Geoscience Reference
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e bx
y
=
a
×
+
c
(5.1)
where the constant (a) defines the expected magnitude of the juvenile growth phase
of ring growth (referred to by Helama et al. 2005a , b as the 'juvenile growth max-
imum'); the constant (c) defines an assumed constant growth rate of old-age trees;
and constant (b) describes the rate of diminution of ring width with age (referred to
by Helama et al. 2005a , b as the 'growth trend concavity').
In what they term 'environmental curve standardisation (ECS), Helama et al.
( 2005b ) do not apply this single fitted function (5.1) to all of their measurement
data. Instead, they perform time-dependent standardization by generating a series
of RCS curves, each based on data from a 750-year time slice, overlapping each of
its neighbors by 250 years. Each RCS curve is applied only to the data from the
central 250 years of its corresponding time window. In this way, each 250-year non-
overlapping period of the chronology is based on standardization with a different
RCS curve. However, within each 250-year standardization application, only the
RCS concavity (parameter b) is varied; the (a) and (c) parameters are maintained at
the values calculated for the single, original overall period RCS curve.
They find a relationship between the number of tree samples (interpreted as spa-
tial tree density) and the concavity (b) parameter (reported as 0.683, Helama et al.
2005b , Fig. 2d, and 0.73, Helama et al. 2005a , Fig. 5). The lack of any significant
association between tree density and juvenile growth maximum (a) in these data
(Helama et al. 2005b , Fig. 2c) presumably led them to conclude that concavity was
independent of average tree growth rate.
In Table 5.1 , we demonstrate that this conclusion is erroneous by using a sub-
set of Finnish Lapland tree-ring measurements (Eronen et al. 2002 ; Helama et al.
2002 ) that form a major part (1087 trees) of the Helama et al. ( 2005b ) dataset (1205
trees). Figure 5.14 shows these measurement data sorted, by relative growth rate,
Table 5.1 Parameters from modified negative exponential curves fitted to RCS curves a
a
b
c
at
Bt
ct
rwr
Slowest
0.48
0.020
0.26
0.48
0.022
0.24
0.40
2nd
0.68
0.015
0.23
0.69
0.022
0.30
0.54
3rd
0.83
0.024
0.37
0.84
0.021
0.34
0.63
4th
0.95
0.014
0.29
0.95
0.019
0.37
0.75
5th
1.14
0.011
0.34
1.13
0.016
0.39
0.90
Fastest
1.41
0.011
0.36
1.36
0.013
0.47
1.18
Mean
0.92
0.016
0.31
0.91
0.019
0.35
Mean difference
0.01
0.004
0.06
a First a, b, and c are fitted to the full period of the regional curve standardization (RCS) curves,
and second, at, bt, and ct are fitted to the truncated period of the RCS curves; i.e., the period with
four or more series. 'rwr' is ring width reduction in the first 50 years of the truncated RCS curves.
Values are shown for six growth rate classes, slowest to fastest. The means are shown and for the
columns and also the mean differences between the full and truncated RCS curve parameters are
shown. Growth rate is assessed as the ratio of the diameter growth of each tree to the diameter
growth of the single RCS curve over the life of that tree.
 
 
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