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FIGURE 10.9 Standardization of ring-width measurements is necessary to remove the decrease in size associated with increasing age of the tree. If the ring widths for the three specimens shown in the upper figure are simply averaged by year, without removing the effect of the tree's age, the mean ring-width chronology shown below them exhibits intervals of high and low growth, associated with the varying age of the samples. This age variability is generally removed by fitting a curve to each ring-width series, and dividing each ring width by the corresponding value of the curve.The resulting values, shown in the lower half of the figure, are referred to as indices, and may be averaged among specimens differing in age to produce a mean chronology for a site (lowermost record) (Fritts, 1971).

compared, it is first necessary to remove the growth function peculiar to that particular tree. Only then can a master chronology be constructed from multiple cores. Growth functions are removed by fitting a curve to the data and dividing each measured ring-width value by the "expected" value on the growth curve (Fig. 10.9). Commonly, a negative exponential function, or a lowpass digital filter is applied to the data. Cook et al. (1990) recommend that a cubic-smoothing spline be used, in which the 50% frequency response equals -75% of the record length (n). This means that low frequency variations in the data (with a period >0.75 n) are largely removed from the standardized data, so the analyst then has an explicit understanding of the frequency domain that the resulting series represents (Cook and Peters, 1981).

The standardization procedure leads to a new time series of ring-width indices, with a mean of one and a variance that is fairly constant through time (Fritts, 1971). Ring-width indices from individual cores are then averaged, year by year, to produce a master chronology for the sample site, independent of growth function and differing sample age (Fig. 10.9, lowest graph). Averaging the standardized indices also increases the (climatic) signal-to-noise ratio (S/N). This is because climatically related variance, common to all records, is not lost by averaging, whereas non-climatic "noise," which varies from tree to tree, will be partially cancelled in the averaging process. It is thus important that a large enough number of cores be obtained initially to help enhance the climatic signal common to all the samples (Cook et al., 1990).

Standardization is an essential prerequisite to the use of ring-width data in dendroclimatic reconstruction but it poses significant methodological problems. Consider, for example, the ring-width chronologies shown in Fig. 10.10. Drought-sensitive conifers from the southwestern United States characteristically show ring-width variations like those in Fig. 10.10a. For most of the chronology a negative exponential function, of the form y - ae'bt + k, fits the data well. However, this is not the case for the early section of the record, which must be either discarded or fitted by a different mathematical function. Obviously, the precise functions selected will have an important influence on the resulting values of the ring-width indices. In the case of trees growing in a closed canopy forest, the growth curve is often quite variable and unlike the negative exponential values characteristic of arid-site conifers. Periods of growth enhancement or suppression related to non-climatic factors such as competition, management, insect infestation, etc., are often apparent in the records. In such cases (Fig. 10.10b) some other function might be fitted to the data and individual ring widths would then be divided by the local value of this curve to produce a series of ring-width indices. Care must be exercised not to select a function (such as a complex polynomial) that describes the raw data too precisely, or all of the (low frequency) climatic information may be removed; most analysts select the simplest function possible to avoid this problem but inevitably the procedure selected is somewhat arbitrary. Further problems arise when complex growth functions are observed, such as those in Fig. 10.10c. In this case it would be difficult to decide on the use of a polynomial function (dashed line) or a negative exponential function (solid line) and in either case the first few observations should perhaps be discarded. Such difficulties are less significant in densitometric or isotope dendroclimatic studies because there is generally less of a growth trend in density

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FIGURE 10.10 Some problems in standardization of ring widths. In (a) most of the tree-ring series can be fitted by the exponential function shown. However, the early part of the record must be discarded. In (b) the two ring-width series required higher-order polynomials to fit the lower frequency variations of each record (the greater the number of coefficients for each equation, the greater the degree of complexity in the shape of the curve). In (c) the series could be standardized using either a polynomial (dashed) or exponential function (solid line). Depending on the function selected and its complexity, low-frequency climatic information may be eliminated. The final ring-width indices depend very much on the standardization procedure employed (examples selected from Fritts, 1976).

and isotope data; hence these approaches may yield more low-frequency climatic information than is possible in the measurement of ring widths alone (Schweingru-ber and Briffa, 1996).

It is clear that standardization procedures are not easy to apply and may actually remove important low-frequency climatic information. It is not possible, a priori, to decide if part of the long-term change in ring width is due to a coincident climatic trend. The problem is exacerbated if one is attempting to construct a long-term dendrochronological record, when only tree fragments or historical timbers spanning limited time intervals are available, and the corresponding growth function may not be apparent.

The consequences of different approaches to standardization are well illustrated by the studies of long tree-ring series (Scots pine, Pinus sylvestris) from northern Fennoscandia by Briffa et al. (1990, 1992a). In order to produce a long dendro-climatic reconstruction extending over 1500 yr, Briffa et al. (1990) constructed a composite chronology made up of many overlapping cores which varied in their individual length, from less than 100 to more than 200 yr (Figs. 10.11 and 10.13). In the shorter segments, the growth function is significant over the entire segment length, but in longer segments the growth factor becomes less significant (see Fig. 10.9, upper panel). In Briffa et al. (1990) each segment was standardized individually (the procedure used in almost all dendroclimatic studies), in this case by the use of a cubic spline function that retains variance at periods less than -2/3 of the record length. Thus, in a 100 yr segment, variance at periods >66 yr would be removed, whereas in a 300 yr segment, variance at periods up to 200 yr would be retained. All standardized cores were then averaged together, producing the record shown in Fig. 10.12c. This shows considerable interannual to decadal scale variability, but little long-term low frequency variability. In fact, as the mean segment length varies over time (Fig. 10.11) so too will the low frequency variance represented in the composite series.

In Briffa et al. (1992a) the standardization procedure was revised by first aligning all core segments by their relative age, then averaging them (i.e., all values of the first year in each segment (it) were averaged, then all values of t2 etc. ... to tn). This assumes that in each segment used, tx was at, or very close to, the center of the tree and that there is a tree-growth function (dependent only on biological age) that is

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