class 7, extracting signal from tree rings
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E X T R A C 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
Eastern hemlockTsuga canadensis
Earlywood
Latewood
Total ring-width
Same environmental forcings
Similar growth pa!erns
Same environmental forcings
Similar growth pa!erns
TREE-RING WIDTH DATApith
bark
how do we interpret tree-ring width measurements?
The rates of biological processes in trees, including the formation of woody cells, are constrained by the primary environmental variable that is most limiting.
THE PRINCIPLE OF LIMITING FACTORS
temperature water day length
THE
LIMITING FACTOR IS NOT THE
ONLY FACTOR THAT INFLUENCES TREE GROWTH.
Photograph: Andy Frasse!o
Photograph: kevmann16
climate
ecology
climate
climateforest dynamics
landscape change
tree age or size
TREE-RING WIDTH DATA
SIGNAL vs. NOISE
SIGNAL vs. NOISE
the environmental factorof interest
SIGNAL vs. NOISE
everything else
SIGNAL vs. NOISE
SIGNAL vs. NOISE
THE PRINCIPLE OF AGGREGATE TREE GROWTHAny 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
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
NOT used for CALCULATIONS
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 trendcaused by physiological aging
THE PRINCIPLE OF AGGREGATE TREE GROWTH
Tree age
Ring width
0
2.5
5.0
7.5
10.0
0 25 50 75 100
At = a × exp-bt + k
Atdoes not have a universal or predictable shape.
Gt = At + δD1t + δD2t + Et
growth trend in year ‘t’
You’ll notice that your reading defines another term, Gt, which is the sum of all growth factors OTHER than climate.
Rt = At + Ct + δD1t + δD2t + Et
climate during year ‘t’
THE PRINCIPLE OF AGGREGATE TREE GROWTH
temperature water day length
THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et
disturbance within the forest
Rt = At + Ct + δD1t + δD2t + Et
disturbance from outside the forest
THE PRINCIPLE OF AGGREGATE TREE GROWTH
δD1t + δD2t
Both disturbance terms include a value for ‘delta’, which can be either ‘0’ (no disturbance)
or ‘1’ (disturbance).
Rt = At + Ct + δD1t + δD2t + Et
random processesnot accounted by other sources
THE PRINCIPLE OF AGGREGATE TREE GROWTH
SIGNAL vs. NOISE
Rt = At + Ct + δD1t + δD2t + Et
replicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplication
replicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplication
replicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplication
replicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplication
replicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplication
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’.
THE PRINCIPLE OF REPLICATION
never trust one tree
mean of all trees
can be assumed to be uncorrelated within and between trees in a stand.
Et
Endogenous (‘originating within’) disturbances will be random events in both space and time, if the stand of trees is large enough.
δD1t
o#en is shared by most or all trees within a stand, but may not be shared by all forest stands within a region.
δD2t
never trust one tree
Source: St. George et al., Quaternary Research, 2008
Source: Cook et al., Earth Science Reviews, 2007
Atis the tough one.
“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.
STANDARDIZATION
one of the simplest cases
Changes in ringwidth due to tree age (or size) can sometimes be approximated as
a negative exponential function.
At = a × exp-bt + ksometimes, not always!
(A) the ‘raw’ring-width data
(B) the ‘detrending’ curve
DIVIDE(A) the raw ring-width databy (B) the ‘detrending’ curve
the ‘detrended’ring-width
index
Atremoving
THE PRINCIPLE OF
AGGREGATE TREE GROWTH
THE PRINCIPLE OF
REPLICATION
STANDARDIZATION
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