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E XT R AC T I N G S I G N A L F R O M T R E E R I N G S
Same environmental
forcings




              Similar
      growth pa erns
Earlywood


        Latewood


Total ring-width



                   Eastern hemlock
                   Tsuga canadensis
Same environmental
forcings




              Similar
      growth pa erns
Same environmental
              forcings




Similar
growth pa erns
TREE-RING WIDTH DATA
pith




                        bark
how do we interpret tree-ring width measurements?
THE PRINCIPLE OF
      LIMITING FACTORS
The rates of biological processes in trees, including the
formation of woody cells, are constrained by the primary
environmental variable that is most limiting.
temperature   water   day length
THE

LIMITING FACTOR
          IS NOT THE

 ONLY FACTOR
 THAT INFLUENCES TREE GROWTH.
Photograph: Andy Frasse o
Photograph: kevmann16
tree age
 or size
                   climate             landscape
                                         change
 forest dynamics
                                                   c
                             ecology
TREE-RING WIDTH DATA
SIGNAL vs. NOISE
the environmental factor
       of interest



          SIGNAL vs. NOISE
SIGNAL vs. NOISE

         everything else
SIGNAL vs. NOISE
SIGNAL vs. NOISE
THE PRINCIPLE OF
AGGREGATE TREE GROWTH
Any individual tree-growth series can be "decomposed" into a
set of environmental signals that affected the tree’s growth
through its lifespan.
a conceptual model of tree growth
helps us THINK about
       signals in tree rings

a conceptual model of tree growth
helps us THINK about
       signals in tree rings

a conceptual model of tree growth

          NOT used for
          CALCULATIONS
THE PRINCIPLE OF AGGREGATE TREE GROWTH




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




Rt = At + Ct + δD1t + δD2t + Et
         tree growth in year ‘t’
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
Ring width




             Tree age
10.0



 7.5

                At = a ×   exp-bt   +k
5.0



 2.5



  0
       0   25      50           75       100
At
does not have a universal or predictable shape.
growth trend in year ‘t’




 Gt = At + δD1t + δD2t + Et
 You’ll notice that your reading defines another term, Gt,
which is the sum of all growth factors OTHER than climate.
THE PRINCIPLE OF AGGREGATE TREE GROWTH




Rt = At + Ct + δD1t + δD2t + Et
                         climate during year ‘t’
temperature   water   day length
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
δD1t + δD2t
  Both disturbance terms include a value for
‘delta’, which can be either ‘0’ (no disturbance)
               or ‘1’ (disturbance).
THE PRINCIPLE OF AGGREGATE TREE GROWTH




Rt = At + Ct + δD1t + δD2t + Et

                         random processes
                   not accounted by other sources
SIGNAL
  vs.
  NOISE
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
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’.
never trust
    one tree
mean of
all trees
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.
never trust
    one tree
Source: St. George et al.,
Quaternary Research, 2008
Source: Cook et al., Earth Science Reviews, 2007
At
is the tough one.
STANDARDIZATION
“Standardization” describes a suite of mathematical methods
that a empt to remove long-term trends in ringwidth caused
by normal physiological aging processes and changes in the
surrounding forest community.
one of the simplest cases
ays!
                a   lw
           ,not
      im es
 om et
s
           At = a ×      exp -bt     +k
    Changes in ringwidth due to tree age (or size)
        can sometimes be approximated as
         a negative exponential function.
(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
removing   At
THE PRINCIPLE OF
AGGREGATE TREE GROWTH

      THE PRINCIPLE OF
     REPLICATION


  STANDARDIZATION
Class 7, Extracting signal from tree rings
Class 7, Extracting signal from tree rings

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Class 7, Extracting signal from tree rings