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October 18
        30                       the ‘detrended’
                                   ring-width
Signal processing I
The linear aggregate model of tree growth
                                      index
DOWNLOAD THESE DATA


    Cat Mesa (NM556)             Fenton Lake (NM550)

Abouselman Spring (NM555)     Rito de los Frijoles (NM501)

      Baca (NM558)          Los Alamos New Mexico (NM046)
h p://www.ldeo.columbia.edu/tree-ring-laboratory/resources/so ware
TREE-RING WIDTH DATA
pith




                        bark
THE PRINCIPLE OF AGGREGATE TREE GROWTH




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




Rt = At + Ct + δD1t + δD2t + Et
                size-related growth trend
                caused by physiological aging
At
does not have a universal or predictable shape.
STANDARDIZATION
the ‘detrended’
  ring-width
     index
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


    Cat Mesa (NM556)             Fenton Lake (NM550)

Abouselman Spring (NM555)     Rito de los Frijoles (NM501)

      Baca (NM558)          Los Alamos New Mexico (NM046)
USE FOUR DIFFERENT APPROACHES
      TO STANDARDIZATION
             Horizontal line
       Negative exponential curve
           20-yr flexible spline
Flexible spline set to 67% of series length
GEOG5839
               XT C L AS S
                     NE
                          WHO WILL FIND THE FIRST

                      “DIRTY DOG”?
Source: Terry Bain

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GEOG5839.15, signal processing