Athens October 2011 Tree rings and plagues: some new observations
Class 7, Extracting signal from tree rings
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Transcript of 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
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Same environmental forcings
Similar growth pa!erns
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Eastern hemlockTsuga canadensis
Earlywood
Latewood
Total ring-width
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Same environmental forcings
Similar growth pa!erns
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Same environmental forcings
Similar growth pa!erns
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TREE-RING WIDTH DATApith
bark
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how do we interpret tree-ring width measurements?
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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
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temperature water day length
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THE
LIMITING FACTOR IS NOT THE
ONLY FACTOR THAT INFLUENCES TREE GROWTH.
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Photograph: Andy Frasse!o
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Photograph: kevmann16
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climate
ecology
climate
climateforest dynamics
landscape change
tree age or size
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TREE-RING WIDTH DATA
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SIGNAL vs. NOISE
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SIGNAL vs. NOISE
the environmental factorof interest
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SIGNAL vs. NOISE
everything else
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SIGNAL vs. NOISE
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SIGNAL vs. NOISE
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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.
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a conceptual model of tree growth
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a conceptual model of tree growth
helps us THINK about signals in tree rings
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a conceptual model of tree growth
helps us THINK about signals in tree rings
NOT used for CALCULATIONS
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Rt = At + Ct + δD1t + δD2t + Et
THE PRINCIPLE OF AGGREGATE TREE GROWTH
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Rt = At + Ct + δD1t + δD2t + Et
tree growth in year ‘t’
THE PRINCIPLE OF AGGREGATE TREE GROWTH
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Rt = At + Ct + δD1t + δD2t + Et
THE PRINCIPLE OF AGGREGATE TREE GROWTH
=
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Rt = At + Ct + δD1t + δD2t + Et
size-related growth trendcaused by physiological aging
THE PRINCIPLE OF AGGREGATE TREE GROWTH
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Tree age
Ring width
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0
2.5
5.0
7.5
10.0
0 25 50 75 100
At = a × exp-bt + k
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Atdoes not have a universal or predictable shape.
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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.
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Rt = At + Ct + δD1t + δD2t + Et
climate during year ‘t’
THE PRINCIPLE OF AGGREGATE TREE GROWTH
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temperature water day length
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THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et
disturbance within the forest
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Rt = At + Ct + δD1t + δD2t + Et
disturbance from outside the forest
THE PRINCIPLE OF AGGREGATE TREE GROWTH
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δD1t + δD2t
Both disturbance terms include a value for ‘delta’, which can be either ‘0’ (no disturbance)
or ‘1’ (disturbance).
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Rt = At + Ct + δD1t + δD2t + Et
random processesnot accounted by other sources
THE PRINCIPLE OF AGGREGATE TREE GROWTH
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SIGNAL vs. NOISE
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Rt = At + Ct + δD1t + δD2t + Et
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replicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplication
replicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplication
replicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplication
replicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplication
replicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplicationreplication
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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
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never trust one tree
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mean of all trees
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can be assumed to be uncorrelated within and between trees in a stand.
Et
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Endogenous (‘originating within’) disturbances will be random events in both space and time, if the stand of trees is large enough.
δD1t
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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
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never trust one tree
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Source: St. George et al., Quaternary Research, 2008
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Source: Cook et al., Earth Science Reviews, 2007
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Atis the tough one.
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“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
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one of the simplest cases
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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!
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(A) the ‘raw’ring-width data
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(B) the ‘detrending’ curve
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DIVIDE(A) the raw ring-width databy (B) the ‘detrending’ curve
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the ‘detrended’ring-width
index
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Atremoving
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THE PRINCIPLE OF
AGGREGATE TREE GROWTH
THE PRINCIPLE OF
REPLICATION
STANDARDIZATION
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