ‘Standard’ chronology ‘Residual’ chronology
  • 188. READING On the average value of correlated time series, with applications in dendroclimatology and hydrometeorology Tom Wigley, Keith Briffa and Phil Jones Journal of Climate and Applied Meteorology, 1984
  • 189.
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  • 192. READING Millennial precipitation reconstruction for the Jemez Mountains, New Mexico, reveals changing drought signal Ramzi Touchan, Connie Woodhouse, Dave Meko and Craig Allen International Journal of Climatology, 2011
  • 193. PRODUCE CHRONOLOGIES FOR THESE DATA Bear Canyon West (NM586) Rito de los Frijoles (NM501) Fenton Lake Recollection (NM587) Baca (NM558) Los Alamos (NM044) Abouselman Spring (NM555) Los Alamos (NM046) Cat Mesa (NM556)