GEOG5839.12, the linear aggreate model of tree growth
68
the ‘detrended’ ring-width index October 18 The linear aggregate model of tree growth October 18 The linear aggregate model of tree growth
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Transcript of GEOG5839.12, the linear aggreate model of tree growth
the ‘detrended’ring-width
index
October 18
The linear aggregate model of tree growthOctober 18
The linear aggregate model of tree growth
Ed Cook Lamont-Doherty Earth Observatory
h!p://www.ldeo.columbia.edu/tree-ring-laboratory/
THE PRINCIPLE OF AGGREGATE TREE GROWTHAny individual tree-growth series can be "decomposed" into a set of environmental signals that a"ected the tree’s growth through its lifespan.
Tree-ring width data
pith
bark
climate
ecologyforest dynamics
landscape change
tree age or size
SIGNAL vs. NOISE
SIGNAL vs. NOISE
the environmental factorof interest
SIGNAL vs. NOISE
everything else
Rt = At + Ct + δD1t + δD2t + Et
THE PRINCIPLE OF AGGREGATE TREE GROWTH
a conceptual model of tree growth
helps us THINK about signals in tree rings
NOT used for CALCULATIONS
Eastern hemlockTsuga canadensis
Earlywood
Latewood
Total ring-width
Rt = At + Ct + δD1t + δD2t + Et
tree growth in year ‘t’
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
Artist: Giuseppe Penone
Tree age
Ring width
Atdoes 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
0
2.5
5.0
7.5
10.0
0 25 50 75 100
At = a # exp-bt + k
Rt = At + Ct + δD1t + δD2t + Et
climate during year ‘t’
THE PRINCIPLE OF AGGREGATE TREE GROWTH
THE PRINCIPLE OF AGGREGATE TREE GROWTH
Rt = At + Ct + δD1t + δD2t + Et
Source: United States Forest Service
Source: Eli Sagor
A disturbance is a temporary event that causes a major change in the structure of an ecosystem.
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
climate
Rt = At + Ct + δD1t + δD2t + Et
SIGNAL vs. NOISE
Rt = At + Ct + δD1t + δD2t + Et
never trust one tree
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
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
Source: St. George et al., Quaternary Research, 2008
Source: St. George et al., unpublished
The global network of public tree-ring width data includes measurements of nearly 20 million tree rings at more than 3,000 locations.
climate
Rt = At + Ct + δD1t + δD2t + Et
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
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
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!
0
2.5
5.0
7.5
10.0
0 25 50 75 100
At = a # exp-bt + k
(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
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
Atdoes not have a universal or predictable shape.
THE ‘SEGMENT-LENGTH’
CURSE
THE PRINCIPLE OF
ECOLOGICAL AMPLITUDE
THE PRINCIPLE OF
SITE SELECTION
THE PRINCIPLE OF
AGGREGATE TREE GROWTH
THE PRINCIPLE OF
REPLICATION
STANDARDIZATION
THE PRINCIPLE OF
CROSS-DATING
Source: Danny Margoles
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